domyn/Domyn-Edge-Teacher-Math
Text Generation • 4B • Updated • 546
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Text Generation
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Text
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parquet
Languages:
English
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10K - 100K
License:
messages listlengths 2 2 | tools stringclasses 0
values | task stringclasses 1
value | source stringclasses 2
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values | metadata stringlengths 202 406 | reward stringlengths 68 11.6k | token_length int64 37 3.33k | uuid stringlengths 36 36 |
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"content": "During the softball season, Judy had $35$ hits. Among her hits were $1$ home run, $1$ tr... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "80\\%", "solution": "1. **Identify the total number of hits**: Judy had a total of 35 hits during the season.\n\n2. **Determine the number of hits that were not singles**: \n - Home runs: 1\n - Triples: 1\n - Doubles: 5\n - Total non-single hits = 1 (home run) + 1 (triple) + 5 (doub... | 83 | c2b369b9-093e-5969-a298-47dae2f3efba |
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"content": "Quadrilateral $ABCD$ satisfies $\\angle ABC = \\angle ACD = 90^{\\circ}, AC=20,$ and $CD=... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "360", "solution": "1. **Assign Variables and Use Pythagorean Theorem in $\\triangle ABC$:**\n Let $AB = x$ and $BC = y$. Since $\\angle ABC = 90^\\circ$, by the Pythagorean theorem, we have:\n \\[\n x^2 + y^2 = AC^2 = 20^2 = 400.\n \\]\n\n2. **Calculate Area of $\\triangle ACD$:**\n... | 105 | 8daa180a-91f7-59c3-8c04-cca5edd5138d |
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"content": "Five positive consecutive integers starting with $a$ have average $b$. What is the averag... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "$a+4$", "solution": "1. **Define the sequence and calculate the average $b$:** \n The five consecutive integers starting with $a$ are $a, a+1, a+2, a+3, a+4$. The average of these integers, $b$, is calculated as follows:\n \\[\n b = \\frac{a + (a+1) + (a+2) + (a+3) + (a+4)}{5} = \\fr... | 62 | 65f06c47-4325-5df9-91de-7cfc6aae5daf |
[
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"content": "If $a$ and $b$ are digits for which\n$\\begin{array}{ccc}& 2 & a\\ \\times & b & 3\\ \\hl... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "7", "solution": "1. **Identify the multiplication setup**: The multiplication setup is given as:\n \\[\n \\begin{array}{ccc}\n & 2 & a\\\\ \n \\times & b & 3\\\\ \n \\hline \n & 6 & 9\\\\ \n 9 & 2\\\\ \n \\hline \n 9 & 8 & 9\n \\end{array}\n \\]\n This represents the... | 103 | ab82b110-b4ce-5300-bf38-7636239f7c0b |
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"content": "Four circles, no two of which are congruent, have centers at $A$, $B$, $C$, and $D$, and ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "192", "solution": "1. **Understanding the Problem**: We are given four circles with centers at $A$, $B$, $C$, and $D$. Points $P$ and $Q$ lie on all four circles. The radius of circle $A$ is $\\frac{5}{8}$ times the radius of circle $B$, and similarly for circles $C$ and $D$. The distances ... | 168 | ab6e887a-ad7e-5838-b824-aa5b794f625a |
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"content": "For all non-zero numbers $x$ and $y$ such that $x = 1/y$, $\\left(x-\\frac{1}{x}\\right)\... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "x^2-y^2", "solution": "1. **Substitute $y$ in terms of $x$:** Given $x = \\frac{1}{y}$, we can rewrite $y$ as $y = \\frac{1}{x}$. \n\n2. **Substitute and simplify the expression:** We start by substituting $y = \\frac{1}{x}$ into the expression $\\left(x-\\frac{1}{x}\\right)\\left(y+\\frac{... | 76 | a40118ca-fc9e-5fcc-859a-017d1d31e27d |
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"content": "The numbers $-2, 4, 6, 9$ and $12$ are rearranged according to these rules:\n\n 1.... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "6.5", "solution": "1. **Identify the largest and smallest numbers**: The largest number in the set $\\{-2, 4, 6, 9, 12\\}$ is $12$, and the smallest is $-2$.\n\n2. **Apply rule 1**: The largest number, $12$, cannot be first but must be in one of the first three places. Thus, $12$ can be in ... | 126 | 9e938364-dab1-5f52-af76-2fc1b3ee416d |
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"content": "Quadrilateral $ABCD$ has $AB = BC = CD$, $m\\angle ABC = 70^\\circ$ and $m\\angle BCD = 1... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "85", "solution": "1. **Assign the unknown and draw necessary diagonals**: Let $\\angle BAD = x$. Draw diagonals $BD$ and $AC$. Let $I$ be the intersection of diagonals $BD$ and $AC$.\n\n2. **Analyze the isosceles triangles**: Since $AB = BC = CD$, triangles $\\triangle ABC$ and $\\triangle ... | 83 | e1a5b100-d3a5-587d-9537-3b5618d36572 |
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"content": "In $\\triangle ABC$ with right angle at $C$, altitude $CH$ and median $CM$ trisect the r... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "4K", "solution": "1. **Draw the triangle and identify key components**: In $\\triangle ABC$, where $\\angle C = 90^\\circ$, draw altitude $CH$ from $C$ to hypotenuse $AB$ and median $CM$ from $C$ to the midpoint $M$ of $AB$. Since $CM$ trisects the right angle, $\\angle MCB = 30^\\circ$ and... | 82 | e96bfc6c-7a47-51c9-ade1-f38c1fe0a622 |
[
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"role": "system",
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"content": "Sides $\\overline{AB}$ and $\\overline{AC}$ of equilateral triangle $ABC$ are tangent to ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{4}{3}-\\frac{4\\sqrt{3}\\pi}{27}", "solution": "1. **Identify the Geometry and Relationships**:\n - Let the radius of the circle be $r$, and its center be $O$.\n - Since $\\overline{AB}$ and $\\overline{AC}$ are tangent to the circle at points $B$ and $C$, respectively, $\\angle ... | 84 | 620242c8-29ac-5490-9b49-4de79d91ab4d |
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"content": "Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roge... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "23\\%", "solution": "1. **Define Variables:**\n Let $m$ represent the cost of the movie ticket and $s$ represent the cost of the soda.\n\n2. **Set Up Equations:**\n According to the problem, we have:\n \\[ m = 0.20(A - s) \\]\n \\[ s = 0.05(A - m) \\]\n\n3. **Convert to Fractional F... | 135 | 3f4dd73b-2f88-5eb9-ae37-7858d5264b34 |
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"content": "A closed box with a square base is to be wrapped with a square sheet of wrapping paper. T... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "2(w+h)^2", "solution": "1. **Understanding the Problem Setup**: We have a square sheet of wrapping paper and a box with a square base of side $w$ and height $h$. The box is placed such that its base vertices lie on the midlines of the wrapping paper. The wrapping paper is folded up to meet ... | 471 | 1d9b3fed-5c18-5dc2-8042-160fa719a730 |
[
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"content": "The figure may be folded along the lines shown to form a number cube. Three number faces ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "14", "solution": "To solve this problem, we need to understand how a cube is formed and how the numbers on the faces are arranged. In a standard die, opposite faces sum up to 7. This means:\n- If one face shows 1, the opposite face shows 6.\n- If one face shows 2, the opposite face shows 5.... | 74 | 54a9490c-74bd-59c6-856c-85d3a9e5c41a |
[
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"content": "Six ants simultaneously stand on the six vertices of a regular octahedron, with each ant ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{5}{256}", "solution": "\nWe approach this problem by counting the number of ways ants can do their desired migration, and then multiply this number by the probability that each case occurs.\n\nLet the octahedron be labeled as $ABCDEF$, with points $B, C, D, E$ being coplanar. Then th... | 94 | 33ea7171-b89b-560d-9dc1-c0627f117604 |
[
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"content": "If $f(x)=3x+2$ for all real $x$, then the statement:\n\"$|f(x)+4|<a$ whenever $|x+2|<b$ a... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "$b \\le a/3$", "solution": "1. **Substitute $f(x)$ into the inequality**: Given $f(x) = 3x + 2$, we substitute this into the inequality $|f(x) + 4| < a$:\n \\[\n |3x + 2 + 4| = |3x + 6|.\n \\]\n Simplifying further, we have:\n \\[\n |3x + 6| = |3(x + 2)| = 3|x + 2|.\n \\]\n\n2... | 87 | f3a2ebb4-99ef-5327-bad8-03f7191ebc92 |
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"content": "A carton contains milk that is $2\\%$ fat, an amount that is $40\\%$ less fat than the am... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{10}{3}", "solution": "1. **Understanding the Problem:**\n The problem states that a carton of milk contains 2% fat, which is 40% less than the fat content in a carton of whole milk. We need to find the percentage of fat in the whole milk.\n\n2. **Setting Up the Equation:**\n Let ... | 79 | 977eeab7-8707-5819-bfc7-96bf7c60fd7d |
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"content": "A long piece of paper $5$ cm wide is made into a roll for cash registers by wrapping it $... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "36\\pi", "solution": "1. **Understanding the Problem:**\n The paper is wrapped around a cardboard tube, forming concentric circles. Each wrap increases the diameter of the roll by the thickness of the paper, which is $5$ cm. The total number of wraps is $600$, and the final diameter of th... | 122 | b4daf454-d484-59aa-a6a3-f641e48d84ac |
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"content": "For each positive integer $n$, let \n\n$a_n = \\frac{(n+9)!}{(n-1)!}$.\nLet $k$ denote th... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "9", "solution": "1. **Expression Simplification**:\n Given $a_n = \\frac{(n+9)!}{(n-1)!}$, we can simplify this as:\n \\[\n a_n = n(n+1)(n+2)\\cdots(n+9)\n \\]\n This is the product of 10 consecutive integers starting from $n$.\n\n2. **Factorization**:\n We can express $a_n$ in ... | 93 | 6a7474ce-55d7-57ba-9db4-ce57c545550b |
[
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"content": "Let $S$ be the set of lattice points in the coordinate plane, both of whose coordinates a... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "85", "solution": "1. **Understanding the Problem:**\n The problem asks us to find the possible values of the slope $m$ of a line such that exactly $300$ lattice points from the set $S$ (where $S$ consists of points $(x,y)$ with $1 \\leq x, y \\leq 30$) lie on or below the line $y = mx$. T... | 124 | 418528be-8b49-570d-86a7-a235119ce265 |
[
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"content": "At Euclid High School, the number of students taking the AMC 10 was $60$ in 2002, $66$ in... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "2002 and 2003", "solution": "To find the largest percentage increase in the number of students taking the AMC 10 between consecutive years, we calculate the percentage increase for each interval:\n\n1. **From 2002 to 2003:**\n \\[\n \\frac{66 - 60}{60} \\times 100\\% = \\frac{6}{60} \\t... | 128 | 2dd1c5fc-2736-5cfb-bac6-dc38c828832f |
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"content": "Four identical squares and one rectangle are placed together to form one large square as ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "3", "solution": "1. **Identify the dimensions of the small squares and the large square**: Let the side length of each small square be $x$. Since there are four small squares placed side by side along one side of the large square, the side length of the large square is $4x$.\n\n2. **Analyze... | 199 | ab1542fa-8573-505a-9c5f-00b52b8926d9 |
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"content": "In a small pond there are eleven lily pads in a row labeled 0 through 10. A frog is sitti... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{63}{146}", "solution": "Define \\( P(N) \\) as the probability that the frog survives starting from pad \\( N \\). We need to find \\( P(1) \\), the probability that the frog escapes starting from pad 1.\n\nThe recursive relationship given in the problem is:\n\\[ P(N) = \\frac{N}{10}... | 178 | dc883d88-732c-522d-b7ce-6ded7914e9be |
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"content": "The numbers $1,2,\\dots,9$ are randomly placed into the $9$ squares of a $3 \\times 3$ gr... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{1}{14}", "solution": "\nTo solve this problem, we need to ensure that the sum of the numbers in each row and each column is odd. We can achieve this by having either three odd numbers or one odd and two even numbers in each row and column. Let's analyze the possible configurations an... | 96 | 8f6f92b3-c888-54c5-800c-af5e040ebd8d |
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"content": "Let $n$ be a positive integer greater than 4 such that the decimal representation of $n!$... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "8", "solution": "To solve this problem, we need to find the number of trailing zeros in $n!$ and $(2n)!$ and set up the condition that the number of zeros in $(2n)!$ is exactly three times the number of zeros in $n!$. The number of trailing zeros in a factorial can be calculated using the f... | 106 | de5bbc86-1153-5c0c-8e8f-80a5a912271c |
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"role": "user",
"content": "Inside a right circular cone with base radius $5$ and height $12$ are three congruent sph... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{90-40\\sqrt{3}}{11}", "solution": "1. **Identify the Geometry of the Problem:**\n The problem involves three congruent spheres inside a right circular cone, each sphere tangent to the others and to the base and side of the cone. The cone has a base radius of $5$ and a height of $12... | 85 | a3296124-a22f-5305-80b1-53694e62b30c |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Square $EFGH$ is inside the square $ABCD$ so that each side of $EFGH$ can be extended to ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "36", "solution": "1. **Understanding the Problem Setup:**\n - We have two squares, $ABCD$ and $EFGH$, where $EFGH$ is inside $ABCD$.\n - Each side of $EFGH$ can be extended to pass through a vertex of $ABCD$.\n - The side length of $ABCD$ is given as $\\sqrt{50}$.\n - The distance f... | 103 | 437dc599-330c-5320-9d5b-dc310a35fd7b |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Points $A, B$ and $C$ on a circle of radius $r$ are situated so that $AB=AC, AB>r$, and t... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{1}{2}\\csc{\\frac{1}{4}}", "solution": "1. **Identify the central angle corresponding to arc $BC$**: Given that the length of minor arc $BC$ is $r$, and knowing that the arc length of a circle is given by $r\\theta$ where $\\theta$ is the central angle in radians, we have:\n \\[\n ... | 87 | 7815b4dc-d39b-503a-a154-9c64df070442 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "A number of linked rings, each $1$ cm thick, are hanging on a peg. The top ring has an ou... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "173", "solution": "1. **Identify the sequence of inside diameters**: The outside diameter of the top ring is $20$ cm, and each subsequent ring has an outside diameter $1$ cm less than the ring above it. Since each ring is $1$ cm thick, the inside diameter of each ring is $2$ cm less than it... | 123 | 45e86ad8-bfe5-5785-8757-cb0a84d13eb1 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "How many squares whose sides are parallel to the axes and whose vertices have coordinates... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "50", "solution": "1. **Understanding the Problem:**\n We need to find the number of squares with integer coordinates for vertices, sides parallel to the axes, and lying entirely within the region bounded by:\n - $y = \\pi x$\n - $y = -0.1$\n - $x = 5.1$\n\n2. **Visualizing the Regio... | 83 | 2c4e0cda-a7d5-5fbf-a46f-9f93715e9f2c |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Suppose $a$, $b$ and $c$ are positive integers with $a+b+c=2006$, and $a!b!c!=m\\cdot 10^... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "492", "solution": "1. **Understanding the Problem**: We need to find the smallest possible value of $n$ in the expression $a!b!c! = m \\cdot 10^n$, where $a+b+c = 2006$ and $m$ is not divisible by $10$. This means we need to minimize the number of factors of $10$ in $a!b!c!$, which is equiv... | 106 | 206f7239-e698-5983-9d6f-fb4b4bddb361 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Liliane has $50\\%$ more soda than Jacqueline, and Alice has $25\\%$ more soda than Jacqu... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "$20\\%$", "solution": "Let's denote the amount of soda Jacqueline has as $J$. According to the problem, Liliane has $50\\%$ more soda than Jacqueline, and Alice has $25\\%$ more soda than Jacqueline. We can express the amounts of soda Liliane and Alice have in terms of $J$.\n\n1. **Calculat... | 76 | 218624f5-1792-5fbf-be5e-a8820baf9eca |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "The number $5^{867}$ is between $2^{2013}$ and $2^{2014}$. How many pairs of integers $(... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "279", "solution": "To solve this problem, we need to understand the relationship between the powers of $5$ and $2$ and how they are distributed between $5^n$ and $5^{n+1}$.\n\n1. **Understanding the relationship between $5^n$ and $2^m$:**\n We know that $5^{867}$ is between $2^{2013}$ and... | 111 | ba823412-35cf-5417-8ef4-38d7f177af99 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "What is the correct ordering of the three numbers $\\frac{5}{19}$, $\\frac{7}{21}$, and $... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{5}{19} < \\frac{7}{21} < \\frac{9}{23}", "solution": "To find the correct ordering of the fractions $\\frac{5}{19}$, $\\frac{7}{21}$, and $\\frac{9}{23}$, we can compare each pair of fractions.\n\n1. **Simplify $\\frac{7}{21}$:**\n \\[\\frac{7}{21} = \\frac{1}{3}\\]\n\n2. **Compare... | 72 | f2d3a423-dbf6-5e59-8f21-897bf336b548 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "A triangle with vertices $(6, 5)$, $(8, -3)$, and $(9, 1)$ is reflected about the line $x... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{32}{3}", "solution": "1. **Identify the vertices and their reflections**: \n - Let $A = (6, 5)$, $B = (8, -3)$, and $C = (9, 1)$. \n - Reflecting over the line $x=8$, we find:\n - $A' = (10, 5)$ since reflecting $(6, 5)$ over $x=8$ moves it 2 units to the left of $x=8$, so it... | 85 | 28ca87f8-7263-5674-9676-6a3179de252f |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Let $B$ be a right rectangular prism (box) with edges lengths $1,$ $3,$ and $4$, together... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "19", "solution": "To solve the problem, we analyze the volume of $S(r)$ by decomposing it into different geometric regions as described in the problem statement. We then calculate the coefficients $a$, $b$, $c$, and $d$ in the volume formula $ar^3 + br^2 + cr + d$.\n\n1. **Region 1: The Rec... | 158 | 86ceb1bb-ce24-512d-a445-9ff5c349d4ff |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not al... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "170", "solution": "1. **Understanding the Problem:**\n - We have 6 individuals: Adam, Benin, Chiang, Deshawn, Esther, and Fiona.\n - Each individual has the same number of internet friends within this group.\n - The number of friends each person has ranges from 1 to 4, as no one can b... | 101 | 71581afe-d5f1-5f74-b4c3-0e21981371b5 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "The ratio of the areas of two concentric circles is $1: 3$. If the radius of the smaller ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "0.73r", "solution": "1. **Identify the given information**: The ratio of the areas of two concentric circles is given as $1:3$. Let the radius of the smaller circle be $r$ and the radius of the larger circle be $R$.\n\n2. **Express the areas of the circles**: The area of a circle is given b... | 71 | ad8cc8d4-0750-55c4-8c56-cb35725cf2f0 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "How many ways are there to paint each of the integers $2, 3, \\cdots , 9$ either red, gre... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "432", "solution": "To solve this problem, we need to consider the constraints imposed by the requirement that each number must have a different color from each of its proper divisors. We start by identifying the divisors of each number from $2$ to $9$:\n\n- $2$: No proper divisors in the li... | 78 | e8aec90b-d151-5db2-9887-037a09723228 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Let $D(n)$ denote the number of ways of writing the positive integer $n$ as a product\n\\... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "112", "solution": "To find $D(96)$, we need to consider all possible ways to write $96$ as a product of integers greater than $1$, where the order of factors matters. We start by noting the prime factorization of $96$:\n\\[ 96 = 2^5 \\cdot 3 \\]\n\nWe will consider different cases based on ... | 169 | 9aa8d86e-5fef-5f14-8a02-5546af37b976 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "The plane is tiled by congruent squares and congruent pentagons as indicated. The percent... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "56", "solution": "1. **Identify the basic unit of tiling**: The tiling pattern consists of a large square divided into 9 smaller squares, each with side length $a$. The large square thus has a side length of $3a$.\n\n2. **Calculate the area of the large square**: The area of the large squar... | 279 | 2050a723-bae9-58a0-bcf1-2fb348148d83 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "In the adjoining plane figure, sides $AF$ and $CD$ are parallel, as are sides $AB$ and $E... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\sqrt{3}", "solution": "1. **Identify the Shape and Symmetry**: The given figure can be visualized as composed of several triangles. Notably, the problem states that sides $AF$ and $CD$ are parallel, as are $AB$ and $EF$, and $BC$ and $ED$. Each side has a length of $1$, and the angles $\\... | 100 | 9f293098-1bfe-5bbb-bff2-7d2df188982c |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "The keystone arch is an ancient architectural feature. It is composed of congruent isosce... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "100", "solution": "1. **Understanding the Geometry of the Keystone Arch**:\n The keystone arch is composed of $9$ congruent isosceles trapezoids. These trapezoids are arranged such that their non-parallel sides (legs) meet at a common point when extended. The bottom sides of the end trape... | 235 | dc6a07fd-f125-5add-9e34-b427647e8b08 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Laura added two three-digit positive integers. All six digits in these numbers are differ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "4", "solution": "1. **Define the problem**: We need to find the smallest possible value for the sum of the digits of $S$, where $S$ is the sum of two three-digit numbers $a$ and $b$. Each digit among $a$ and $b$ is unique.\n\n2. **Set constraints on $a$ and $b$**: Since $a$ and $b$ are thre... | 76 | 4b6e64f1-ec8f-56de-9b96-13ad8e32bd62 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Circles with centers $A$, $B$, and $C$ each have radius $r$, where $1 < r < 2$. The dista... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "1+\\sqrt{3(r^2-1)}", "solution": "1. **Setting up the problem**: We are given three circles with centers at $A$, $B$, and $C$, each having radius $r$ where $1 < r < 2$. The distance between each pair of centers is $2$. We need to find the length of the line segment $B'C'$, where $B'$ and $C... | 131 | 9101acb2-eec8-5277-a54a-9644259c5409 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Each of the $12$ edges of a cube is labeled $0$ or $1$. Two labelings are considered diff... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "20", "solution": "To solve this problem, we need to ensure that each face of the cube has exactly two edges labeled with $1$ and two edges labeled with $0$. We will analyze the possible configurations that satisfy this condition.\n\n#### Step 1: Understanding the Cube's Faces and Edges\nA c... | 110 | f297f280-a5d7-57ac-9eb9-d0ccbc0bed39 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Liquid $X$ does not mix with water. Unless obstructed, it spreads out on the surface of w... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\sqrt{\\frac{2160}{\\pi}}", "solution": "1. **Calculate the volume of liquid $X$:** \n The box has dimensions $6$ cm, $3$ cm, and $12$ cm. The volume $V$ of the box (and hence the volume of liquid $X$) is calculated by multiplying these dimensions:\n \\[\n V = 6 \\text{ cm} \\times ... | 119 | 798100ec-ef55-5535-8055-0b44fd929ffc |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "In triangle $ABC$, $AB=AC$ and $\\measuredangle A=80^\\circ$. If points $D, E$, and $F$ l... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "50^\\circ", "solution": "1. **Identify the properties of triangle $ABC$**: Given that $AB = AC$, triangle $ABC$ is isosceles. Also, $\\angle A = 80^\\circ$. Since the sum of angles in a triangle is $180^\\circ$, and $AB = AC$, the base angles $\\angle B$ and $\\angle C$ are equal. Thus, we ... | 99 | e7d7fb58-58f0-5a8d-8caa-1f9edd591bae |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "A regular octahedron has side length $1$. A plane parallel to two of its opposite faces c... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "14", "solution": "\nTo solve this problem, we need to understand the geometry of the octahedron and how the plane intersects it. An octahedron can be thought of as two square pyramids base-to-base. Each face of the octahedron is an equilateral triangle.\n\n#### Step 1: Understanding the Int... | 145 | 75b202f0-5cda-5ea6-b931-a6fc35a39210 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Terri produces a sequence of positive integers by following three rules. She starts with... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "27", "solution": "To solve the problem, we first need to understand the sequence generated by the rules provided and then determine the $98^\\text{th}$ term of the sequence starting with 98.\n\n1. **Starting the sequence**: We begin with 98 and apply the rules:\n - **98** is even and grea... | 185 | f295533e-5783-51bc-aca2-8314705d61cd |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
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{
"role": "user",
"content": "Six regular hexagons surround a regular hexagon of side length $1$ as shown. What is the ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "$3\\sqrt{3}$", "solution": "1. **Understanding the Configuration**: We are given a central regular hexagon surrounded by six regular hexagons, all of the same side length $1$. We need to find the area of $\\triangle{ABC}$, which is formed by connecting the centers of three adjacent outer he... | 61 | 6034acbd-a1e6-5b72-abf2-dffffc5da988 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Bernardo and Silvia play the following game. An integer between $0$ and $999$ inclusive i... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "7", "solution": "\nTo solve this problem, we need to determine the smallest initial number $N$ such that Bernardo wins the game. We will analyze the sequence of operations and the conditions under which Bernardo wins.\n\n1. **Sequence of Operations**:\n - Bernardo receives $N$, doubles it... | 151 | eb450654-16df-5fbc-aa36-1fc52fff7afa |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Convex quadrilateral $ABCD$ has $AB = 9$ and $CD = 12$. Diagonals $AC$ and $BD$ intersect... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "6", "solution": "1. **Given Information and Assumptions**:\n - Convex quadrilateral $ABCD$ with $AB = 9$, $CD = 12$, and diagonals $AC = 14$.\n - Diagonals $AC$ and $BD$ intersect at $E$.\n - $\\triangle AED$ and $\\triangle BEC$ have equal areas.\n\n2. **Using Equal Areas to Infer Si... | 98 | 8aa44f67-5751-5526-a419-e33425848260 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Michael walks at the rate of $5$ feet per second on a long straight path. Trash pails are... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "5", "solution": "1. **Set up the problem**: Michael walks at $5$ feet per second and trash pails are located every $200$ feet. The garbage truck travels at $10$ feet per second and stops for $30$ seconds at each pail. Michael sees the truck leaving a pail $200$ feet ahead as he passes a pai... | 126 | c872d841-c9cd-50ae-839e-b25122ec3b66 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Makarla attended two meetings during her $9$-hour work day. The first meeting took $45$ m... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "25", "solution": "1. **Convert the work day into minutes**: \n Makarla's work day is $9$ hours long. Since there are $60$ minutes in an hour, the total number of minutes in her work day is:\n \\[\n 9 \\times 60 = 540 \\text{ minutes}\n \\]\n\n2. **Calculate the total time spent in m... | 76 | 76d406e2-8d36-5a4e-ad27-cf8a8498d36a |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "A paint brush is swept along both diagonals of a square to produce the symmetric painted ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "2\\sqrt{2}+2", "solution": "\nLet's denote the side length of the square as $s$ and the width of the brush as $w$. We are given that half the area of the square is painted, so the painted area is $\\frac{s^2}{2}$.\n\n#### Step 1: Analyze the geometry\nThe brush sweeps along both diagonals o... | 78 | e4076c9f-396a-5a82-bf8c-634a4bc2bfe6 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "A sequence of numbers is defined by $D_0=0,D_1=0,D_2=1$ and $D_n=D_{n-1}+D_{n-3}$ for $n\... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "(E,O,E)", "solution": "1. **Define the sequence and initial conditions**: The sequence $\\{D_n\\}$ is defined by $D_0 = 0$, $D_1 = 0$, $D_2 = 1$, and for $n \\geq 3$, $D_n = D_{n-1} + D_{n-3}$.\n\n2. **Compute initial terms**: We calculate the first few terms of the sequence to observe any ... | 133 | 4069bfa2-79f4-58c3-aef9-c6672f98e89e |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "For how many integers $n$ between $1$ and $50$, inclusive, is $\\frac{(n^2-1)!}{(n!)^n}$ ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "34", "solution": "1. **Understanding the Expression**: We start by analyzing the expression \\[\\frac{(n^2-1)!}{(n!)^n}.\\] We need to determine for how many integers $n$ between $1$ and $50$, inclusive, this expression is an integer.\n\n2. **Rewriting the Expression**: We can rewrite the e... | 69 | 6cc18cfb-2f95-5df9-ad0e-7a7af546dcc5 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "If $3^{2x}+9=10\\left(3^{x}\\right)$, then the value of $(x^2+1)$ is",
"reasoning_con... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "1 or 5", "solution": "1. **Rewrite the equation**: Start by rewriting the given equation:\n \\[\n 3^{2x} + 9 = 10 \\cdot 3^x\n \\]\n Rearrange the terms to form a quadratic equation in terms of $3^x$:\n \\[\n 3^{2x} - 10 \\cdot 3^x + 9 = 0\n \\]\n\n2. **Substitute $u$ for $3^x... | 65 | f35359fe-8524-52fc-b19e-0dc37f34c3cd |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled t... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "26.9", "solution": "1. **Identify the total distance traveled**: \n The odometer readings at the start and end of the trip are given as $56,200$ miles and $57,060$ miles, respectively. Therefore, the total distance traveled during the trip is:\n \\[\n 57,060 - 56,200 = 860 \\text{ mil... | 152 | 88bccb8c-693f-51fd-baf2-06f6e7cd3b26 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "A square with side length 8 is cut in half, creating two congruent rectangles. What are t... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "4 \\times 8", "solution": "1. **Identify the original dimensions of the square**: The square has a side length of 8 units. Therefore, each side of the square is 8 units long.\n\n2. **Understand the effect of cutting the square in half**: When the square is cut in half, one dimension is halv... | 59 | 3205332a-5856-5e14-90de-61d71009ec9b |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Professor Gamble buys a lottery ticket, which requires that he pick six different integer... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{1}{4}", "solution": "1. **Understanding the Problem**: Professor Gamble needs to pick six different integers from 1 to 46 such that the sum of the base-ten logarithms of these numbers is an integer. This implies that the product of these numbers must be a power of 10, as the logarith... | 122 | 89fc4040-3f88-5833-886e-cdaf375bb874 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Right triangle $ABC$ has leg lengths $AB=20$ and $BC=21$. Including $\\overline{AB}$ and ... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "12", "solution": "1. **Identify the Triangle and Hypotenuse**: \n Given a right triangle $ABC$ with legs $AB = 20$ and $BC = 21$, we first calculate the length of the hypotenuse $AC$ using the Pythagorean theorem:\n \\[\n AC = \\sqrt{AB^2 + BC^2} = \\sqrt{20^2 + 21^2} = \\sqrt{400 + 4... | 96 | 618694d8-c9d0-5dfe-b01c-4a47f4854872 |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "Two distinct numbers $a$ and $b$ are chosen randomly from the set $\\{2, 2^2, 2^3, ..., 2... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{31}{300}", "solution": "1. **Define the problem in terms of logarithms and powers of 2:**\n Let $a = 2^x$ and $b = 2^y$ where $x$ and $y$ are integers such that $1 \\leq x, y \\leq 25$. We are given that $\\log_a b$ is an integer, say $z$. Therefore, we have:\n \\[\n \\log_a b ... | 84 | 761f37e5-b456-56b0-8535-4ae4904a7e5d |
[
{
"role": "system",
"content": "Write your final answer within \\boxed{}.",
"reasoning_content": null,
"tool_calls": null,
"name": null,
"tool_call_id": null
},
{
"role": "user",
"content": "If $n$ is a multiple of $4$, the sum $s=1+2i+3i^2+\\cdots+(n+1)i^n$, where $i=\\sqrt{-1}$... | null | math | agentica-org/DeepScaleR-Preview-Dataset | mit | {"ability": "math", "data_source": "agentica-org/DeepScaleR-Preview-Dataset", "agent_ref": {"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}, "reasoning": true, "language": "eng"} | {"ground_truth": {"answer": "\\frac{1}{2}(n+2-ni)", "solution": "To solve the problem, we need to evaluate the sum $s = 1 + 2i + 3i^2 + \\cdots + (n+1)i^n$ where $i = \\sqrt{-1}$ and $n$ is a multiple of $4$. We start by analyzing the powers of $i$:\n\n1. **Powers of $i$:**\n - $i^0 = 1$\n - $i^1 = i$\n - $i^2 = ... | 77 | 7ea839a7-3cee-5265-b468-a819467f8ffe |
End of preview. Expand in Data Studio
Domyn Edge Teacher Math Mix
Phased release. Domyn Edge is a rolling release in three bundles. This dataset is part of the second bundle, together with the domain teachers and their post-training data. For an overview, see the launch blog post.
The training data of Domyn Edge Teacher Math, in one config:
| Config | Stage | Train | Test |
|---|---|---|---|
rl |
GRPO, math problems with a verifiable final answer | 20,153 (2.96M tokens) | 815 (0.11M tokens) |
rl: GRPO problems
Math problems with a single verifiable final answer. The final answer in the
response is checked against reward.ground_truth.answer with math-verify. Each
prompt carries a system message that asks for the final answer in \boxed{} or
on a final ANSWER: $ANSWER line.
| Source | License | Train rows | Train tokens | Test rows | Test tokens |
|---|---|---|---|---|---|
| DeepScaleR-Preview-Dataset | MIT | 10,508 | 1.42M | 421 | 0.05M |
| Nemotron-3-Nano-RL-Training-Blend, math slice | ODC-BY 1.0 | 9,645 | 1.53M | 394 | 0.06M |
| Total | 20,153 | 2.96M | 815 | 0.11M |
Tokens are prompt tokens, as in the token_length column. The 4,606 train rows that ask for an
ANSWER: line are copies of other train rows; metadata.augmented_from names the original.
Decontamination
Before training, the problems were decontaminated against the benchmarks we evaluate on: AIME 2024,
AIME 2025, AIME 2026, HMMT February 2025, HMMT February 2026, GSM8K, MGSM,
GPQA Diamond, IMO-AnswerBench, IMO-ProofBench and LiveBench (math). This removed 22 train and 2 test problems. The ANSWER: copies were made afterwards, from
the remaining problems.
How to use
from datasets import load_dataset
rl_train = load_dataset("domyn/Domyn-Edge-Teacher-Math-Mix", "rl", split="train")
rl_test = load_dataset("domyn/Domyn-Edge-Teacher-Math-Mix", "rl", split="test")
Columns
| Column | Type | Description |
|---|---|---|
messages |
list | The prompt: role and content of each message (the other message fields are null). |
tools |
string | Always null in this config. |
task |
string | Task family. |
source |
string | Upstream dataset. |
license |
string | License of the upstream record. |
metadata |
string | JSON-encoded upstream metadata. |
reward |
string | JSON-encoded reward data: ground_truth and the scoring style. Here ground_truth.answer is the reference final answer. |
token_length |
int | Prompt length in tokens. |
uuid |
string | Record identifier. |
To train with NeMo-Gym, as we did, map each row to the math_with_judge_simple_agent input:
responses_create_params.input = messages; question = reward.ground_truth.question, or the
user message when absent; expected_answer = reward.ground_truth.answer; agent_ref =
{"type": "responses_api_agents", "name": "math_with_judge_simple_agent"}.
License
Our contributions to this dataset, including the curation and the mix composition, are released under the Apache License 2.0. Upstream datasets keep their original license terms. Read ATTRIBUTION.md before redistributing any part of this data.
Citation
@misc{domyn_edge_teacher_math_mix_2026,
title = {Domyn Edge Teacher Math Mix},
author = {Domyn},
year = {2026},
note = {Technical report, forthcoming in November 2026.},
publisher = {Hugging Face},
url = {https://huggingface.co/datasets/domyn/Domyn-Edge-Teacher-Math-Mix}
}
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