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problem
string | answer
string | responses
sequence | rewards
sequence | mean_reward
float64 |
|---|---|---|---|---|
Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$
|
70
| ["<think>\nOkay, so I need to find all integer bases b greater than 9 where the number 17_b is a div(...TRUNCATED) |
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | 1 |
"In $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{AB}$ so that $AD < AE < AB$, while points(...TRUNCATED) |
588
| ["<think>\nOkay, let me try to tackle this geometry problem. It seems a bit complex with all these p(...TRUNCATED) |
[
1,
1,
1,
0,
1,
0,
1,
1,
1,
1,
1,
1,
0,
1,
1,
1
] | 0.8125 |
"The $9$ members of a baseball team went to an ice-cream parlor after their game. Each player had a (...TRUNCATED) |
16
| ["<think>\nOkay, so there's this problem about a baseball team with 9 players who each got a single (...TRUNCATED) |
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | 1 |
"Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $1(...TRUNCATED) |
117
| ["<think>\nOkay, so I need to find the number of ordered pairs (x, y) where both x and y are integer(...TRUNCATED) |
[
1,
1,
1,
1,
0,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1,
1
] | 0.8125 |
"There are $8!= 40320$ eight-digit positive integers that use each of the digits $1, 2, 3, 4, 5, 6, (...TRUNCATED) |
279
| ["<think>\nOkay, so I need to find the number of eight-digit numbers using each of the digits 1 thro(...TRUNCATED) |
[
1,
1,
1,
0,
0,
0,
1,
0,
0,
0,
0,
1,
0,
1,
1,
1
] | 0.5 |
"An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the(...TRUNCATED) |
504
| ["<think>\nOkay, so I need to find $ r^2 + s^2 $ where $ r $ and $ s $ are the lengths of the two pa(...TRUNCATED) |
[
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | 1 |
"The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are randomly grouped into s(...TRUNCATED) |
821
| ["<think>\nOkay, let's try to tackle this probability problem. So, we have twelve letters: A, B, C, (...TRUNCATED) |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
"Let $k$ be a real number such that the system \\begin{align*} &|25 + 20i - z| = 5 \\ &|z - 4 - k| =(...TRUNCATED) |
77
| ["<think>\nOkay, so I need to solve this problem where there's a system of equations involving compl(...TRUNCATED) |
[
0,
0,
0,
0,
0,
1,
0,
1,
0,
0,
1,
0,
0,
0,
0,
1
] | 0.25 |
"The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin.(...TRUNCATED) |
62
| ["<think>\nOkay, so I need to solve this problem where a parabola y = x² - 4 is rotated 60 degrees (...TRUNCATED) |
[
0,
0,
0,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
0
] | 0.125 |
"The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each(...TRUNCATED) |
81
| ["<think>\nOkay, so I need to figure out the number of different ways to fill a 3x9 grid with number(...TRUNCATED) |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
End of preview.
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