Datasets:
Dataset Viewer
image
imagewidth (px) 1.8k
1.8k
| face_arrays
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,
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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,
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],
[
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,
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0,
0,
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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[
0,
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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,
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1,
1,
0
],
[
1,
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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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1,
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[
[
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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,
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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]
],
[
[
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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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],
[
[
1,
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[
0,
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[
0,
1,
1,
1,
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[
0,
1,
1,
1,
0
],
[
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,
1,
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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,
1,
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[
1,
1,
1,
1,
1
],
[
0,
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,
1,
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]
],
[
[
0,
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[
0,
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1,
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,
1,
1,
1,
0
],
[
1,
1,
1,
1,
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],
[
0,
0,
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1,
0
]
],
[
[
1,
0,
1,
1,
0
],
[
1,
1,
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1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
0,
0,
0
]
],
[
[
0,
1,
1,
1,
0
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[
1,
1,
1,
1,
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[
1,
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[
0,
1,
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1,
1
],
[
1,
1,
1,
0,
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]
],
[
[
1,
0,
0,
0,
1
],
[
0,
1,
1,
1,
1
],
[
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,
1,
1,
1
],
[
0,
1,
1,
1,
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],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
0,
1
]
],
[
[
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1,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
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1,
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],
[
0,
1,
1,
1,
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],
[
0,
1,
1,
1,
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]
],
[
[
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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1,
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[
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],
[
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)
|
|
[
[
[
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0,
0,
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],
[
1,
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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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[
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[
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[
0,
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1,
1,
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],
[
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,
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1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
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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[
[
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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],
[
[
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,
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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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]
],
[
[
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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,
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],
[
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,
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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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[
0,
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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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[
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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,
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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[
1,
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1,
1,
1
],
[
1,
1,
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,
0
]
],
[
[
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)
|
|
[
[
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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,
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)
|
|
[
[
[
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0,
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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[
1,
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[
1,
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[
1,
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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,
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,
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1,
0
],
[
0,
1,
1,
1,
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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0,
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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,
1,
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[
0,
1,
1,
1,
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],
[
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,
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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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[
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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[
[
0,
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[
1,
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[
1,
1,
1,
1,
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],
[
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,
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]
],
[
[
1,
1,
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1
],
[
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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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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[
1,
1,
1,
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],
[
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)
|
|
[
[
[
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0,
1,
0
],
[
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1,
1,
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],
[
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1
],
[
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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]
],
[
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],
[
[
0,
1,
0,
0,
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,
0,
1,
0,
1
],
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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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[
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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[
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[
[
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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,
1,
0,
1,
1
],
[
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,
0
]
],
[
[
1,
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1,
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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[
1,
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[
1,
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1,
0
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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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[
1,
0,
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]
],
[
[
0,
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[
1,
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1,
1,
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],
[
1,
1,
1,
1,
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],
[
1,
1,
1,
1,
1
],
[
1,
0,
0,
0,
1
]
],
[
[
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,
0,
1,
0
],
[
1,
1,
1,
1,
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],
[
0,
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[
0,
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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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1,
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],
[
1,
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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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]
],
[
[
0,
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[
0,
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[
1,
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1,
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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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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[
0,
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1,
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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]
],
[
[
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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0,
1,
1,
1
],
[
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1,
1,
1,
1
],
[
1,
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1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
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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],
[
[
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],
[
0,
1,
1,
1,
0
],
[
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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],
[
0,
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1,
1,
0
],
[
0,
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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)
|
|
[
[
[
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0,
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],
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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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[
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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],
[
1,
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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,
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1,
1
],
[
1,
1,
1,
1,
0
],
[
1,
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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,
1,
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[
1,
1,
1,
1,
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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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[
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,
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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,
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[
0,
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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,
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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,
1,
1,
1
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[
1,
0,
1,
1,
1
]
],
[
[
0,
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[
0,
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1,
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],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
]
],
[
[
0,
0,
0,
1,
0
],
[
0,
1,
1,
1,
1
],
[
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,
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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] | 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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] | 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)
|
|
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],
[
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1,
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],
[
0,
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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)
|
|
[
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],
[
1,
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1,
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],
[
0,
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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)
|
|
[
[
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0
],
[
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[
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[
1,
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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)
|
|
[
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[
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[
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[
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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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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,
0,
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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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[
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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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],
[
[
0,
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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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]
],
[
[
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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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],
[
[
1,
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[
0,
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]
],
[
[
1,
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[
1,
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,
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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,
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,
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1,
1,
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[
0,
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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,
1,
1,
1
],
[
0,
0,
1,
1,
0
]
],
[
[
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,
1,
1,
1
],
[
0,
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]
],
[
[
1,
1,
0,
0,
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],
[
0,
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1,
1,
1
],
[
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,
1,
1,
1,
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],
[
1,
1,
1,
1,
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],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
0,
0
]
],
[
[
0,
0,
0,
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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1,
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[
1,
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[
0,
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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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],
[
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)
|
|
[
[
[
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1,
1,
1
],
[
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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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[
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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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[
0,
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[
0,
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],
[
[
0,
1,
1,
0,
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],
[
0,
1,
1,
1,
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],
[
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,
0
],
[
1,
1,
1,
1,
0
],
[
0,
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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,
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1,
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[
1,
1,
1,
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[
1,
1,
1,
1,
1
],
[
1,
0,
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1,
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]
],
[
[
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,
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1,
0
],
[
1,
1,
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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[
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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[
1,
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[
1,
1,
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],
[
[
1,
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[
1,
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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,
1,
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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]
],
[
[
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[
1,
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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,
1,
0,
0,
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[
1,
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1,
1,
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],
[
0,
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[
0,
1,
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1,
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],
[
0,
1,
1,
0,
1
]
],
[
[
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,
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)
|
|
[
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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: (Top, 2, 3)
B: (Front, 2, 3)
C: (Right, 1, 2)
D: (Bottom, 3, 2)
E: (Left, 4, 1)
F: (Back, 3, 4)
|
|
[
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[
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],
[
1,
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1,
1,
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],
[
1,
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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,
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0,
0,
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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1,
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[
1,
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],
[
[
1,
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1,
1,
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],
[
1,
1,
1,
1,
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],
[
1,
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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)
|
|
[
[
[
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1,
1,
0
],
[
0,
1,
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1,
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],
[
1,
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1
],
[
0,
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1
],
[
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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[
0,
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[
1,
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1,
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[
1,
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]
],
[
[
1,
1,
0,
0,
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],
[
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,
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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,
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1,
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],
[
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,
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],
[
1,
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[
0,
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]
],
[
[
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[
1,
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],
[
0,
1,
1,
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],
[
0,
1,
1,
1,
1
],
[
1,
0,
0,
0,
0
]
],
[
[
1,
1,
0,
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[
0,
1,
1,
1,
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],
[
1,
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[
1,
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1,
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],
[
0,
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
],
[
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,
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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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[
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[
0,
1,
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0,
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]
],
[
[
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)
|
|
[
[
[
1,
1,
1,
1,
0
],
[
0,
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1,
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],
[
0,
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1
],
[
0,
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1,
1,
1
],
[
1,
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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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[
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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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[
1,
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[
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[
1,
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]
],
[
[
0,
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[
0,
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1,
1,
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],
[
0,
1,
1,
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],
[
0,
1,
1,
1,
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],
[
0,
0,
1,
1,
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]
],
[
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
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,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
0,
0
]
],
[
[
1,
0,
0,
0,
0
],
[
0,
1,
1,
1,
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],
[
1,
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[
0,
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[
1,
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]
],
[
[
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[
1,
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[
1,
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[
0,
1,
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1,
1
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[
1,
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,
1,
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]
],
[
[
0,
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1,
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],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
1,
0
]
],
[
[
0,
0,
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
]
],
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
]
],
[
[
0,
0,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
],
[
1,
1,
1,
1,
1
],
[
0,
1,
0,
0,
1
]
],
[
[
0,
0,
0,
0,
0
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
1,
1
]
],
[
[
0,
1,
1,
0,
1
],
[
0,
1,
1,
1,
0
],
[
0,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
0,
0,
1
]
],
[
[
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,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
1,
0,
0
]
],
[
[
1,
1,
0,
0,
0
],
[
0,
1,
1,
1,
1
],
[
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,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
0,
1,
0
]
],
[
[
1,
1,
0,
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,
1,
1,
0
],
[
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,
1,
1,
1
],
[
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,
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0,
1
]
],
[
[
0,
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0,
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],
[
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,
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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[
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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, 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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0,
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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,
0
]
],
[
[
1,
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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[
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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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[
0,
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[
1,
1,
1,
1,
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[
0,
1,
1,
1,
1
],
[
0,
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1,
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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1,
1
],
[
0,
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[
0,
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[
0,
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],
[
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[
0,
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[
1,
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[
1,
1,
1,
1,
0
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[
0,
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1,
1,
0
]
],
[
[
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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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]
],
[
[
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,
0
],
[
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,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
1
]
],
[
[
1,
0,
0,
1,
0
],
[
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
],
[
1,
1,
1,
1,
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],
[
0,
1,
1,
1,
0
],
[
1,
1,
0,
0,
1
]
],
[
[
0,
0,
0,
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
]
],
[
[
0,
1,
1,
0,
0
],
[
0,
1,
1,
1,
0
],
[
0,
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1,
1,
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],
[
0,
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],
[
0,
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]
],
[
[
0,
1,
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1,
0
],
[
0,
1,
1,
1,
1
],
[
1,
1,
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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[
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,
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0,
1,
0
],
[
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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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[
1,
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[
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[
[
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1,
0,
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[
1,
1,
1,
1,
1
],
[
1,
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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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[
1,
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[
1,
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[
0,
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],
[
[
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0,
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[
[
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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,
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,
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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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[
1,
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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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]
],
[
[
0,
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[
1,
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[
0,
1,
1,
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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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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[
0,
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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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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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],
[
1,
1,
1,
1,
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],
[
0,
1,
1,
1,
0
],
[
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)
|
|
[
[
[
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,
1,
0
],
[
0,
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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,
1
],
[
1,
1,
1,
1,
1
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
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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1,
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[
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[
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[
0,
1,
1,
1,
0
],
[
1,
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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: (Back, 4, 3)
C: (Top, 3, 4)
D: (Front, 3, 2)
E: (Bottom, 4, 1)
F: (Left, 1, 2)
|
|
[
[
[
1,
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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1,
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[
1,
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1,
1,
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],
[
0,
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1,
1,
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]
],
[
[
0,
0,
0,
0,
0
],
[
1,
1,
1,
1,
1
],
[
0,
1,
1,
1,
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,
1,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
0,
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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,
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[
1,
1,
1,
1,
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],
[
1,
1,
1,
1,
0
],
[
0,
0,
1,
1,
0
]
],
[
[
0,
1,
0,
0,
1
],
[
1,
1,
1,
1,
1
],
[
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,
1,
1,
1
],
[
0,
1,
1,
1,
0
],
[
1,
0,
0,
1,
0
]
],
[
[
1,
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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[
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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1,
1,
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],
[
0,
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0,
1,
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]
],
[
[
0,
1,
0,
0,
1
],
[
0,
1,
1,
1,
0
],
[
1,
1,
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,
0
]
],
[
[
0,
0,
1,
0,
0
],
[
1,
1,
1,
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,
1,
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[
1,
1,
1,
1,
1
],
[
1,
1,
0,
1,
0
]
],
[
[
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,
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1,
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[
0,
1,
1,
1,
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]
],
[
[
1,
1,
1,
0,
1
],
[
1,
1,
1,
1,
0
],
[
1,
1,
1,
1,
0
],
[
0,
1,
1,
1,
1
],
[
0,
0,
0,
1,
1
]
],
[
[
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)
|
End of preview. Expand
in Data Studio
MARBLE: A Hard Benchmark for Multimodal Spatial Reasoning and Planning
🌐 Homepage | 📖 Paper | 🤗 Dataset | 🔗 Code
Introduction
MARBLE is a challenging multimodal reasoning benchmark designed to scrutinize multimodal language models (MLLMs) in their ability to carefully reason step-by-step through complex multimodal problems and environments. MARBLE is composed of two highly challenging tasks, M-Portal and M-Cube, that require the crafting and understanding of multistep plans leveraging spatial, visual, and physical constraints. We find that current MLLMs perform poorly on MARBLE—all the 12 advanced models obtain near-random performance on M-Portal and 0% accuracy on M-Cube. Only in simplified subtasks some models outperform the random baseline, indicating that complex reasoning is still a challenge for existing MLLMs. Moreover, we show that perception remains a bottleneck, where MLLMs occasionally fail to extract information from the visual inputs. By shedding a light on the limitations of MLLMs, we hope that MARBLE will spur the development of the next generation of models with the ability to reason and plan across many, multimodal reasoning steps.
Dataset Details
The benchmark consists of two datasets M-Portal and M-CUBE, each also contains 2 subtasks respectively (portal_binary and portal_blanks for M-PORTAL and cube and cube_easy for M-CUBE). Besides, M-CUBE also contains a simple perception tasks cube_perception.
M-PORTAL: multi-step spatial-planning puzzles modelled on levels from Portal 2.
map_name: Portal 2 map name.images: images for each map (images.zip).system_promptanduser_prompt: instruction of the problem.answer: solution.
M-CUBE: 3D Cube assemblies from six jigsaw pieces, inspired by Happy Cube puzzles.
image: image of 6 jigsaw pieces.face_arrays: 6 jigsaw pieces converted to binary arrays (0=gap, 1=bump).question: instruction of the Happy Cube Puzzle.reference_solution: one of the valid solutions.
Evaluation
Please refer to 🔗 Code
Overall Results
Performance on M-PORTAL:
| Model | Plan-correctness (F1 %) | Fill-the-blanks (Acc %) |
|---|---|---|
| GPT-o3 | 6.6 | 17.6 |
| Gemini-2.5-pro | 4.7 | 16.1 |
| DeepSeek-R1-0528* | 0.0 | 8.4 |
| Claude-3.7-Sonnet | 6.3 | 6.8 |
| DeepSeek-R1* | 6.1 | 5.5 |
| Seed1.5-VL | 7.6 | 3.5 |
| GPT-o4-mini | 0.0 | 3.1 |
| GPT-4o | 6.5 | 0.4 |
| Llama-4-Scout | 6.5 | 0.2 |
| Qwen2.5-VL-72B | 6.6 | 0.2 |
| InternVL3-78B | 6.4 | 0.0 |
| Qwen3-235B-A22B* | 0.0 | 0.0 |
| Random | 6.1 | 3e-3 |
Performance on M-CUBE:
| Model | CUBE (Acc %) | CUBE-easy (Acc %) |
|---|---|---|
| GPT-o3 | 0.0 | 72.0 |
| GPT-o4-mini | 0.0 | 16.0 |
| DeepSeek-R1* | 0.0 | 14.0 |
| Gemini-2.5-pro | 0.0 | 11.0 |
| DeepSeek-R1-0528* | 0.0 | 8.0 |
| Claude-3.7-Sonnet | 0.0 | 7.4 |
| InternVL3-78B | 0.0 | 2.8 |
| Seed1.5-VL | 0.0 | 2.0 |
| GPT-4o | 0.0 | 2.0 |
| Qwen2.5-VL-72B | 0.0 | 2.0 |
| Llama-4-Scout | 0.0 | 1.6 |
| Qwen3-235B-A22B* | 0.0 | 0.3 |
| Random | 1e-5 | 3.1 |
Contact
- Yulun Jiang: [email protected]
BibTex
@article{jiang2025marble,
title={MARBLE: A Hard Benchmark for Multimodal Spatial Reasoning and Planning},
author={Jiang, Yulun and Chai, Yekun and Brbi'c, Maria and Moor, Michael},
journal={arXiv preprint arXiv:2506.22992},
year={2025},
url={https://arxiv.org/abs/2506.22992}
}
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