messages listlengths 1 1 | ground_truth stringlengths 1 83 | dataset stringclasses 1 value | source stringclasses 3 values | olmo_completions listlengths 7 72 | frontier_id stringlengths 64 64 | verifier_scores listlengths 7 72 | avg_score float64 0 0.5 |
|---|---|---|---|---|---|---|---|
[{"content":"A 8-gon is colored so that in clockwise order, the vertices are colored as follows: ver(...TRUNCATED) | 8 | math | Omega_Filtered_LC | ["OK, that which means that we have at most 8,200 minus 2,000 kinds of red Para-winkle goldfish avai(...TRUNCATED) | 5ebda4a2bc628f9ff9fa86b5cc83d1ff597f69670fb2373e67be67044a8167ad | [
0,
0,
0,
0,
0,
0,
1,
0,
0,
0,
0,
0,
1,
0,
0,
0
] | 0.125 |
[{"content":"Find the largest real $ T$ such that for each non-negative real numbers $ a,b,c,d,e$ su(...TRUNCATED) | \frac{\sqrt{30}}{30 + 12\sqrt{6}} | math | MathSub_Filtered_LC | ["Identify the constraints and variables in the problem. The constraints are that \\( a, b, c, d, \\(...TRUNCATED) | 1e0f84080660507822d90019688a592f8ed88008646449fbf9335cd1404a197f | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
[{"content":"Let $S$ be the set \\{1,2, \\ldots, 2012\\}. A perfectutation is a bijective function $(...TRUNCATED) | 2 | math | MathSub_Filtered_LC | ["This problem is difficult and requires a deep understanding of bijective functions and permutation(...TRUNCATED) | c15d20c19ac863deb0bdc324d85f7f11ab23d7212ec2efc43450397392676def | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
[{"content":"Problem 7.1. (15 points) Find the smallest ten-digit natural number, all digits of whic(...TRUNCATED) | 9024675318 | math | MathSub_Filtered_LC | ["Understood. To solve this problem, we need to find a ten-digit number with unique digits that sati(...TRUNCATED) | 718d5199a5fb7665a7e605414228f2b04416aac664601642329383a838657b0d | [
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
[{"content":"Determine the smallest positive integer $m$ with the property that $m^3-3m^2+2m$ is div(...TRUNCATED) | 1660 | math | MathSub_Filtered_LC | ["Using the Chinese Remainder Theorem, we can solve the congruences separately.\nFor $79$:\nWe can r(...TRUNCATED) | d09425200e9c690b77f7d20fd78bac01da8668af20a478c2610629f62b33aa93 | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
0,
0
] | 0.0625 |
[{"content":"Four small spheres each with radius $6$ are each internally tangent to a large sphere w(...TRUNCATED) | 56 | math | MathSub_Filtered_LC | ["First, let's understand the diagram given. There's a large sphere with radius 17, and 4 smaller sp(...TRUNCATED) | 1949ebe6831b9f12a938ec9231cf381dbf80f1e4bb79171c2d1f5bef69b579bf | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
[{"content":"A function $f$ is defined for all real numbers and satisfies $f(3+x)=f(3-x)$ and $f(8+x(...TRUNCATED) | 601 | math | MathSub_Filtered_LC | ["First, let's think about the given properties of the function f(x). \n\n1. Symmetry about x=3: f(3(...TRUNCATED) | 8aa40422bea002e17485b18377f9ac7b006439a5a13549fd8e775f5d8ea39f27 | [
1,
0,
0,
0,
0,
0,
0,
0
] | 0.125 |
[{"content":"A farmer's rectangular field is partitioned into a $2$ by $2$ grid of $4$ rectangular s(...TRUNCATED) | 84 | math | MathSub_Filtered_LC | ["Okay, let's tackle this problem step by step. We have a 2x2 grid of four sections, each to be plan(...TRUNCATED) | 45fb2f78151ea2d013eba757da865dd84086221c443ec8af1600a94ca9b46c99 | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
[{"content":"Suppose that we are given 40 points equally spaced around the perimeter of a square, so(...TRUNCATED) | 841 | math | MathSub_Filtered_LC | ["Let's break this down. Each side of the square has 10 points, and since there are four sides, we h(...TRUNCATED) | 80a7415f3d3c2d661bc39ecc31a35c8d52c89eeb306117bc8e13150d823f1abc | [
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
[{"content":"Given real numbers \\( x \\) and \\( y \\) satisfying\n\\[ 2^x + 3^y = 4^x + 9^y, \\]\n(...TRUNCATED) | (1, 2] | math | Orz_Filtered_LC | ["Based on the equation \\( 2^x + 3^y = 4^x + 9^y \\), it appears that we can rewrite \\( 4^x \\) as(...TRUNCATED) | 48aed7462bfa1f9c09fa2904dbb60673493d962d78e6af6db8a436a7041230ef | [
0,
0,
0,
0,
0,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0.0625 |
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 11