problem string | answer string | responses sequence | rewards sequence | mean_reward float64 | og_problem string | hint string | thoughts sequence | solutions sequence | remaining_responses int64 | is_adherence sequence | strategy_identification sequence |
|---|---|---|---|---|---|---|---|---|---|---|---|
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 70 | ["<think>\nOkay, let's tackle this problem step by step. The question is to find the sum of all inte(...TRUNCATED) | [
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] | 1 | Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$ | "<notes>\n <note>\n <description>Convert a numeral from base b to its decimal (integer) equivale(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. The question is to find the sum of all inte(...TRUNCATED) | ["To solve the problem of finding the sum of all integer bases $ b > 9 $ for which $ 17_b $ divides (...TRUNCATED) | 16 | [
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"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 588 | ["<think>\nOkay, let's try to solve this problem step by step. First, I need to understand the given(...TRUNCATED) | [
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] | 0.8125 | "In $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{AB}$ so that $AD < AE < AB$, while points(...TRUNCATED) | "<notes>\n <note>\n <description>When two points are reflections across a third point on a line,(...TRUNCATED) | ["<think>\nOkay, let's try to solve this problem step by step. First, I need to understand the given(...TRUNCATED) | ["To solve the problem, we are given a triangle $ \\triangle ABC $ with points $ D $, $ E $ on $ AB (...TRUNCATED) | 16 | [
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] | [["1. Assigning coordinates to points in a geometric figure.\n2. Reflection of points to find new co(...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 16 | ["<think>\nOkay, let's tackle this problem step by step. \n\nFirst, the problem states that there ar(...TRUNCATED) | [
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] | 0.875 | "The $9$ members of a baseball team went to an ice-cream parlor after their game. Each player had a (...TRUNCATED) | "<notes>\n <note>\n <description>When distributing N identical items into K labeled boxes with l(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. \n\nFirst, the problem states that there ar(...TRUNCATED) | ["To solve the problem, we need to determine the number of assignments of ice cream flavors to 9 pla(...TRUNCATED) | 16 | [
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] | [["1. Definition of variables\n2. System of equations setup\n3. Inequality constraints\n4. Enumerati(...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 117 | ["<think>\nOkay, let's try to solve this problem step by step. The question is asking for the number(...TRUNCATED) | [
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] | 0.6875 | "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $1(...TRUNCATED) | "<notes>\n <note>\n <description>Use the discriminant test to determine whether a binary quadrat(...TRUNCATED) | ["<think>\nOkay, let's try to solve this problem step by step. The question is asking for the number(...TRUNCATED) | ["To determine the number of ordered pairs $(x, y)$ such that both $x$ and $y$ are integers in the r(...TRUNCATED) | 16 | [
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] | [["1. Factoring the quadratic equation\n2. Identifying linear equations from factored form\n3. Setti(...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 279 | ["<think>\nOkay, let's tackle this problem step by step. The question is asking for the difference b(...TRUNCATED) | [
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] | 0.5 | "There are $8!= 40320$ eight-digit positive integers that use each of the digits $1, 2, 3, 4, 5, 6, (...TRUNCATED) | "<notes>\n <note>\n <description>Use the divisibility rule for 11: a number is divisible by 11 i(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. The question is asking for the difference b(...TRUNCATED) | ["To solve the problem, we need to determine the number of **eight-digit positive integers** that us(...TRUNCATED) | 16 | [
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] | [["1. **Divisibility Rules**: Understanding and applying the rules for divisibility by 2 and 11.\n2.(...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 504 | ["<think>\nOkay, let's tackle this problem step by step. So, we have an isosceles trapezoid with an (...TRUNCATED) | [
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] | 1 | "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the(...TRUNCATED) | "<notes>\n <note>\n <description>In any tangential quadrilateral (one that has an inscribed circ(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. So, we have an isosceles trapezoid with an (...TRUNCATED) | ["To solve the problem, we analyze the given isosceles trapezoid with an inscribed circle. The radiu(...TRUNCATED) | 16 | [
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] | [["1. Area formula for a tangential trapezoid.\n2. Relationship between height and inradius.\n3. Pyt(...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 821 | ["<think>\nOkay, let's try to solve this probability problem. So, we have twelve letters: A, B, C, D(...TRUNCATED) | [
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] | 0 | "The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are randomly grouped into s(...TRUNCATED) | "<notes>\n <note>\n <description>When elements are paired uniformly without additional structure(...TRUNCATED) | ["<think>\nOkay, let's try to solve this probability problem. So, we have twelve letters: A, B, C, D(...TRUNCATED) | ["To solve the problem, we are given 12 letters $ A, B, C, D, E, F, G, H, I, J, K, L $, which are ra(...TRUNCATED) | 15 | [
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] | [["1. Total pairings calculation using double factorial.\n2. Sorting pairs alphabetically to form wo(...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 77 | ["<think>\nOkay, let's tackle this problem step by step. So, we need to find all real numbers k such(...TRUNCATED) | [
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] | 0.125 | "Let $k$ be a real number such that the system \\begin{align*} &|25 + 20i - z| = 5 \\ &|z - 4 - k| =(...TRUNCATED) | "<notes>\n <note>\n <description>Interpret complex‐number conditions using the real plane: any(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. So, we need to find all real numbers k such(...TRUNCATED) | ["To solve the problem, we analyze the system of equations:\n\n$$\n\\begin{cases}\n|25 + 20i - z| = (...TRUNCATED) | 16 | [
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] | [["1. Geometric interpretation of loci (circle and perpendicular bisector)\n2. Derivation of line eq(...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 62 | ["<think>\nOkay, let's tackle this problem step by step. So, we have the parabola y = x² - 4, which(...TRUNCATED) | [
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] | 0 | "The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin.(...TRUNCATED) | "<notes>\n <note>\n <description>Rotation of points in the plane by an angle θ about the origin(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. So, we have the parabola y = x² - 4, which(...TRUNCATED) | ["To solve the given problem, we are asked to find the **y-coordinate** of the **unique point** in t(...TRUNCATED) | 16 | [
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] | [["1. **Geometric Relations**: Understanding the rotation of the parabola and its intersection with (...TRUNCATED) |
"# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked wit(...TRUNCATED) | 81 | ["<think>\nOkay, let's try to tackle this problem step by step. So, the question is about counting t(...TRUNCATED) | [
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] | 0 | "The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each(...TRUNCATED) | "<notes>\n <note>\n <description>When a problem is symmetric under permutations of labels, fix o(...TRUNCATED) | ["<think>\nOkay, let's try to tackle this problem step by step. So, the question is about counting t(...TRUNCATED) | ["To solve the problem, we analyze the constraints and structure of the $3 \\times 9$ grid filled wi(...TRUNCATED) | 16 | [
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