data_source stringclasses 4
values | prompt listlengths 1 1 | ability stringclasses 4
values | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler-preview | [
{
"role": "user",
"content": "The operation $\\otimes$ is defined for all nonzero numbers by $a \\otimes b = \\frac{a^{2}}{b}$. Determine $[(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)]$.\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{2}{3}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 0,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The operation $\\otimes$ is defined for a... |
deepscaler-preview | [
{
"role": "user",
"content": "Doug constructs a square window using $8$ equal-size panes of glass. The ratio of the height to width for each pane is $5 : 2$, and the borders around and between the panes are $2$ inches wide. In inches, what is the side length of the square window?\n\nPlease think step by ste... | math | {
"style": "rule",
"ground_truth": "26",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 1,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Doug constructs a square window using $8$... |
deepscaler-preview | [
{
"role": "user",
"content": "Let $P(x)$ be a polynomial of degree $3n$ such that\n\\begin{align*} P(0) = P(3) = \\dots = P(3n) &= 2, \\\\ P(1) = P(4) = \\dots = P(3n+1-2) &= 1, \\\\ P(2) = P(5) = \\dots = P(3n+2-2) &= 0. \\end{align*}\nAlso, $P(3n+1) = 730$. Determine $n$.\n\nPlease think step by step, and... | math | {
"style": "rule",
"ground_truth": "1",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 2,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Let $P(x)$ be a polynomial of degree $3n$... |
deepscaler-preview | [
{
"role": "user",
"content": "Let $f$ be the function defined by $f(x)=ax^2-\\sqrt{2}$ for some positive $a$. If $f(f(\\sqrt{2}))=-\\sqrt{2}$ then $a=$\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 3,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Let $f$ be the function defined by $f(x)=... |
deepscaler-preview | [
{
"role": "user",
"content": "At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in Mrs. Young's class taking the AMC $8$ this year. How many mathematics students... | math | {
"style": "rule",
"ground_truth": "28",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 4,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "At Euclid Middle School the mathematics t... |
deepscaler-preview | [
{
"role": "user",
"content": "If $991+993+995+997+999=5000-N$, then $N=$\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 5,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "If $991+993+995+997+999=5000-N$, then $N=... |
deepscaler-preview | [
{
"role": "user",
"content": "The total in-store price for an appliance is $99.99$. A television commercial advertises the same product for three easy payments of $29.98$ and a one-time shipping and handling charge of $9.98$. How many cents are saved by buying the appliance from the television advertiser?\n... | math | {
"style": "rule",
"ground_truth": "7",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 6,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The total in-store price for an appliance... |
deepscaler-preview | [
{
"role": "user",
"content": "Points $A,B,C,D,E$ and $F$ lie, in that order, on $\\overline{AF}$, dividing it into five segments, each of length 1. Point $G$ is not on line $AF$. Point $H$ lies on $\\overline{GD}$, and point $J$ lies on $\\overline{GF}$. The line segments $\\overline{HC}, \\overline{JE},$ a... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{3}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 7,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Points $A,B,C,D,E$ and $F$ lie, in that o... |
deepscaler-preview | [
{
"role": "user",
"content": "The graph, $G$ of $y=\\log_{10}x$ is rotated $90^{\\circ}$ counter-clockwise about the origin to obtain a new graph $G'$. What is the equation for $G'$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10^{-x}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 8,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The graph, $G$ of $y=\\log_{10}x$ is rota... |
deepscaler-preview | [
{
"role": "user",
"content": "A set of consecutive positive integers beginning with $1$ is written on a blackboard. One number is erased. The average (arithmetic mean) of the remaining numbers is $35\\frac{7}{17}$. What number was erased?\n\nPlease think step by step, and put your final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "7",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 9,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A set of consecutive positive integers be... |
deepscaler-preview | [
{
"role": "user",
"content": "A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths $15$ and $25$ meters. What fraction of the yard is occupied by the flow... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 10,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A rectangular yard contains two flower b... |
deepscaler-preview | [
{
"role": "user",
"content": "What is the sum of all possible values of $t$ between $0$ and $360$ such that the triangle in the coordinate plane whose vertices are $(\\cos 40^\\circ,\\sin 40^\\circ)$, $(\\cos 60^\\circ,\\sin 60^\\circ)$, and $(\\cos t^\\circ,\\sin t^\\circ)$ is isosceles?\n\nPlease think st... | math | {
"style": "rule",
"ground_truth": "380",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 11,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "What is the sum of all possible values o... |
deepscaler-preview | [
{
"role": "user",
"content": "In the adjoining figure, points $B$ and $C$ lie on line segment $AD$, and $AB, BC$, and $CD$ are diameters of circle $O, N$, and $P$, respectively. Circles $O, N$, and $P$ all have radius $15$ and the line $AG$ is tangent to circle $P$ at $G$. If $AG$ intersects circle $N$ at p... | math | {
"style": "rule",
"ground_truth": "20",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 12,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In the adjoining figure, points $B$ and ... |
deepscaler-preview | [
{
"role": "user",
"content": "The first three terms of an arithmetic progression are $x - 1, x + 1, 2x + 3$, in the order shown. The value of $x$ is:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 13,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The first three terms of an arithmetic p... |
deepscaler-preview | [
{
"role": "user",
"content": "Alicia had two containers. The first was $\\frac{5}{6}$ full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was $\\frac{3}{4}$ full of water. What is the ratio of the volume of ... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{10}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 14,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Alicia had two containers. The first was... |
deepscaler-preview | [
{
"role": "user",
"content": "An architect is building a structure that will place vertical pillars at the vertices of regular hexagon $ABCDEF$, which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The heights of pillars at $A$, ... | math | {
"style": "rule",
"ground_truth": "17",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 15,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "An architect is building a structure tha... |
deepscaler-preview | [
{
"role": "user",
"content": "The points $(2,-3)$, $(4,3)$, and $(5, k/2)$ are on the same straight line. The value(s) of $k$ is (are):\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 16,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The points $(2,-3)$, $(4,3)$, and $(5, k... |
deepscaler-preview | [
{
"role": "user",
"content": "In a certain year the price of gasoline rose by $20\\%$ during January, fell by $20\\%$ during February, rose by $25\\%$ during March, and fell by $x\\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the near... | math | {
"style": "rule",
"ground_truth": "17",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 17,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In a certain year the price of gasoline ... |
deepscaler-preview | [
{
"role": "user",
"content": "Quadrilateral $ABCD$ satisfies $\\angle ABC = \\angle ACD = 90^{\\circ}, AC=20,$ and $CD=30.$ Diagonals $\\overline{AC}$ and $\\overline{BD}$ intersect at point $E,$ and $AE=5.$ What is the area of quadrilateral $ABCD?$\n\nPlease think step by step, and put your final answer wi... | math | {
"style": "rule",
"ground_truth": "360",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 18,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Quadrilateral $ABCD$ satisfies $\\angle ... |
deepscaler-preview | [
{
"role": "user",
"content": "The angle bisector of the acute angle formed at the origin by the graphs of the lines $y = x$ and $y=3x$ has equation $y=kx.$ What is $k?$\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1+\\sqrt{5}}{2}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 19,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The angle bisector of the acute angle fo... |
deepscaler-preview | [
{
"role": "user",
"content": "A set $S$ of points in the $xy$-plane is symmetric about the origin, both coordinate axes, and the line $y=x$. If $(2,3)$ is in $S$, what is the smallest number of points in $S$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 20,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A set $S$ of points in the $xy$-plane is... |
deepscaler-preview | [
{
"role": "user",
"content": "Five positive consecutive integers starting with $a$ have average $b$. What is the average of $5$ consecutive integers that start with $b$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "$a+4$",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 21,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Five positive consecutive integers start... |
deepscaler-preview | [
{
"role": "user",
"content": "At noon on a certain day, Minneapolis is $N$ degrees warmer than St. Louis. At $4{:}00$ the temperature in Minneapolis has fallen by $5$ degrees while the temperature in St. Louis has risen by $3$ degrees, at which time the temperatures in the two cities differ by $2$ degrees. ... | math | {
"style": "rule",
"ground_truth": "60",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 22,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "At noon on a certain day, Minneapolis is... |
deepscaler-preview | [
{
"role": "user",
"content": "Consider all 1000-element subsets of the set $\\{1, 2, 3, \\dots , 2015\\}$. From each such subset choose the least element. The arithmetic mean of all of these least elements is $\\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.\n\nPleas... | math | {
"style": "rule",
"ground_truth": "2016",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 23,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Consider all 1000-element subsets of the... |
deepscaler-preview | [
{
"role": "user",
"content": "A man on his way to dinner shortly after $6:00$ p.m. observes that the hands of his watch form an angle of $110^{\\circ}$. Returning before $7:00$ p.m. he notices that again the hands of his watch form an angle of $110^{\\circ}$. The number of minutes that he has been away is:\... | math | {
"style": "rule",
"ground_truth": "40",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 24,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A man on his way to dinner shortly after... |
deepscaler-preview | [
{
"role": "user",
"content": "A 3x3x3 cube is made of $27$ normal dice. Each die's opposite sides sum to $7$. What is the smallest possible sum of all of the values visible on the $6$ faces of the large cube?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90",
"reward_weights": [
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"key": "math",
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} | {
"split": "train",
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"num_generations": 1,
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],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A 3x3x3 cube is made of $27$ normal dice... |
deepscaler-preview | [
{
"role": "user",
"content": "In the multiplication problem below $A$, $B$, $C$, $D$ are different digits. What is $A+B$?\n$\\begin{array}{cccc} & A & B & A\\\\ \\times & & C & D\\\\ \\hline C & D & C & D\\\\ \\end{array}$\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
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"reward_weights": [
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"key": "math",
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} | {
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"validation": {
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"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In the multiplication problem below $A$,... |
deepscaler-preview | [
{
"role": "user",
"content": "Andrea and Lauren are $20$ kilometers apart. They bike toward one another with Andrea traveling three times as fast as Lauren, and the distance between them decreasing at a rate of $1$ kilometer per minute. After $5$ minutes, Andrea stops biking because of a flat tire and waits... | math | {
"style": "rule",
"ground_truth": "65",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
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"rubrics": null,
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} | {
"split": "train",
"index": 27,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Andrea and Lauren are $20$ kilometers ap... |
deepscaler-preview | [
{
"role": "user",
"content": "The sum of two natural numbers is $17402$. One of the two numbers is divisible by $10$. If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?\n\nPlease think step by step, and put your final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "14238",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
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],
"rubrics": null,
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} | {
"split": "train",
"index": 28,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The sum of two natural numbers is $17402... |
deepscaler-preview | [
{
"role": "user",
"content": "What is the value of $2^{0^{1^9}} + (2^0)^{1^9}$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 29,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "What is the value of $2^{0^{1^9}} + (2^0... |
deepscaler-preview | [
{
"role": "user",
"content": "If $a$ and $b$ are digits for which\n$\\begin{array}{ccc}& 2 & a\\ \\times & b & 3\\ \\hline & 6 & 9\\ 9 & 2 & \\ \\hline 9 & 8 & 9\\end{array}$\nthen $a+b =$\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 30,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "If $a$ and $b$ are digits for which\n$\\... |
deepscaler-preview | [
{
"role": "user",
"content": "If $x, 2x+2, 3x+3, \\dots$ are in geometric progression, the fourth term is:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-13\\frac{1}{2}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 31,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "If $x, 2x+2, 3x+3, \\dots$ are in geomet... |
deepscaler-preview | [
{
"role": "user",
"content": "At $2:15$ o'clock, the hour and minute hands of a clock form an angle of:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22\\frac {1}{2}^{\\circ}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 32,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "At $2:15$ o'clock, the hour and minute h... |
deepscaler-preview | [
{
"role": "user",
"content": "A finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first t... | math | {
"style": "rule",
"ground_truth": "37",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 33,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A finite sequence of three-digit integer... |
deepscaler-preview | [
{
"role": "user",
"content": "Square $EFGH$ has one vertex on each side of square $ABCD$. Point $E$ is on $AB$ with $AE=7\\cdot EB$. What is the ratio of the area of $EFGH$ to the area of $ABCD$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{25}{32}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 34,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Square $EFGH$ has one vertex on each sid... |
deepscaler-preview | [
{
"role": "user",
"content": "Chandler wants to buy a $500$ dollar mountain bike. For his birthday, his grandparents send him $50$ dollars, his aunt sends him $35$ dollars and his cousin gives him $15$ dollars. He earns $16$ dollars per week for his paper route. He will use all of his birthday money and all... | math | {
"style": "rule",
"ground_truth": "25",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 35,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Chandler wants to buy a $500$ dollar mou... |
deepscaler-preview | [
{
"role": "user",
"content": "The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12}{7}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 36,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The harmonic mean of a set of non-zero n... |
deepscaler-preview | [
{
"role": "user",
"content": "Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150 words per minute. If Julie speaks at the ideal rate, what number of words would be an appropriate length for her speech?\n\nPl... | math | {
"style": "rule",
"ground_truth": "5650",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 37,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Julie is preparing a speech for her clas... |
deepscaler-preview | [
{
"role": "user",
"content": "Let $ABC$ be an equilateral triangle. Extend side $\\overline{AB}$ beyond $B$ to a point $B'$ so that $BB'=3 \\cdot AB$. Similarly, extend side $\\overline{BC}$ beyond $C$ to a point $C'$ so that $CC'=3 \\cdot BC$, and extend side $\\overline{CA}$ beyond $A$ to a point $A'$ so ... | math | {
"style": "rule",
"ground_truth": "16",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 38,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Let $ABC$ be an equilateral triangle. Ex... |
deepscaler-preview | [
{
"role": "user",
"content": "If the following instructions are carried out by a computer, what value of \\(X\\) will be printed because of instruction \\(5\\)?\n\n1. START \\(X\\) AT \\(3\\) AND \\(S\\) AT \\(0\\). \n2. INCREASE THE VALUE OF \\(X\\) BY \\(2\\). \n3. INCREASE THE VALUE OF \\(S\\) BY THE ... | math | {
"style": "rule",
"ground_truth": "23",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 39,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "If the following instructions are carrie... |
deepscaler-preview | [
{
"role": "user",
"content": "Letters $A, B, C,$ and $D$ represent four different digits selected from $0, 1, 2, \\ldots ,9.$ If $(A+B)/(C+D)$ is an integer that is as large as possible, what is the value of $A+B$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 40,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Letters $A, B, C,$ and $D$ represent fou... |
deepscaler-preview | [
{
"role": "user",
"content": "A shopper plans to purchase an item that has a listed price greater than $\\$100$ and can use any one of the three coupons. Coupon A gives $15\\%$ off the listed price, Coupon B gives $\\$30$ off the listed price, and Coupon C gives $25\\%$ off the amount by which the listed pr... | math | {
"style": "rule",
"ground_truth": "50",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 41,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A shopper plans to purchase an item that... |
deepscaler-preview | [
{
"role": "user",
"content": "In $\\triangle ABC$, $\\angle ABC=45^\\circ$. Point $D$ is on $\\overline{BC}$ so that $2 \\cdot BD=CD$ and $\\angle DAB=15^\\circ$. Find $\\angle ACB.$\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "75^\\circ",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 42,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In $\\triangle ABC$, $\\angle ABC=45^\\c... |
deepscaler-preview | [
{
"role": "user",
"content": "Mary's top book shelf holds five books with the following widths, in centimeters: $6$, $\\dfrac{1}{2}$, $1$, $2.5$, and $10$. What is the average book width, in centimeters?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 43,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Mary's top book shelf holds five books w... |
deepscaler-preview | [
{
"role": "user",
"content": "A student council must select a two-person welcoming committee and a three-person planning committee from among its members. There are exactly $10$ ways to select a two-person team for the welcoming committee. It is possible for students to serve on both committees. In how many... | math | {
"style": "rule",
"ground_truth": "10",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 44,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A student council must select a two-pers... |
deepscaler-preview | [
{
"role": "user",
"content": "Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be $2$ : $1$ ?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 45,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Two years ago Pete was three times as ol... |
deepscaler-preview | [
{
"role": "user",
"content": "A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter ... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 46,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A square piece of paper, 4 inches on a s... |
deepscaler-preview | [
{
"role": "user",
"content": "Positive integers $a$ and $b$ are such that the graphs of $y=ax+5$ and $y=3x+b$ intersect the $x$-axis at the same point. What is the sum of all possible $x$-coordinates of these points of intersection?\n\nPlease think step by step, and put your final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "-8",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 47,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Positive integers $a$ and $b$ are such t... |
deepscaler-preview | [
{
"role": "user",
"content": "Four circles, no two of which are congruent, have centers at $A$, $B$, $C$, and $D$, and 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 the radius of circle $C$ is $\\frac{5}{8}$ times the radius of cir... | math | {
"style": "rule",
"ground_truth": "192",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 48,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Four circles, no two of which are congru... |
deepscaler-preview | [
{
"role": "user",
"content": "Medians $AD$ and $CE$ of $\\triangle ABC$ intersect in $M$. The midpoint of $AE$ is $N$. \nLet the area of $\\triangle MNE$ be $k$ times the area of $\\triangle ABC$. Then $k$ equals:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 49,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Medians $AD$ and $CE$ of $\\triangle ABC... |
deepscaler-preview | [
{
"role": "user",
"content": "Find the minimum value of $\\sqrt{x^2+y^2}$ if $5x+12y=60$.\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{60}{13}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 50,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Find the minimum value of $\\sqrt{x^2+y^... |
deepscaler-preview | [
{
"role": "user",
"content": "On average, for every 4 sports cars sold at the local dealership, 7 sedans are sold. The dealership predicts that it will sell 28 sports cars next month. How many sedans does it expect to sell?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "49",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 51,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "On average, for every 4 sports cars sold... |
deepscaler-preview | [
{
"role": "user",
"content": "Two fair dice, each with at least $6$ faces are rolled. On each face of each die is printed a distinct integer from $1$ to the number of faces on that die, inclusive. The probability of rolling a sum of $7$ is $\\frac34$ of the probability of rolling a sum of $10,$ and the prob... | math | {
"style": "rule",
"ground_truth": "17",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 52,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Two fair dice, each with at least $6$ fa... |
deepscaler-preview | [
{
"role": "user",
"content": "Two long cylindrical tubes of the same length but different diameters lie parallel to each other on a flat surface. The larger tube has radius $72$ and rolls along the surface toward the smaller tube, which has radius $24$. It rolls over the smaller tube and continues rolling a... | math | {
"style": "rule",
"ground_truth": "312",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 53,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Two long cylindrical tubes of the same l... |
deepscaler-preview | [
{
"role": "user",
"content": "The number $2.5252525\\ldots$ can be written as a fraction.\nWhen reduced to lowest terms the sum of the numerator and denominator of this fraction is:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "349",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 54,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The number $2.5252525\\ldots$ can be wri... |
deepscaler-preview | [
{
"role": "user",
"content": "For all non-zero numbers $x$ and $y$ such that $x = 1/y$, $\\left(x-\\frac{1}{x}\\right)\\left(y+\\frac{1}{y}\\right)$ equals\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^2-y^2",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 55,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "For all non-zero numbers $x$ and $y$ suc... |
deepscaler-preview | [
{
"role": "user",
"content": "The values of $k$ for which the equation $2x^2-kx+x+8=0$ will have real and equal roots are:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9 and -7",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 56,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The values of $k$ for which the equation... |
deepscaler-preview | [
{
"role": "user",
"content": "How many perfect cubes lie between $2^8+1$ and $2^{18}+1$, inclusive?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "58",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 57,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "How many perfect cubes lie between $2^8+... |
deepscaler-preview | [
{
"role": "user",
"content": "A line that passes through the origin intersects both the line $x = 1$ and the line $y=1+ \\frac{\\sqrt{3}}{3} x$. The three lines create an equilateral triangle. What is the perimeter of the triangle?\n\nPlease think step by step, and put your final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "3 + 2\\sqrt{3}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 58,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A line that passes through the origin in... |
deepscaler-preview | [
{
"role": "user",
"content": "Alicia earns 20 dollars per hour, of which $1.45\\%$ is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 59,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Alicia earns 20 dollars per hour, of whi... |
deepscaler-preview | [
{
"role": "user",
"content": "How many positive factors of 36 are also multiples of 4?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 60,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "How many positive factors of 36 are also... |
deepscaler-preview | [
{
"role": "user",
"content": "The numbers $-2, 4, 6, 9$ and $12$ are rearranged according to these rules:\n\n 1. The largest isn't first, but it is in one of the first three places. \n 2. The smallest isn't last, but it is in one of the last three places. \n 3. The median isn't first or... | math | {
"style": "rule",
"ground_truth": "6.5",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 61,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The numbers $-2, 4, 6, 9$ and $12$ are r... |
deepscaler-preview | [
{
"role": "user",
"content": "The circumference of the circle with center $O$ is divided into $12$ equal arcs, marked the letters $A$ through $L$ as seen below. What is the number of degrees in the sum of the angles $x$ and $y$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
... | math | {
"style": "rule",
"ground_truth": "90",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 62,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The circumference of the circle with cen... |
deepscaler-preview | [
{
"role": "user",
"content": "Mary thought of a positive two-digit number. She multiplied it by $3$ and added $11$. Then she switched the digits of the result, obtaining a number between $71$ and $75$, inclusive. What was Mary's number?\n\nPlease think step by step, and put your final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "12",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 63,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Mary thought of a positive two-digit num... |
deepscaler-preview | [
{
"role": "user",
"content": "Trapezoid $ABCD$ has $\\overline{AB} \\parallel \\overline{CD}, BC=CD=43$, and $\\overline{AD} \\perp \\overline{BD}$. Let $O$ be the intersection of the diagonals $\\overline{AC}$ and $\\overline{BD}$, and let $P$ be the midpoint of $\\overline{BD}$. Given that $OP=11$, the le... | math | {
"style": "rule",
"ground_truth": "194",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 64,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Trapezoid $ABCD$ has $\\overline{AB} \\p... |
deepscaler-preview | [
{
"role": "user",
"content": "If $q_1(x)$ and $r_1$ are the quotient and remainder, respectively, when the polynomial $x^8$ is divided by $x + \\frac{1}{2}$, and if $q_2(x)$ and $r_2$ are the quotient and remainder, respectively, when $q_1(x)$ is divided by $x + \\frac{1}{2}$, then $r_2$ equals\n\nPlease th... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{16}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 65,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "If $q_1(x)$ and $r_1$ are the quotient a... |
deepscaler-preview | [
{
"role": "user",
"content": "The expression $\\frac{1^{4y-1}}{5^{-1}+3^{-1}}$ is equal to:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{15}{8}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 66,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The expression $\\frac{1^{4y-1}}{5^{-1}+... |
deepscaler-preview | [
{
"role": "user",
"content": "Carrie has a rectangular garden that measures $6$ feet by $8$ feet. She plants the entire garden with strawberry plants. Carrie is able to plant $4$ strawberry plants per square foot, and she harvests an average of $10$ strawberries per plant. How many strawberries can she expe... | math | {
"style": "rule",
"ground_truth": "1920",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 67,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Carrie has a rectangular garden that mea... |
deepscaler-preview | [
{
"role": "user",
"content": "The sides of a triangle have lengths $6.5$, $10$, and $s$, where $s$ is a whole number. What is the smallest possible value of $s$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 68,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The sides of a triangle have lengths $6.... |
deepscaler-preview | [
{
"role": "user",
"content": "In the cube $ABCDEFGH$ with opposite vertices $C$ and $E,$ $J$ and $I$ are the midpoints of segments $\\overline{FB}$ and $\\overline{HD},$ respectively. Let $R$ be the ratio of the area of the cross-section $EJCI$ to the area of one of the faces of the cube. What is $R^2?$\n\n... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{4}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 69,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In the cube $ABCDEFGH$ with opposite ver... |
deepscaler-preview | [
{
"role": "user",
"content": "A square and an equilateral triangle have the same perimeter. Let $A$ be the area of the circle circumscribed about the square and $B$ the area of the circle circumscribed around the triangle. Find $A/B$.\n\nPlease think step by step, and put your final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\frac{27}{32}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 70,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A square and an equilateral triangle hav... |
deepscaler-preview | [
{
"role": "user",
"content": "Quadrilateral $ABCD$ has $AB = BC = CD$, $m\\angle ABC = 70^\\circ$ and $m\\angle BCD = 170^\\circ$. What is the degree measure of $\\angle BAD$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "85",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 71,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Quadrilateral $ABCD$ has $AB = BC = CD$,... |
deepscaler-preview | [
{
"role": "user",
"content": "Let $(a_n)$ and $(b_n)$ be the sequences of real numbers such that\n\\[ (2 + i)^n = a_n + b_ni \\]for all integers $n\\geq 0$, where $i = \\sqrt{-1}$. What is\n\\[\\sum_{n=0}^\\infty\\frac{a_nb_n}{7^n}\\,?\\]\n\nPlease think step by step, and put your final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{16}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 72,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Let $(a_n)$ and $(b_n)$ be the sequences... |
deepscaler-preview | [
{
"role": "user",
"content": "An $11 \\times 11 \\times 11$ wooden cube is formed by gluing together $11^3$ unit cubes. What is the greatest number of unit cubes that can be seen from a single point?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "331",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 73,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "An $11 \\times 11 \\times 11$ wooden cub... |
deepscaler-preview | [
{
"role": "user",
"content": "If each of two intersecting lines intersects a hyperbola and neither line is tangent to the hyperbola, then the possible number of points of intersection with the hyperbola is:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2, 3, or 4",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 74,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "If each of two intersecting lines inters... |
deepscaler-preview | [
{
"role": "user",
"content": "The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?\n\nPlease think step by step, and put your final answer wi... | math | {
"style": "rule",
"ground_truth": "139",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 75,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The Fort Worth Zoo has a number of two-l... |
deepscaler-preview | [
{
"role": "user",
"content": "If $\\frac{1}{x} - \\frac{1}{y} = \\frac{1}{z}$, then $z$ equals:\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{xy}{y - x}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 76,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "If $\\frac{1}{x} - \\frac{1}{y} = \\frac... |
deepscaler-preview | [
{
"role": "user",
"content": "A rectangular floor measures $a$ by $b$ feet, where $a$ and $b$ are positive integers with $b > a$. An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width $1$ foot aro... | math | {
"style": "rule",
"ground_truth": "2",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 77,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A rectangular floor measures $a$ by $b$ ... |
deepscaler-preview | [
{
"role": "user",
"content": "Ashley, Betty, Carlos, Dick, and Elgin went shopping. Each had a whole number of dollars to spend, and together they had $56$ dollars. The absolute difference between the amounts Ashley and Betty had to spend was $19$ dollars. The absolute difference between the amounts Betty a... | math | {
"style": "rule",
"ground_truth": "10",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 78,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Ashley, Betty, Carlos, Dick, and Elgin w... |
deepscaler-preview | [
{
"role": "user",
"content": "A palindrome between $1000$ and $10000$ is chosen at random. What is the probability that it is divisible by $7$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 79,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A palindrome between $1000$ and $10000$ ... |
deepscaler-preview | [
{
"role": "user",
"content": "What is the greatest three-digit positive integer $n$ for which the sum of the first $n$ positive integers is not a divisor of the product of the first $n$ positive integers?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "996",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 80,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "What is the greatest three-digit positiv... |
deepscaler-preview | [
{
"role": "user",
"content": "In $\\triangle ABC$ with right angle at $C$, altitude $CH$ and median $CM$ trisect the right angle. If the area of $\\triangle CHM$ is $K$, then the area of $\\triangle ABC$ is\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4K",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 81,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In $\\triangle ABC$ with right angle at... |
deepscaler-preview | [
{
"role": "user",
"content": "Claire adds the degree measures of the interior angles of a convex polygon and arrives at a sum of $2017$. She then discovers that she forgot to include one angle. What is the degree measure of the forgotten angle?\n\nPlease think step by step, and put your final answer within ... | math | {
"style": "rule",
"ground_truth": "143",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 82,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Claire adds the degree measures of the i... |
deepscaler-preview | [
{
"role": "user",
"content": "Zara has a collection of $4$ marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?\n\nPlease think step by step, and put yo... | math | {
"style": "rule",
"ground_truth": "12",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 83,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Zara has a collection of $4$ marbles: an... |
deepscaler-preview | [
{
"role": "user",
"content": "Triangle $ABC$ has vertices $A = (3,0)$, $B = (0,3)$, and $C$, where $C$ is on the line $x + y = 7$. What is the area of $\\triangle ABC$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 84,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Triangle $ABC$ has vertices $A = (3,0)$,... |
deepscaler-preview | [
{
"role": "user",
"content": "Everyday at school, Jo climbs a flight of $6$ stairs. Jo can take the stairs $1$, $2$, or $3$ at a time. For example, Jo could climb $3$, then $1$, then $2$. In how many ways can Jo climb the stairs?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "24",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 85,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Everyday at school, Jo climbs a flight o... |
deepscaler-preview | [
{
"role": "user",
"content": "A team won $40$ of its first $50$ games. How many of the remaining $40$ games must this team win so it will have won exactly $70 \\%$ of its games for the season?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 86,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "A team won $40$ of its first $50$ games.... |
deepscaler-preview | [
{
"role": "user",
"content": "In this diagram, not drawn to scale, Figures $I$ and $III$ are equilateral triangular regions with respective areas of $32\\sqrt{3}$ and $8\\sqrt{3}$ square inches. Figure $II$ is a square region with area $32$ square inches. Let the length of segment $AD$ be decreased by $12\\... | math | {
"style": "rule",
"ground_truth": "25",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 87,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In this diagram, not drawn to scale, Fig... |
deepscaler-preview | [
{
"role": "user",
"content": "Positive integers $a$ and $b$ are each less than $6$. What is the smallest possible value for $2 \\cdot a - a \\cdot b$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-15",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 88,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Positive integers $a$ and $b$ are each l... |
deepscaler-preview | [
{
"role": "user",
"content": "In square $ABCD$, points $P$ and $Q$ lie on $\\overline{AD}$ and $\\overline{AB}$, respectively. Segments $\\overline{BP}$ and $\\overline{CQ}$ intersect at right angles at $R$, with $BR = 6$ and $PR = 7$. What is the area of the square?\n\nPlease think step by step, and put yo... | math | {
"style": "rule",
"ground_truth": "117",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 89,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In square $ABCD$, points $P$ and $Q$ lie... |
deepscaler-preview | [
{
"role": "user",
"content": "The equations of $L_1$ and $L_2$ are $y=mx$ and $y=nx$, respectively. Suppose $L_1$ makes twice as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does $L_2$, and that $L_1$ has 4 times the slope of $L_2$. If $L_1$ is not horizonta... | math | {
"style": "rule",
"ground_truth": "2",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 90,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "The equations of $L_1$ and $L_2$ are $y=... |
deepscaler-preview | [
{
"role": "user",
"content": "An amusement park has a collection of scale models, with a ratio of $1: 20$, of buildings and other sights from around the country. The height of the United States Capitol is $289$ feet. What is the height in feet of its duplicate to the nearest whole number?\n\nPlease think st... | math | {
"style": "rule",
"ground_truth": "14",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 91,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "An amusement park has a collection of sc... |
deepscaler-preview | [
{
"role": "user",
"content": "Sides $\\overline{AB}$ and $\\overline{AC}$ of equilateral triangle $ABC$ are tangent to a circle at points $B$ and $C$ respectively. What fraction of the area of $\\triangle ABC$ lies outside the circle?\n\nPlease think step by step, and put your final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{3}-\\frac{4\\sqrt{3}\\pi}{27}",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 92,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Sides $\\overline{AB}$ and $\\overline{A... |
deepscaler-preview | [
{
"role": "user",
"content": "Given $0 \\le x_0 < 1$, let\n\\[x_n = \\begin{cases} 2x_{n-1} & \\text{ if } 2x_{n-1} < 1 \\\\ 2x_{n-1} - 1 & \\text{ if } 2x_{n-1} \\ge 1 \\end{cases}\\]for all integers $n > 0$. For how many $x_0$ is it true that $x_0 = x_5$?\n\nPlease think step by step, and put your final a... | math | {
"style": "rule",
"ground_truth": "31",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 93,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Given $0 \\le x_0 < 1$, let\n\\[x_n = \\... |
deepscaler-preview | [
{
"role": "user",
"content": "Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower holds 0.1 liters. How tall, in meters, should Logan make his tower?\n\nPlease think ... | math | {
"style": "rule",
"ground_truth": "0.4",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 94,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Logan is constructing a scaled model of ... |
deepscaler-preview | [
{
"role": "user",
"content": "In $\\triangle PQR$, $PR=15$, $QR=20$, and $PQ=25$. Points $A$ and $B$ lie on $\\overline{PQ}$, points $C$ and $D$ lie on $\\overline{QR}$, and points $E$ and $F$ lie on $\\overline{PR}$, with $PA=QB=QC=RD=RE=PF=5$. Find the area of hexagon $ABCDEF$.\n\nPlease think step by ste... | math | {
"style": "rule",
"ground_truth": "150",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 95,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "In $\\triangle PQR$, $PR=15$, $QR=20$, a... |
deepscaler-preview | [
{
"role": "user",
"content": "What is the tens digit of $7^{2011}$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 96,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "What is the tens digit of $7^{2011}$?\n\... |
deepscaler-preview | [
{
"role": "user",
"content": "For a set of four distinct lines in a plane, there are exactly $N$ distinct points that lie on two or more of the lines. What is the sum of all possible values of $N$?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 97,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "For a set of four distinct lines in a pl... |
deepscaler-preview | [
{
"role": "user",
"content": "Let $f(t)=\\frac{t}{1-t}$, $t \\not= 1$. If $y=f(x)$, then $x$ can be expressed as\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-f(-y)",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 98,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "Let $f(t)=\\frac{t}{1-t}$, $t \\not= 1$.... |
deepscaler-preview | [
{
"role": "user",
"content": "For every dollar Ben spent on bagels, David spent $25$ cents less. Ben paid $\\$12.50$ more than David. How much did they spend in the bagel store together?\n\nPlease think step by step, and put your final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "$87.50",
"reward_weights": [
{
"key": "math",
"weight": 1
},
{
"key": "length",
"weight": 1
}
],
"rubrics": null,
"criteria_weights": null
} | {
"split": "train",
"index": 99,
"num_generations": 1,
"validation": {
"core": [
"correctness_reward"
],
"pass_at_k": [
"correctness_reward"
],
"macro": {
"task": "math",
"metric": "correctness_reward"
}
},
"question": "For every dollar Ben spent on bagels, Da... |
End of preview. Expand in Data Studio
MRRL-Mixed base
base/train is the shared, unbalanced prompt pool for model-specific sampling and calibration.
Sources
- agentica-org/DeepScaleR-Preview-Dataset, revision
b6ae8c60f5c1f2b594e2140b91c49c9ad0949e29. - PRIME-RL/Eurus-2-RL-Data, revision
9776b13264b5aaa0b16495fcf086a0a8d86fd655. - allenai/Dolci-RL-Zero-Code-7B, revision
054c0a1f9c5fd52566ad9124aa2e702924803cd3. - open-r1/verifiable-coding-problems-python_decontaminated-tested, revision
77ace849f7cc8f10d23945c748f9ff464427f83b. - sojuL/RubricHub_v1, revision
3837d55971473a872e84879c88f708b8da3ec2ef. Math uses DeepScaleR; Code uses Eurus, Dolci and Open-R1's tested Python problems; IF/Writing use RubricHub'srurbichub_v1_Instruction_Following,rurbichub_v1_Writingandrurbichub_v1_Chatfiles. Rows retain source repository, revision and subset.
Preparation
- Validate prompts, Math gold parsing, rubric weights and executable IF rules.
- Normalize Code interfaces/tests; check available Dolci and required Open-R1 reference programs with the training executor (5s per-test timeout, 120s total execution budget). Keep at most 25 uniformly sampled, prompt-seeded tests per question.
- Render every Code prompt as
### Question / ### Formatfrom the bare statement (chat, Eurus and Open-R1 wrappers stripped for all sources); drop questions with fewer than 15 words before their first input/example block. - Deduplicate normalized prompts across all four tasks; remove exact evaluation-question matches and embedded copies of evaluation questions >=80 characters. This does not detect semantic paraphrases.
- Require the complete chat prompt to be <=2048 tokens under all three tokenizers: Qwen/Qwen3-4B-Base, RLLab/olmo-3-7b-it-sft, RLLab/gemma-3-4b-text-it.
- Store outer reward weights separately from rubric-criterion weights; length/RM references are filled by the model-specific sampler.
Overlap sources (upstream, not local evaluation files): Eurus, eval-set/aime24, eval-set/aime25, eval-set/amc23, eval-set/minervamath, eval-set/olympiadbench, eval-set/math500, code_generation_lite/v6, MMLU-Pro/default, ZebraLogic/grid_mode, humanevalplus, mbppplus, IFEval, IFBench, WritingBench, WritingBench-validation, Arena-Hard-v2, GPQA-Diamond, ResearchQA, Creative-Writing-v3.
Task counts: {"code": 35636, "if": 94108, "math": 38685, "writing": 25629}.
Refer to the source repositories for dataset licenses.
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