Datasets:
Dataset Viewer
image
imagewidth (px) 1.8k
1.8k
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sequencelengths 6
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| question
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 3, 2)
B: (Back, 4, 3)
C: (Left, 2, 1)
D: (Bottom, 4, 1)
E: (Right, 4, 3)
F: (Front, 2, 1)
|
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 2, 3)
B: (Back, 4, 3)
C: (Bottom, 3, 4)
D: (Front, 2, 3)
E: (Top, 2, 3)
F: (Right, 3, 4)
|
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 4, 1)
B: (Bottom, 4, 1)
C: (Back, 1, 4)
D: (Top, 1, 4)
E: (Right, 1, 2)
F: (Front, 2, 1)
|
|
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 4, 3)
B: (Left, 4, 3)
C: (Right, 1, 4)
D: (Back, 2, 1)
E: (Bottom, 1, 4)
F: (Front, 4, 1)
|
|
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]
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 2, 1)
B: (Left, 2, 1)
C: (Top, 4, 1)
D: (Front, 4, 1)
E: (Right, 1, 4)
F: (Bottom, 1, 4)
|
|
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 3, 4)
B: (Back, 2, 3)
C: (Bottom, 2, 1)
D: (Top, 3, 2)
E: (Left, 3, 4)
F: (Right, 4, 1)
|
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1,
1,
1,
1,
1
],
[
1,
0,
1,
0,
0
]
],
[
[
0,
1,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
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0,
0
]
],
[
[
0,
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1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
0,
1,
0,
1
]
],
[
[
0,
1,
0,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
1,
0
]
],
[
[
1,
1,
1,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
1,
1
]
],
[
[
0,
1,
0,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 2, 3)
B: (Left, 4, 3)
C: (Bottom, 3, 2)
D: (Right, 1, 2)
E: (Front, 3, 4)
F: (Back, 3, 4)
|
|
[
[
[
1,
0,
0,
0,
0
],
[
1,
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],
[
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],
[
0,
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],
[
0,
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]
],
[
[
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[
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[
1,
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[
1,
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[
0,
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],
[
[
1,
1,
1,
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[
0,
1,
1,
1,
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],
[
1,
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1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 4, 3)
B: (Bottom, 4, 3)
C: (Left, 4, 1)
D: (Back, 1, 4)
E: (Right, 2, 1)
F: (Top, 1, 2)
|
|
[
[
[
1,
1,
1,
1,
0
],
[
1,
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],
[
1,
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],
[
1,
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],
[
0,
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],
[
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1,
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[
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1,
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[
[
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[
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[
0,
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[
1,
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[
0,
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1,
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]
],
[
[
0,
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0,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 4, 3)
B: (Bottom, 2, 3)
C: (Top, 3, 2)
D: (Left, 2, 3)
E: (Back, 3, 4)
F: (Right, 1, 2)
|
|
[
[
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
0,
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]
],
[
[
0,
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[
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[
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[
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[
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[
1,
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[
1,
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]
],
[
[
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[
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1,
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[
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[
0,
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[
[
1,
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[
0,
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[
0,
1,
1,
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[
0,
1,
1,
1,
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],
[
1,
1,
0,
0,
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]
],
[
[
1,
0,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
0,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 1, 4)
B: (Front, 3, 2)
C: (Left, 3, 4)
D: (Right, 3, 4)
E: (Bottom, 2, 1)
F: (Top, 3, 2)
|
|
[
[
[
0,
1,
0,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
1,
0
]
],
[
[
0,
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1
],
[
0,
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[
1,
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[
1,
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[
0,
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],
[
[
1,
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[
0,
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[
0,
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1,
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[
1,
1,
1,
1,
1
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[
0,
1,
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0
]
],
[
[
1,
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[
0,
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[
1,
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[
1,
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[
0,
1,
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]
],
[
[
0,
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[
0,
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1,
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[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
0,
1
]
],
[
[
0,
1,
1,
0,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 2)
B: (Bottom, 2, 1)
C: (Top, 4, 1)
D: (Left, 4, 3)
E: (Back, 3, 2)
F: (Front, 2, 3)
|
|
[
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
]
],
[
[
0,
0,
0,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
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],
[
1,
1,
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[
0,
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]
],
[
[
1,
0,
1,
1,
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[
1,
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1
],
[
1,
1,
1,
1,
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[
0,
1,
1,
1,
0
],
[
0,
1,
0,
0,
0
]
],
[
[
0,
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1,
1,
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[
1,
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[
1,
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[
0,
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[
1,
1,
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]
],
[
[
1,
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1
],
[
0,
1,
1,
1,
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],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
0,
1
]
],
[
[
0,
1,
1,
0,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 4, 1)
B: (Top, 1, 4)
C: (Back, 4, 1)
D: (Right, 3, 4)
E: (Bottom, 4, 1)
F: (Left, 1, 4)
|
|
[
[
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
0,
0,
1,
0
]
],
[
[
0,
0,
0,
0,
0
],
[
1,
1,
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1,
1
],
[
0,
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[
0,
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[
1,
1,
1,
0,
1
]
],
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
]
],
[
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
],
[
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
],
[
[
1,
1,
0,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
0,
0,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 4, 3)
B: (Left, 2, 1)
C: (Right, 4, 1)
D: (Top, 4, 3)
E: (Front, 3, 2)
F: (Bottom, 3, 2)
|
|
[
[
[
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[
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[
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[
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[
1,
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[
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[
[
1,
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[
1,
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1,
1,
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[
0,
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1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 1, 2)
B: (Right, 4, 1)
C: (Top, 3, 4)
D: (Front, 1, 2)
E: (Back, 3, 2)
F: (Left, 2, 3)
|
|
[
[
[
0,
1,
0,
0,
0
],
[
1,
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],
[
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],
[
0,
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],
[
0,
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],
[
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[
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[
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[
1,
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[
1,
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[
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],
[
[
0,
1,
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],
[
0,
1,
1,
1,
1
],
[
1,
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1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 2, 3)
B: (Left, 3, 2)
C: (Bottom, 1, 4)
D: (Back, 4, 3)
E: (Top, 2, 3)
F: (Right, 2, 3)
|
|
[
[
[
0,
0,
0,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
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1,
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]
],
[
[
1,
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[
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[
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[
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[
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[
1,
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[
0,
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],
[
[
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1,
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[
1,
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[
[
1,
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0,
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[
1,
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[
0,
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1,
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[
0,
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]
],
[
[
0,
0,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 2, 1)
B: (Top, 3, 4)
C: (Back, 2, 1)
D: (Front, 4, 3)
E: (Right, 1, 4)
F: (Left, 4, 1)
|
|
[
[
[
1,
0,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
]
],
[
[
0,
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[
0,
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[
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[
1,
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[
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[
[
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[
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[
0,
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[
0,
1,
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1,
1
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[
0,
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1
]
],
[
[
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[
1,
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[
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[
0,
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[
1,
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]
],
[
[
1,
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[
0,
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1,
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[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
1,
0
]
],
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
0,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 4)
B: (Back, 2, 1)
C: (Top, 3, 2)
D: (Front, 2, 3)
E: (Bottom, 2, 1)
F: (Left, 4, 1)
|
|
[
[
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
1,
1
]
],
[
[
1,
0,
0,
1,
0
],
[
1,
1,
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1,
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],
[
1,
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[
1,
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[
0,
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],
[
[
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[
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[
1,
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[
0,
1,
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1,
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[
0,
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1,
1
]
],
[
[
0,
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[
1,
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[
1,
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[
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[
0,
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],
[
[
0,
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[
0,
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[
0,
1,
1,
1,
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],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
0,
1
]
],
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 3, 4)
B: (Top, 2, 3)
C: (Right, 2, 1)
D: (Left, 3, 2)
E: (Front, 1, 2)
F: (Back, 2, 3)
|
|
[
[
[
0,
0,
0,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
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]
],
[
[
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[
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[
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],
[
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[
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[
1,
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1,
1,
1
],
[
1,
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1,
0,
0
]
],
[
[
1,
1,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
]
],
[
[
0,
1,
0,
0,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
0,
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]
],
[
[
0,
1,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 1, 4)
B: (Right, 2, 1)
C: (Bottom, 1, 4)
D: (Top, 4, 3)
E: (Back, 1, 2)
F: (Left, 2, 1)
|
|
[
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
0,
1,
0,
0
]
],
[
[
0,
0,
1,
1,
0
],
[
1,
1,
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1
],
[
1,
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],
[
1,
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[
1,
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],
[
[
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[
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[
1,
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[
1,
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],
[
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],
[
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[
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[
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[
0,
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]
],
[
[
0,
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[
0,
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1,
1,
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],
[
1,
1,
1,
1,
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],
[
0,
1,
1,
1,
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],
[
0,
0,
0,
0,
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]
],
[
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
0,
1,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 2, 1)
B: (Bottom, 2, 1)
C: (Left, 3, 4)
D: (Front, 2, 3)
E: (Right, 1, 2)
F: (Back, 2, 1)
|
|
[
[
[
0,
0,
0,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
]
],
[
[
0,
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1,
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],
[
0,
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[
0,
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[
1,
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[
0,
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],
[
[
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[
1,
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[
0,
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[
0,
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1,
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],
[
0,
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]
],
[
[
0,
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[
0,
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1,
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],
[
0,
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[
1,
1,
1,
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1
],
[
1,
1,
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1
]
],
[
[
0,
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1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
0,
1
]
],
[
[
0,
0,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 1, 4)
B: (Back, 2, 1)
C: (Front, 1, 4)
D: (Right, 4, 1)
E: (Top, 3, 4)
F: (Bottom, 2, 1)
|
|
[
[
[
0,
1,
1,
0,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
0,
0
]
],
[
[
0,
1,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
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1
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[
1,
1,
1,
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1
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[
0,
1,
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1
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],
[
[
0,
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[
0,
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[
1,
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1,
1,
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[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
1
]
],
[
[
0,
1,
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0,
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[
1,
1,
1,
1,
1
],
[
0,
1,
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1
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[
1,
1,
1,
1,
1
],
[
0,
1,
1,
0,
0
]
],
[
[
1,
0,
1,
0,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
]
],
[
[
1,
1,
0,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
0,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 4, 1)
B: (Left, 2, 1)
C: (Front, 3, 4)
D: (Right, 1, 2)
E: (Bottom, 1, 4)
F: (Back, 1, 4)
|
|
[
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
]
],
[
[
0,
1,
0,
0,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
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1
]
],
[
[
0,
1,
0,
0,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
0,
1,
1
]
],
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
],
[
[
0,
1,
0,
0,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
0,
0,
1,
0
]
],
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
0,
0,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 2)
B: (Bottom, 3, 2)
C: (Top, 4, 3)
D: (Left, 2, 1)
E: (Back, 4, 3)
F: (Front, 1, 4)
|
|
[
[
[
1,
0,
0,
0,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
1,
0
]
],
[
[
1,
1,
0,
0,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
0,
1,
1,
1
]
],
[
[
0,
0,
0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
1,
0
]
],
[
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
1,
0
]
],
[
[
1,
1,
0,
0,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
1,
0
]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 4, 3)
B: (Left, 4, 3)
C: (Front, 4, 3)
D: (Right, 2, 1)
E: (Bottom, 4, 1)
F: (Back, 1, 2)
|
|
[
[
[
0,
1,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
0,
1
]
],
[
[
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[
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[
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[
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[
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],
[
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[
1,
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1,
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],
[
1,
1,
1,
1,
0
],
[
1,
0,
1,
1,
0
]
],
[
[
0,
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],
[
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[
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[
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[
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]
],
[
[
0,
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1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
0,
1,
0
]
],
[
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 2, 1)
B: (Right, 2, 3)
C: (Front, 4, 1)
D: (Top, 4, 3)
E: (Back, 1, 2)
F: (Bottom, 3, 2)
|
|
[
[
[
1,
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1,
0,
1
],
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[
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],
[
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[
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],
[
[
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[
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[
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[
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[
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[
1,
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[
1,
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],
[
[
0,
1,
0,
1,
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],
[
0,
1,
1,
1,
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],
[
1,
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1,
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0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 1, 2)
B: (Top, 4, 3)
C: (Front, 3, 2)
D: (Right, 3, 4)
E: (Bottom, 4, 1)
F: (Left, 4, 3)
|
|
[
[
[
0,
1,
0,
0,
1
],
[
1,
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],
[
1,
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0
],
[
0,
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],
[
0,
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]
],
[
[
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[
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[
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[
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[
1,
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],
[
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[
1,
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[
1,
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[
1,
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[
0,
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],
[
[
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[
0,
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[
1,
1,
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],
[
0,
1,
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1,
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],
[
0,
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]
],
[
[
0,
1,
0,
1,
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],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 4)
B: (Top, 4, 1)
C: (Back, 1, 2)
D: (Bottom, 1, 2)
E: (Left, 2, 1)
F: (Front, 2, 3)
|
|
[
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
1,
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]
],
[
[
1,
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[
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[
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[
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[
[
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[
1,
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[
1,
1,
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1,
0
],
[
0,
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1
]
],
[
[
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[
1,
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[
1,
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[
1,
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[
1,
0,
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],
[
[
0,
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[
1,
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[
1,
1,
1,
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],
[
1,
1,
1,
1,
1
],
[
1,
0,
0,
0,
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]
],
[
[
0,
0,
1,
0,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 4, 1)
B: (Front, 4, 3)
C: (Top, 1, 2)
D: (Back, 2, 3)
E: (Right, 2, 1)
F: (Bottom, 2, 3)
|
|
[
[
[
0,
1,
0,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
0,
1,
1
]
],
[
[
1,
0,
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1,
0
],
[
1,
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],
[
0,
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[
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[
0,
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],
[
[
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[
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[
0,
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[
0,
1,
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1,
0
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[
1,
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]
],
[
[
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[
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[
1,
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[
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[
0,
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],
[
[
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[
0,
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[
1,
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1,
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],
[
1,
1,
1,
1,
1
],
[
1,
1,
0,
1,
1
]
],
[
[
0,
1,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 2, 3)
B: (Left, 3, 4)
C: (Bottom, 2, 1)
D: (Right, 3, 4)
E: (Top, 3, 2)
F: (Front, 4, 1)
|
|
[
[
[
0,
1,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
0,
0,
0,
0
]
],
[
[
1,
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1,
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],
[
1,
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[
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[
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[
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[
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[
0,
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[
0,
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1,
1,
1
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[
0,
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]
],
[
[
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[
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[
1,
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[
1,
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],
[
[
1,
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[
1,
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1,
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],
[
0,
1,
1,
1,
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],
[
1,
1,
1,
1,
0
],
[
1,
0,
0,
1,
0
]
],
[
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 2, 1)
B: (Left, 2, 3)
C: (Bottom, 3, 4)
D: (Back, 4, 3)
E: (Top, 2, 1)
F: (Right, 2, 3)
|
|
[
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[
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1,
1,
1
],
[
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1,
1,
1
],
[
1,
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1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
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1,
0,
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]
],
[
[
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[
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[
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[
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[
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[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 2, 3)
B: (Back, 1, 4)
C: (Front, 2, 1)
D: (Top, 1, 4)
E: (Bottom, 2, 1)
F: (Left, 3, 2)
|
|
[
[
[
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[
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[
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[
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[
1,
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[
1,
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[
[
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[
1,
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[
0,
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],
[
0,
1,
1,
1,
0
],
[
0,
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1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 3, 4)
B: (Bottom, 1, 2)
C: (Right, 2, 1)
D: (Top, 4, 1)
E: (Front, 1, 4)
F: (Left, 1, 4)
|
|
[
[
[
0,
1,
0,
1,
1
],
[
0,
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],
[
1,
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0
],
[
0,
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],
[
1,
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]
],
[
[
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[
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1,
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[
[
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1,
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[
0,
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[
0,
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[
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],
[
[
0,
1,
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1,
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],
[
0,
1,
1,
1,
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],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 4, 1)
B: (Right, 3, 2)
C: (Front, 2, 3)
D: (Back, 1, 4)
E: (Top, 2, 3)
F: (Left, 2, 1)
|
|
[
[
[
1,
1,
0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
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]
],
[
[
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[
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[
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0,
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[
[
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[
1,
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[
0,
1,
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[
1,
1,
1,
1,
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[
0,
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0,
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],
[
[
1,
1,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 1, 2)
B: (Front, 3, 4)
C: (Top, 3, 4)
D: (Back, 1, 4)
E: (Left, 3, 4)
F: (Right, 4, 1)
|
|
[
[
[
1,
1,
0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
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]
],
[
[
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[
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[
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[
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[
1,
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],
[
[
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1,
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],
[
[
1,
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[
1,
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[
0,
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[
1,
1,
1,
1,
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],
[
1,
1,
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1,
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]
],
[
[
1,
1,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 3, 4)
B: (Back, 3, 4)
C: (Right, 2, 3)
D: (Front, 3, 4)
E: (Left, 4, 1)
F: (Bottom, 2, 3)
|
|
[
[
[
0,
0,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
1
]
],
[
[
1,
1,
1,
0,
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],
[
0,
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[
1,
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[
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[
1,
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],
[
[
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[
1,
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[
0,
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[
1,
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1,
1,
0
],
[
0,
0,
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1,
0
]
],
[
[
0,
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1,
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[
0,
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[
0,
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[
1,
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[
1,
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]
],
[
[
0,
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1,
1
],
[
0,
1,
1,
1,
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],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 2, 3)
B: (Right, 3, 2)
C: (Top, 2, 1)
D: (Front, 2, 1)
E: (Left, 3, 4)
F: (Back, 1, 4)
|
|
[
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
0,
0
]
],
[
[
1,
1,
0,
0,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
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1,
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[
1,
0,
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]
],
[
[
0,
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[
0,
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],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
]
],
[
[
0,
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1,
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[
0,
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1,
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],
[
0,
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[
0,
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1,
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[
0,
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]
],
[
[
0,
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1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
0,
0,
0,
0
]
],
[
[
0,
1,
0,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 4, 1)
B: (Front, 4, 3)
C: (Bottom, 4, 3)
D: (Back, 4, 1)
E: (Top, 1, 2)
F: (Right, 1, 4)
|
|
[
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[
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[
1,
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],
[
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 2, 3)
B: (Bottom, 1, 2)
C: (Back, 4, 3)
D: (Right, 3, 4)
E: (Left, 4, 1)
F: (Top, 2, 3)
|
|
[
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[
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[
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],
[
0,
1,
1,
1,
0
],
[
0,
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0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 3, 2)
B: (Right, 2, 3)
C: (Front, 1, 4)
D: (Top, 4, 1)
E: (Back, 1, 4)
F: (Left, 1, 2)
|
|
[
[
[
0,
0,
1,
0,
0
],
[
1,
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1,
1
],
[
1,
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],
[
1,
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1,
1,
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],
[
1,
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],
[
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[
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[
1,
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],
[
[
0,
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1,
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],
[
1,
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1,
1,
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],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 2, 1)
B: (Bottom, 2, 3)
C: (Right, 3, 2)
D: (Left, 1, 4)
E: (Back, 2, 1)
F: (Front, 3, 2)
|
|
[
[
[
0,
1,
0,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
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1
],
[
1,
1,
1,
1,
1
],
[
0,
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]
],
[
[
1,
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[
1,
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[
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[
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[
0,
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[
1,
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],
[
[
1,
1,
1,
0,
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],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 2, 1)
B: (Front, 1, 4)
C: (Left, 3, 4)
D: (Back, 4, 3)
E: (Top, 2, 1)
F: (Right, 2, 1)
|
|
[
[
[
0,
0,
0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
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1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
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]
],
[
[
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[
1,
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[
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[
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[
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1,
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[
1,
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[
0,
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1,
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[
0,
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]
],
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 2, 3)
B: (Back, 2, 1)
C: (Bottom, 3, 4)
D: (Left, 1, 4)
E: (Right, 1, 4)
F: (Top, 3, 2)
|
|
[
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
1,
0
]
],
[
[
0,
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1
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[
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[
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[
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1,
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[
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[
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0,
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[
0,
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[
1,
1,
1,
1,
0
],
[
0,
1,
0,
1,
1
]
],
[
[
0,
0,
1,
0,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 3, 4)
B: (Back, 3, 4)
C: (Bottom, 1, 2)
D: (Right, 3, 2)
E: (Front, 2, 3)
F: (Top, 3, 2)
|
|
[
[
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[
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],
[
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[
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[
[
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1,
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[
1,
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[
1,
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[
0,
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],
[
[
1,
0,
1,
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[
1,
1,
1,
1,
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[
1,
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1,
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],
[
0,
1,
1,
1,
1
],
[
1,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 1, 2)
B: (Front, 3, 4)
C: (Bottom, 4, 3)
D: (Right, 3, 2)
E: (Back, 1, 4)
F: (Top, 1, 2)
|
|
[
[
[
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],
[
1,
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],
[
0,
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]
],
[
[
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[
1,
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[
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[
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[
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[
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[
1,
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[
[
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[
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[
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[
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],
[
[
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0,
1,
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],
[
1,
1,
1,
1,
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],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 4, 3)
B: (Top, 3, 4)
C: (Back, 2, 1)
D: (Right, 3, 4)
E: (Bottom, 2, 1)
F: (Front, 3, 2)
|
|
[
[
[
1,
0,
0,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
1,
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]
],
[
[
0,
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[
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[
1,
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[
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[
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[
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[
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[
1,
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[
0,
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]
],
[
[
1,
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[
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[
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[
0,
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],
[
[
1,
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[
1,
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],
[
1,
1,
1,
1,
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],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
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]
],
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 4, 3)
B: (Bottom, 2, 3)
C: (Front, 3, 2)
D: (Top, 1, 2)
E: (Back, 3, 4)
F: (Left, 2, 3)
|
|
[
[
[
1,
0,
1,
0,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
0,
1
]
],
[
[
0,
1,
1,
1,
0
],
[
1,
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[
1,
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[
1,
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[
1,
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[
[
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[
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[
1,
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[
0,
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],
[
[
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[
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[
0,
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],
[
[
0,
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[
0,
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[
0,
1,
1,
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],
[
1,
1,
1,
1,
1
],
[
0,
0,
0,
0,
1
]
],
[
[
1,
0,
0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 1, 4)
B: (Right, 1, 4)
C: (Top, 4, 3)
D: (Front, 3, 2)
E: (Bottom, 2, 3)
F: (Back, 2, 3)
|
|
[
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
0,
1,
0,
0
]
],
[
[
1,
1,
0,
0,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
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],
[
1,
1,
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1,
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[
0,
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]
],
[
[
0,
0,
1,
1,
1
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[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
0,
0,
0
]
],
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
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],
[
1,
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[
0,
1,
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1,
1
],
[
0,
0,
1,
1,
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]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
]
],
[
[
0,
0,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
0,
0,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 1, 4)
B: (Top, 2, 1)
C: (Front, 3, 4)
D: (Right, 2, 3)
E: (Left, 4, 1)
F: (Bottom, 2, 1)
|
|
[
[
[
0,
0,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
0,
1
]
],
[
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
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[
0,
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],
[
[
1,
1,
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],
[
0,
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1,
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],
[
0,
1,
1,
1,
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[
1,
1,
1,
1,
0
],
[
0,
0,
0,
0,
1
]
],
[
[
0,
1,
0,
1,
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[
1,
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1,
1,
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[
1,
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[
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[
1,
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]
],
[
[
0,
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1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
0,
0,
0,
0
]
],
[
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 4, 1)
B: (Top, 4, 1)
C: (Right, 1, 4)
D: (Bottom, 2, 3)
E: (Left, 4, 1)
F: (Back, 4, 3)
|
|
[
[
[
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],
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[
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],
[
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[
1,
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],
[
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[
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[
[
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[
1,
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[
1,
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[
0,
1,
1,
1,
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],
[
0,
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1,
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]
],
[
[
1,
0,
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0,
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],
[
1,
1,
1,
1,
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],
[
1,
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1,
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],
[
1,
1,
1,
1,
0
],
[
0,
0,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 4, 1)
B: (Back, 1, 2)
C: (Right, 4, 3)
D: (Bottom, 2, 1)
E: (Front, 4, 3)
F: (Left, 1, 4)
|
|
[
[
[
1,
0,
1,
1,
1
],
[
0,
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],
[
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],
[
1,
1,
1,
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],
[
0,
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]
],
[
[
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[
1,
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[
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[
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[
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[
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[
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[
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[
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],
[
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[
1,
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[
1,
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[
0,
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],
[
[
1,
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[
0,
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[
0,
1,
1,
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[
0,
1,
1,
1,
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],
[
0,
1,
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]
],
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 2, 1)
B: (Back, 4, 1)
C: (Front, 1, 2)
D: (Left, 4, 3)
E: (Bottom, 1, 4)
F: (Right, 4, 1)
|
|
[
[
[
0,
1,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
0,
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1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
0,
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]
],
[
[
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[
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[
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[
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[
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[
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[
1,
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],
[
[
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1,
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[
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[
0,
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],
[
[
1,
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[
1,
1,
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1,
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],
[
1,
1,
1,
1,
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[
1,
1,
1,
1,
1
],
[
1,
0,
0,
1,
0
]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 3, 4)
B: (Right, 2, 1)
C: (Front, 1, 2)
D: (Left, 3, 2)
E: (Back, 4, 1)
F: (Bottom, 2, 1)
|
|
[
[
[
1,
1,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
0,
1
]
],
[
[
0,
0,
0,
1,
0
],
[
1,
1,
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1,
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],
[
1,
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[
1,
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[
0,
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],
[
[
1,
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[
1,
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[
1,
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1,
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[
0,
1,
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1,
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[
0,
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1,
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]
],
[
[
1,
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[
0,
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[
0,
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[
1,
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[
1,
1,
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]
],
[
[
1,
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1,
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],
[
1,
1,
1,
1,
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],
[
0,
1,
1,
1,
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],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
]
],
[
[
0,
0,
1,
0,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 2)
B: (Bottom, 3, 4)
C: (Left, 1, 2)
D: (Top, 4, 3)
E: (Back, 3, 4)
F: (Front, 2, 1)
|
|
[
[
[
0,
0,
0,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
1,
0
]
],
[
[
0,
0,
1,
1,
1
],
[
1,
1,
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1,
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],
[
0,
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[
0,
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[
1,
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]
],
[
[
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[
1,
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[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
]
],
[
[
0,
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0,
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[
1,
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1,
1,
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],
[
0,
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[
0,
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1,
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[
0,
1,
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]
],
[
[
1,
1,
0,
0,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
1,
1
]
],
[
[
1,
0,
0,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 4, 1)
B: (Bottom, 3, 4)
C: (Right, 2, 3)
D: (Front, 4, 3)
E: (Left, 1, 2)
F: (Back, 2, 3)
|
|
[
[
[
0,
0,
0,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
1,
1
]
],
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
],
[
[
1,
0,
0,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
0,
1,
1,
0
]
],
[
[
0,
1,
1,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
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[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
]
],
[
[
0,
0,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
0,
1,
0
]
],
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 2, 1)
B: (Left, 1, 4)
C: (Back, 3, 4)
D: (Bottom, 2, 3)
E: (Right, 2, 3)
F: (Front, 1, 2)
|
|
[
[
[
1,
0,
0,
1,
1
],
[
1,
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1,
1
],
[
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],
[
1,
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],
[
0,
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]
],
[
[
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[
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[
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[
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[
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[
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],
[
0,
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]
],
[
[
1,
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[
0,
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1,
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[
1,
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[
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],
[
0,
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]
],
[
[
0,
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],
[
1,
1,
1,
1,
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],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
]
],
[
[
1,
0,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 2, 3)
B: (Front, 2, 3)
C: (Right, 1, 2)
D: (Bottom, 3, 2)
E: (Left, 4, 1)
F: (Back, 3, 4)
|
|
[
[
[
1,
1,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
0,
0
]
],
[
[
1,
1,
0,
0,
0
],
[
1,
1,
1,
1,
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],
[
1,
1,
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],
[
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[
0,
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],
[
[
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[
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[
1,
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[
0,
1,
1,
1,
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[
0,
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1,
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]
],
[
[
1,
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[
0,
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1,
1,
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],
[
1,
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[
0,
1,
1,
1,
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],
[
0,
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]
],
[
[
0,
1,
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1,
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],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
0,
0,
0,
0
]
],
[
[
1,
1,
0,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 4)
B: (Top, 3, 4)
C: (Front, 3, 2)
D: (Bottom, 4, 1)
E: (Left, 4, 3)
F: (Back, 3, 2)
|
|
[
[
[
0,
0,
0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
0,
0,
0,
0
]
],
[
[
0,
0,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
0,
0
]
],
[
[
0,
0,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
0,
0,
1,
0
]
],
[
[
1,
0,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
0,
1
]
],
[
[
1,
1,
1,
0,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
1,
0
]
],
[
[
1,
0,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 1, 2)
B: (Bottom, 2, 1)
C: (Right, 4, 3)
D: (Front, 2, 3)
E: (Left, 2, 1)
F: (Back, 2, 1)
|
|
[
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
0,
1
]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
0,
1
]
],
[
[
0,
1,
0,
0,
0
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[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
0,
0,
0
]
],
[
[
0,
1,
0,
0,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
0,
1
]
],
[
[
0,
0,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
0,
1,
1,
0
]
],
[
[
1,
1,
0,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 3, 4)
B: (Back, 4, 1)
C: (Bottom, 3, 4)
D: (Top, 4, 3)
E: (Right, 1, 4)
F: (Left, 4, 3)
|
|
[
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
],
[
[
1,
0,
0,
0,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
0,
1
]
],
[
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
0,
1
]
],
[
[
0,
0,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
0,
0,
1,
0
]
],
[
[
1,
0,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
1,
1
]
],
[
[
1,
1,
0,
0,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 4, 1)
B: (Front, 3, 2)
C: (Top, 3, 4)
D: (Left, 3, 4)
E: (Back, 1, 2)
F: (Right, 1, 4)
|
|
[
[
[
0,
1,
0,
0,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
0,
0
]
],
[
[
1,
0,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
0,
1
]
],
[
[
0,
0,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
0,
0
]
],
[
[
1,
1,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
],
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
]
],
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 1, 2)
B: (Back, 4, 1)
C: (Right, 1, 2)
D: (Front, 2, 3)
E: (Left, 3, 4)
F: (Top, 3, 2)
|
|
[
[
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
],
[
[
0,
1,
0,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
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1,
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],
[
0,
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[
1,
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],
[
[
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[
0,
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[
0,
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1,
1,
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[
0,
1,
1,
1,
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],
[
0,
0,
0,
1,
1
]
],
[
[
0,
0,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
],
[
[
0,
1,
0,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
0,
1,
0,
1
]
],
[
[
0,
1,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
0,
1,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Back, 4, 3)
B: (Front, 1, 4)
C: (Bottom, 4, 3)
D: (Left, 2, 1)
E: (Top, 2, 3)
F: (Right, 1, 2)
|
|
[
[
[
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1,
0
],
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[
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[
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],
[
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[
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[
[
0,
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[
1,
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[
1,
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0
],
[
0,
1,
1,
1,
0
],
[
0,
0,
0,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 2, 1)
B: (Right, 2, 1)
C: (Top, 1, 4)
D: (Front, 4, 3)
E: (Bottom, 1, 2)
F: (Back, 1, 2)
|
|
[
[
[
1,
1,
0,
1,
0
],
[
1,
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],
[
1,
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],
[
1,
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],
[
1,
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[
[
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[
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[
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[
1,
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[
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[
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],
[
[
0,
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0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
0,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 4, 3)
B: (Back, 1, 2)
C: (Right, 1, 2)
D: (Left, 2, 3)
E: (Bottom, 3, 2)
F: (Front, 1, 2)
|
|
[
[
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
1
]
],
[
[
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[
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[
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[
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[
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[
1,
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[
0,
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]
],
[
[
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1,
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[
1,
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[
1,
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],
[
[
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[
0,
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[
0,
1,
1,
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[
1,
1,
1,
1,
0
],
[
0,
1,
0,
0,
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]
],
[
[
0,
0,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 4, 3)
B: (Back, 2, 1)
C: (Front, 2, 1)
D: (Bottom, 3, 2)
E: (Right, 2, 3)
F: (Left, 1, 4)
|
|
[
[
[
0,
0,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
1,
1
]
],
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
1,
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1,
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[
0,
1,
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[
0,
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],
[
[
1,
1,
0,
0,
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[
0,
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],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
0,
1
]
],
[
[
1,
0,
0,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
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[
0,
1,
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[
1,
1,
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1,
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]
],
[
[
1,
1,
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0,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
]
],
[
[
0,
1,
1,
0,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
0,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 2, 1)
B: (Right, 1, 4)
C: (Left, 2, 1)
D: (Front, 3, 2)
E: (Back, 3, 4)
F: (Top, 3, 4)
|
|
[
[
[
0,
1,
0,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
1,
0
]
],
[
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
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1,
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[
1,
0,
1,
0,
0
]
],
[
[
1,
0,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
1
]
],
[
[
1,
0,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
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1
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[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
1
]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
1,
1
]
],
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
0,
1,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 2, 1)
B: (Left, 4, 1)
C: (Front, 2, 3)
D: (Top, 1, 4)
E: (Back, 2, 1)
F: (Bottom, 2, 3)
|
|
[
[
[
1,
1,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
1,
1
]
],
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
0,
1
]
],
[
[
0,
1,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
0,
0,
1,
0
]
],
[
[
0,
0,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
0,
1
]
],
[
[
0,
1,
0,
0,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
0,
0
]
],
[
[
0,
1,
0,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 4)
B: (Back, 2, 3)
C: (Bottom, 2, 3)
D: (Front, 1, 2)
E: (Top, 1, 2)
F: (Left, 3, 4)
|
|
[
[
[
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1,
1
],
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[
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[
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],
[
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1,
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[
[
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[
0,
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[
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],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 4, 3)
B: (Top, 3, 4)
C: (Front, 2, 3)
D: (Bottom, 2, 1)
E: (Back, 3, 4)
F: (Left, 4, 1)
|
|
[
[
[
0,
0,
0,
0,
0
],
[
0,
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1,
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],
[
0,
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],
[
1,
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],
[
0,
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]
],
[
[
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[
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[
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],
[
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[
[
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[
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[
1,
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[
1,
1,
1,
1,
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],
[
0,
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1,
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]
],
[
[
1,
1,
0,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 1, 4)
B: (Bottom, 3, 2)
C: (Right, 1, 4)
D: (Back, 1, 2)
E: (Top, 3, 2)
F: (Front, 4, 3)
|
|
[
[
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
0,
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]
],
[
[
1,
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[
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[
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[
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[
1,
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[
1,
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]
],
[
[
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0,
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[
[
1,
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[
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[
1,
1,
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[
0,
1,
1,
1,
1
],
[
0,
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1,
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]
],
[
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 4, 1)
B: (Top, 3, 4)
C: (Back, 4, 3)
D: (Right, 1, 4)
E: (Bottom, 2, 3)
F: (Front, 4, 1)
|
|
[
[
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
1,
0
]
],
[
[
0,
0,
0,
0,
0
],
[
1,
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[
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[
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[
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[
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[
1,
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[
1,
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1,
0
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[
0,
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0
]
],
[
[
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[
1,
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[
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[
0,
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]
],
[
[
0,
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[
0,
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1,
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],
[
1,
1,
1,
1,
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],
[
1,
1,
1,
1,
1
],
[
1,
0,
0,
1,
1
]
],
[
[
1,
1,
0,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
0,
0,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 4, 1)
B: (Right, 1, 4)
C: (Top, 1, 2)
D: (Back, 4, 3)
E: (Front, 3, 4)
F: (Left, 1, 2)
|
|
[
[
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
1,
0
]
],
[
[
1,
0,
0,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
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],
[
1,
1,
1,
1,
1
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[
0,
1,
1,
1,
1
]
],
[
[
1,
0,
0,
1,
0
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[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
0,
1
]
],
[
[
1,
0,
0,
0,
0
],
[
1,
1,
1,
1,
1
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[
1,
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[
0,
1,
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[
1,
1,
0,
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1
]
],
[
[
0,
0,
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1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
],
[
[
0,
0,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 1, 2)
B: (Bottom, 4, 3)
C: (Back, 3, 4)
D: (Top, 4, 3)
E: (Front, 3, 2)
F: (Left, 2, 1)
|
|
[
[
[
1,
0,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
0,
0,
1,
0
]
],
[
[
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[
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[
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[
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[
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[
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[
1,
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1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
0,
1,
0
]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
0,
1
]
],
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
1,
1
]
],
[
[
0,
1,
1,
0,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
0,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Left, 3, 4)
B: (Bottom, 3, 4)
C: (Right, 1, 4)
D: (Back, 4, 3)
E: (Front, 2, 1)
F: (Top, 2, 3)
|
|
[
[
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[
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],
[
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[
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[
1,
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1,
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[
1,
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1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 2, 1)
B: (Left, 1, 4)
C: (Back, 4, 3)
D: (Bottom, 3, 4)
E: (Right, 2, 3)
F: (Front, 3, 4)
|
|
[
[
[
1,
0,
0,
1,
0
],
[
0,
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],
[
1,
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],
[
1,
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],
[
0,
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],
[
[
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[
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[
[
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[
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[
1,
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[
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],
[
[
0,
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1,
0,
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],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 3, 2)
B: (Back, 1, 4)
C: (Top, 4, 3)
D: (Bottom, 2, 1)
E: (Front, 3, 2)
F: (Left, 4, 3)
|
|
[
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
0,
0,
0,
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]
],
[
[
1,
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[
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[
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[
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[
1,
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[
1,
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[
0,
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],
[
[
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1,
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1,
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[
0,
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[
[
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0,
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[
0,
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[
0,
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[
0,
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]
],
[
[
0,
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0,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 3, 4)
B: (Right, 1, 2)
C: (Back, 4, 1)
D: (Front, 3, 4)
E: (Left, 4, 1)
F: (Top, 1, 2)
|
|
[
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
0,
1
]
],
[
[
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[
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[
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[
1,
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[
0,
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],
[
[
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[
1,
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[
1,
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[
1,
1,
1,
1,
1
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[
1,
1,
1,
0,
1
]
],
[
[
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[
1,
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[
1,
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[
1,
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],
[
[
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[
1,
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[
0,
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1,
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],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
0,
0
]
],
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 3, 4)
B: (Right, 3, 2)
C: (Back, 4, 1)
D: (Left, 2, 1)
E: (Front, 2, 1)
F: (Bottom, 4, 1)
|
|
[
[
[
1,
1,
0,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
0,
1,
1,
0
]
],
[
[
0,
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1,
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0
],
[
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[
1,
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[
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[
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[
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[
1,
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[
0,
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1,
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[
0,
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]
],
[
[
0,
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[
1,
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[
0,
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[
1,
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],
[
[
0,
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[
1,
1,
1,
1,
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[
0,
1,
1,
1,
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],
[
0,
1,
1,
1,
0
],
[
1,
0,
0,
0,
0
]
],
[
[
1,
1,
1,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
0,
1,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 4, 3)
B: (Top, 2, 1)
C: (Bottom, 3, 4)
D: (Back, 4, 1)
E: (Front, 3, 4)
F: (Left, 4, 1)
|
|
[
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[
1,
1,
0,
0,
0
],
[
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1,
1,
1,
1
],
[
1,
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1,
1,
1
],
[
0,
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1,
0
],
[
0,
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],
[
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1,
0
],
[
0,
1,
1,
0,
0
]
],
[
[
0,
0,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
1,
1
]
],
[
[
0,
0,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
0,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 1, 4)
B: (Front, 2, 3)
C: (Back, 2, 1)
D: (Left, 2, 1)
E: (Top, 3, 2)
F: (Bottom, 2, 3)
|
|
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[
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] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Right, 1, 4)
B: (Back, 4, 3)
C: (Top, 3, 4)
D: (Front, 3, 2)
E: (Bottom, 4, 1)
F: (Left, 1, 2)
|
|
[
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1,
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[
[
0,
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[
1,
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1,
1,
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],
[
0,
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0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Top, 3, 4)
B: (Back, 1, 2)
C: (Bottom, 4, 3)
D: (Left, 3, 2)
E: (Front, 3, 4)
F: (Right, 2, 3)
|
|
[
[
[
0,
0,
0,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
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1,
1,
1
],
[
0,
1,
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1,
0
],
[
0,
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],
[
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1,
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[
1,
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[
1,
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[
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[
[
0,
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[
1,
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1,
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[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 1, 2)
B: (Top, 2, 3)
C: (Right, 4, 1)
D: (Back, 1, 4)
E: (Front, 2, 1)
F: (Left, 1, 2)
|
|
[
[
[
0,
1,
0,
1,
0
],
[
1,
1,
1,
1,
1
],
[
1,
1,
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1
],
[
0,
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1,
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],
[
1,
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],
[
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[
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],
[
[
0,
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0,
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],
[
0,
1,
1,
1,
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],
[
1,
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1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
0,
1,
0,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Front, 2, 3)
B: (Right, 3, 2)
C: (Left, 1, 4)
D: (Top, 3, 2)
E: (Back, 3, 2)
F: (Bottom, 3, 2)
|
|
[
[
[
0,
0,
1,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
0,
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]
],
[
[
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[
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1,
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[
1,
1,
1,
1,
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[
0,
1,
1,
1,
1
],
[
0,
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1,
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],
[
[
0,
0,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
1,
1
]
]
] | You are a spatial-reasoning assistant that solves Happy Cube puzzles.
INPUT
• Six jigsaw-style pieces, labelled A–F.
• Each piece is described by the bump/gap pattern on its four edges (Edge1, Edge2, Edge3 and Edge4) as shown in the image, the center squares are always filled.
Task
Build a 5 × 5 × 5 cube that uses every piece exactly once.
• Assign each piece to one cube face (Top, Bottom, Front, Back, Left, Right) with proper orientation (rotation and/or flip).
• The finished cube closed perfectly—no overlaps, no gaps.
The first and last 'square' of the edge contribute to the corners of the cube, make sure:
• When two cube faces touch, the non-corner part of their edges must be complementary bit-for-bit.
• At cube corners (where three faces meet), all connecting edges must align seamlessly.
NOTE
For each piece, report the orientation via the following mental exercise:
1. Hold the finished cube in both hands.
2. Turn the whole cube until the face you are about to name is now facing you like the front of a box.
3. In this view, write down the edge numbers located on left and top.
• Format: (Cube-Face, Left-Edge#, Top-Edge#)
Note that left-edge and top-edge must be adjacent.
OUTPUT
Answer the question with the arrangement of 6 pieces. Your response should end with:
The final solution is
```
A: (Cube-Face, Left-Edge#, Top-Edge#)
B: (Cube-Face, Left-Edge#, Top-Edge#)
C: (Cube-Face, Left-Edge#, Top-Edge#)
D: (Cube-Face, Left-Edge#, Top-Edge#)
E: (Cube-Face, Left-Edge#, Top-Edge#)
F: (Cube-Face, Left-Edge#, Top-Edge#)
``` | A: (Bottom, 1, 2)
B: (Left, 2, 1)
C: (Front, 1, 2)
D: (Back, 3, 2)
E: (Top, 3, 2)
F: (Right, 3, 4)
|
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