prompt string | ground_truth string | verifier_name string | rollout_text string | rollout_tokens list | rollout_is_correct bool | sibling_rollouts list | probe_positions list | mc_values list | num_continuations int64 |
|---|---|---|---|---|---|---|---|---|---|
<|im_start|>user
The letters of the alphabet are given numeric values based on the two conditions below.
$\bullet$ Only the numeric values of $-2,$ $-1,$ $0,$ $1$ and $2$ are used.
$\bullet$ Starting with A and going through Z, a numeric value is assigned to each letter according to the following pattern: $$
1, 2, ... | -1 | math | To find the sum of the numeric values of the letters in the word "numeric," we first need to determine the numeric values for each letter based on the given pattern.
The numeric values repeat every 8 letters, with the pattern 1, 2, 1, 0, -1, -2, -1, 0.
The word "numeric" consists of the letters N, U, M, E, R, I, C. L... | [
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279,
2629,
315,
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2750,
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1... | true | [
{
"is_correct": false,
"text": "핱\n엮\n햼\n�\n핯\n린\n윁\n졢\nחסר\n��gen닥\n해다\n혈입\n혼ющ\n힡\n슷그노타엉\nHomework\nפורסם על ידי 복스팟 - 11:15\nThe word \"numeric\" can be broken down into individual letters and their corresponding numeric values based on the given pattern.\n\nn --> 2\nu --> 1\nm --> 0\ne --> -1\nr --> -2\... | [] | [] | 32 |
<|im_start|>user
The letters of the alphabet are given numeric values based on the two conditions below.
$\bullet$ Only the numeric values of $-2,$ $-1,$ $0,$ $1$ and $2$ are used.
$\bullet$ Starting with A and going through Z, a numeric value is assigned to each letter according to the following pattern: $$
1, 2, ... | -1 | math | 핱
엮
햼
�
핯
린
윁
졢
חסר
��gen닥
해다
혈입
혼ющ
힡
슷그노타엉
Homework
פורסם על ידי 복스팟 - 11:15
The word "numeric" can be broken down into individual letters and their corresponding numeric values based on the given pattern.
n --> 2
u --> 1
m --> 0
e --> -1
r --> -2
i --> -1
c --> 1
Adding these values together:
2 + 1 + 0 + (-1) + (... | [
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1440... | false | [
{
"is_correct": true,
"text": "To find the sum of the numeric values of the letters in the word \"numeric,\" we first need to determine the numeric values for each letter based on the given pattern.\n\nThe numeric values repeat every 8 letters, with the pattern 1, 2, 1, 0, -1, -2, -1, 0.\n\nThe word \"numer... | [] | [] | 32 |
<|im_start|>user
A cube with $3$-inch edges is made using $27$ cubes with $1$-inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white? The answer should be in the form \f... | 14 | math | Assistant: To solve the problem, let's break it down step by step:
1. **Cube Construction**: We have a large cube made up of 27 smaller cubes (3x3x3). This large cube has a surface area of \(6 \times 3^2 = 54\) square inches.
2. **Corner Black Cubes**: The eight black cubes are placed at the corners of the larger cube... | [
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... | true | [
{
"is_correct": false,
"text": "We are given a larger cube consisting of $27$ smaller cubes (each smaller cube has $1$-inch edges), with a total edge length of $3$ inches for the larger cube. These cubed are grouped into $27$ smaller cubes:\n\n- $19$ of these smaller cubes are white.\n- $8$ of these smaller... | [] | [] | 32 |
"<|im_start|>user\nA cube with $3$-inch edges is made using $27$ cubes with $1$-inch edges. Nineteen(...TRUNCATED) | 14 | math | "We are given a larger cube consisting of $27$ smaller cubes (each smaller cube has $1$-inch edges),(...TRUNCATED) | [1654,525,2661,264,8131,23739,30606,315,400,17,22,3,9155,54104,320,9547,9155,23739,702,400,16,3,12,3(...TRUNCATED) | false | [{"is_correct":true,"text":"Assistant: To solve the problem, let's break it down step by step:\n\n1.(...TRUNCATED) | [] | [] | 32 |
"<|im_start|>user\nLet $N_{10}$ be the answer to problem 10.\n\nCompute the number of ordered pairs (...TRUNCATED) | 0 | math | "To solve the equation \\( m^2 + n^2 = mn + N_{10} \\), we need to first determine the value of \\( (...TRUNCATED) | [1249,11625,279,23606,17767,296,61,17,488,308,61,17,284,27938,488,451,15159,16,15,92,1124,701,582,11(...TRUNCATED) | true | [{"is_correct":false,"text":"Ymdqub colors.\nWe'll furnish you containing shielding other sensations(...TRUNCATED) | [
1000
] | [
0.78125
] | 32 |
"<|im_start|>user\nLet $N_{10}$ be the answer to problem 10.\n\nCompute the number of ordered pairs (...TRUNCATED) | 0 | math | "Ymdqub colors.\nWe'll furnish you containing shielding other sensations ofstructionsThat is little (...TRUNCATED) | [89224,80,392,7987,624,1654,3278,51159,498,8482,96676,1008,71497,315,19657,4792,374,2632,65258,61164(...TRUNCATED) | false | [{"is_correct":true,"text":"To solve the equation \\( m^2 + n^2 = mn + N_{10} \\), we need to first (...TRUNCATED) | [
1000
] | [
0.03125
] | 32 |
"<|im_start|>user\nThe members of a band are arranged in a rectangular formation. When they are arra(...TRUNCATED) | 150 | math | "To find the number of members in the band, let's denote the total number of members as \\( N \\). A(...TRUNCATED) | [1249,1477,279,1372,315,3613,304,279,7055,11,1077,594,78064,279,2790,1372,315,3613,438,17767,451,112(...TRUNCATED) | true | [{"is_correct":false,"text":"We are told that in the rectangular formation, the members can be repre(...TRUNCATED) | [] | [] | 32 |
"<|im_start|>user\nThe members of a band are arranged in a rectangular formation. When they are arra(...TRUNCATED) | 150 | math | "We are told that in the rectangular formation, the members can be represented by \\((8n-2)\\). Solv(...TRUNCATED) | [1654,525,3229,429,304,279,51424,18003,11,279,3613,646,387,15251,553,1124,1188,23,77,12,17,10699,568(...TRUNCATED) | false | [{"is_correct":false,"text":"Let $n$ be the number of members in the band. When they are arranged in(...TRUNCATED) | [] | [] | 32 |
"<|im_start|>user\nFind the number of ordered triples of integers \\((a, b, c)\\), with \\(a \\ge 2\(...TRUNCATED) | 2 | math | "We start with the given equations:\n\\[\n\\log_a b = c^{2005}\n\\]\nand\n\\[\na + b + c = 2005.\n\\(...TRUNCATED) | [1654,1191,448,279,2661,37906,510,59,9640,59,839,4306,293,284,272,47822,17,15,15,20,532,59,921,437,1(...TRUNCATED) | true | [{"is_correct":false,"text":"We need to find the integer triples \\((a, b, c)\\) that satisfy both \(...TRUNCATED) | [] | [] | 32 |
"<|im_start|>user\nFind the number of ordered triples of integers \\((a, b, c)\\), with \\(a \\ge 2\(...TRUNCATED) | 2 | math | "We need to find the integer triples \\((a, b, c)\\) that satisfy both \\(\\log_a b = c^{2005}\\) an(...TRUNCATED) | [1654,1184,311,1477,279,7546,88561,1124,1188,64,11,293,11,272,10699,8,429,26553,2176,1124,11520,839,(...TRUNCATED) | false | [{"is_correct":true,"text":"We start with the given equations:\n\\[\n\\log_a b = c^{2005}\n\\]\nand\(...TRUNCATED) | [] | [] | 32 |
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