problem string | answer string | tokenized_prompt string | responses list | rewards list | mean_reward float64 |
|---|---|---|---|---|---|
Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$ | 70 | <|im_start|>user
Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, let's see. The problem is asking for the sum of all integer bases b > 9 for which 17 base b is a divisor of 97 base b. Hmm. Alright, first, I need to recall how numbers in different bases work. So, 17 in base b would be equal to 1*b + 7, right? Similarly, 97 in base b would be 9*b + 7. So the proble... | [
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 | "<|im_start|>user\nIn $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{AB}$ so that $AD < AE <(...TRUNCATED) | ["<think>\nOkay, so I need to find the area of this heptagon AFNBCEM in triangle ABC. The problem gi(...TRUNCATED) | [
1,
1,
1,
1,
1,
1,
1,
1
] | 1 |
"The $9$ members of a baseball team went to an ice-cream parlor after their game. Each player had a (...TRUNCATED) | 16 | "<|im_start|>user\nThe $9$ members of a baseball team went to an ice-cream parlor after their game. (...TRUNCATED) | ["<think>\nOkay, let's see. There's this problem about 9 players who went to an ice cream parlor. Ea(...TRUNCATED) | [
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 | "<|im_start|>user\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers bet(...TRUNCATED) | ["<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,
1,
1,
1,
1
] | 1 |
"There are $8!= 40320$ eight-digit positive integers that use each of the digits $1, 2, 3, 4, 5, 6, (...TRUNCATED) | 279 | "<|im_start|>user\nThere are $8!= 40320$ eight-digit positive integers that use each of the digits $(...TRUNCATED) | ["<think>\nOkay, so I need to find the number of eight-digit numbers formed by the digits 1 through (...TRUNCATED) | [
1,
1,
1,
1,
1,
1,
1,
1
] | 1 |
"An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the(...TRUNCATED) | 504 | "<|im_start|>user\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides.(...TRUNCATED) | ["<think>\nOkay, so I need to find $ r^2 + s^2 $ for an isosceles trapezoid that has an inscribed ci(...TRUNCATED) | [
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 | "<|im_start|>user\nThe twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are rando(...TRUNCATED) | ["<think>\nOkay, so I need to find the probability that the last word in the alphabetical list conta(...TRUNCATED) | [
0,
1,
1,
0,
1,
0,
0,
0
] | 0.375 |
"Let $k$ be a real number such that the system \\begin{align*} &|25 + 20i - z| = 5 \\ &|z - 4 - k| =(...TRUNCATED) | 77 | "<|im_start|>user\nLet $k$ be a real number such that the system \\begin{align*} &|25 + 20i - z| = 5(...TRUNCATED) | ["<think>\nOkay, so I need to solve this problem where I have a system of two equations involving co(...TRUNCATED) | [
1,
0,
1,
1,
0,
1,
1,
1
] | 0.75 |
"The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin.(...TRUNCATED) | 62 | "<|im_start|>user\nThe parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise (...TRUNCATED) | ["<think>\nOkay, so I need to figure out the coordinates of the unique point in the fourth quadrant (...TRUNCATED) | [
1,
1,
0,
1,
0,
0,
1,
0
] | 0.5 |
"The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each(...TRUNCATED) | 81 | "<|im_start|>user\nThe $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ throug(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the number of different ways to fill a 3x9 grid with number(...TRUNCATED) | [
1,
0,
0,
0,
0,
0,
0,
1
] | 0.25 |
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 5