Datasets:
ground_truth listlengths 1 1 | dataset listlengths 1 1 | custom_id stringlengths 32 106 | original_dataset stringclasses 15
values | outputs listlengths 0 8 ⌀ | total_rollouts int64 0 8 ⌀ | total_correct_rollouts float64 0 5 ⌀ | passrate float64 0 0.63 ⌀ | dataset_source stringclasses 4
values | input_ids_prompt listlengths 76 2.05k | input_ids listlengths 75 4.62k | attention_mask listlengths 75 4.62k | labels listlengths 75 4.62k | prompt stringlengths 8 10.6k | id null | key null | constraint_type null | constraint null | conversation_hash null | model null | predicted_label null |
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[
"99"
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"math"
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"The problem involves a 2003x2003 grid where a visitor starts at the northwest corner (A), visits other rooms exactly 100 times except for the southeast corner (B), and returns to A for the first time to leave. We need to determine the number of visits to room B.\n\nKey steps and reasoning:\n\n1. **Grid and Move An... | 7 | 4 | 0.571429 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: (Hungary 2004). A palace has the shape of a square divided into $2003 \times 2003$ rooms, like the squares of a large chessboard. There is a door between two rooms if and only if they share a wall. The main door allows, coming from outside the palace, to enter the palace through the room located at the northwest ... | null | null | null | null | null | null | null |
[
"5"
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"math"
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"To determine the largest \\( k \\) such that Kostya and Andrey underlined \\( k \\) consecutive digits in the concatenated sequence of all three-digit numbers from 100 to 999 and the underlined numbers are equal, we need to find the longest repeating substring in this sequence.\n\n1. **Understanding the Sequence**... | 7 | 1 | 0.142857 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: 5. All three-digit numbers from 100 to 999 are written in a row without spaces. Kostya underlined \( k \) consecutive digits in this sequence, and Andrey underlined other \( k \) consecutive digits in this sequence. It turned out that the \( k \)-digit numbers underlined by the boys are equal. For what largest \(... | null | null | null | null | null | null | null |
[
"6"
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"math"
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"To determine the minimum number of teams \\( n \\) in a round-robin tournament where the sole winner scores less than 50% of the maximum possible points, we analyze the problem step-by-step.\n\n1. **Understanding the Problem**:\n - Each team plays \\( n-1 \\) matches.\n - Maximum points for one team: \\( 3(n-1... | 8 | 4 | 0.5 | hamishivi/math_rlvr_mixture_dpo | [
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The teams held a football tournament in a round-robin format (each team played one match against every other team, with 3 points for a win, 1 point for a draw, and 0 points for a loss). It turned out that the sole winner scored less than $50 \%$ of the maximum possible points for one participant. W... | null | null | null | null | null | null | null |
[
"6"
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"math"
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"To determine the minimum number of teams in a school football championship where one team has the most points but fewer wins than any other team, we analyze the constraints and construct scenarios for different team counts.\n\n1. **Key Constraints**:\n - Each team plays every other team once.\n - Points: 2 for... | 8 | 3 | 0.375 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: 6.8 In the school football championship, each team must play a match against every other team. Each match's winning team gets 2 points, a draw gives each team 1 point, and the losing team gets 0 points. It is known that one team scored the most points (every other team scored fewer points than this team), but it ... | null | null | null | null | null | null | null |
[
"3"
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"math"
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"To determine the minimum number of unit-radius circles required to completely cover a triangle with sides 2, 3, and 4, we start by analyzing the triangle's properties and considering various covering strategies.\n\n1. **Triangle Properties**:\n - **Semi-perimeter (s)**: \\( \\frac{2 + 3 + 4}{2} = 4.5 \\)\n - *... | 8 | 0 | 0 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: 9.4. What is the minimum number of unit-radius circles required to completely cover a triangle with sides $2 ; 3 ; 4$? | null | null | null | null | null | null | null |
[
"Median"
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"math"
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"The statistical measure that remains unchanged after removing the highest and lowest scores is the **median**.\n\n**Explanation:** \nWhen calculating the median of a dataset with an even number of observations (e.g., 10 scores), it is the average of the 5th and 6th values in the sorted list. After removing the lo... | 8 | 0 | 0 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: In a singing competition, a set of sample data is obtained from the scores given by 10 judges. After removing the highest score and the lowest score, which statistical measure of the data set will definitely remain unchanged? Provide your answer as the name of the statistical measure. | null | null | null | null | null | null | null |
[
"1"
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"math"
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"The given equation is \\((x^{2006} + 1)(1 + x^2 + x^4 + \\cdots + x^{2004}) = 2006 x^{2005}\\).\n\nFirst, we recognize the sum \\(1 + x^2 + x^4 + \\cdots + x^{2004}\\) as a geometric series with ratio \\(x^2\\) and 1003 terms. This sum can be simplified using the geometric series formula:\n\\[\n1 + x^2 + x^4 + \\c... | 8 | 5 | 0.625 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: 11. The number of real solutions to the equation $\left(x^{2006}+1\right)\left(1+x^{2}+x^{4}+\cdots+\right.$ $\left.x^{2004}\right)=2006 x^{2005}$ is $\qquad$ | null | null | null | null | null | null | null |
[
"2.094"
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"math"
] | AceReason-Math_filtered-request-1-70 | hamishivi/AceReason-Math_filtered | [
"To find the perimeter of the shaded area in the middle of the square \\(ABCD\\) with side length 1 cm, we consider the quarter circles centered at each corner with radius 1 cm. The intersections of these quarter circles form a central symmetric shape.\n\n1. **Coordinates of Intersection Points**:\n - **Point \\(... | 7 | 3 | 0.428571 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: 5. (3 points) In a square $ABCD$ with a side length of 1 cm, draw quarter circles with a radius of 1 cm, centered at $A, B, C, D$, intersecting at points $E, F, G, H$, as shown in the figure. The perimeter of the shaded area in the middle is $\qquad$ cm. (Take $\pi=3.141$) | null | null | null | null | null | null | null |
[
"2^{n-1}"
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"math"
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"To solve the problem of arranging the numbers \\(1, 2, \\ldots, k\\) such that each number is strictly greater than all preceding numbers or strictly less than all preceding numbers, we need to determine the number of such valid permutations, denoted as \\(a_k\\).\n\n### Key Steps and Reasoning:\n\n1. **Base Cases... | 8 | 3 | 0.375 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: 3. Arrange $1,2, \cdots, k$ in a row so that each number is strictly greater than all the numbers preceding it, or strictly less than all the numbers preceding it. Let the number of different arrangements be $a_{k}(k=1,2, \cdots)$. Then $a_{n}=$ $\qquad$ . | null | null | null | null | null | null | null |
[
"10"
] | [
"math"
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"Petya and Vasya need to travel 4 km to the neighboring village for a football match. Walking at 4 km/h would take them 1 hour (60 minutes), making them 10 minutes late. Therefore, they have a scheduled arrival time of 50 minutes from their departure.\n\nKey steps to",
"Petya and Vasya need to travel 4 kilometers... | 8 | 2 | 0.25 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: Petya and Vasya calculated that if they walk at a speed of 4 km per hour to the neighboring village, which is 4 kilometers away, they will be 10 minutes late for the football match held there for the district championship. How should they proceed to arrive at the match on time and achieve the greatest time gain, ... | null | null | null | null | null | null | null |
[
"\\sqrt{2}"
] | [
"math"
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"Given a unit cube \\(ABCDA_1B_1C_1D_1\\) with two ants starting at vertex \\(A\\), the white ant's initial route is \\(AA_1 \\rightarrow A_1D_1\\) and the black ant's initial route is \\(AB \\rightarrow BB_1\\). Both ants follow the rule that the \\((n+2)\\)-th segment must be skew to the \\(n\\)-th segment. We ne... | 8 | 5 | 0.625 | hamishivi/math_rlvr_mixture_dpo | [
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159... | user: 8. Given that $A B C D-A_{1} B_{1} C_{1} D_{1}$ is a unit cube, two ants, one black and one white, start from point $A$ and crawl along the edges. Each time they complete an edge, it is called “completing a segment”. The white ant’s crawling route is $A A_{1} \rightarrow A_{1} D_{1} \rightarrow \cdots$, and the b... | null | null | null | null | null | null | null |
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