data_source stringclasses 8
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 600,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"index": 601,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 602,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 603,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Regular tetrahedra $J A N E, J O H N$, and $J O A N$ have non-overlapping interio... | math | {
"ground_truth": "$\\frac{5 \\sqrt{2}}{2}$",
"style": "rule"
} | {
"index": 604,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Each positive integer less than or equal to 2019 is written on a blank sheet of p... | math | {
"ground_truth": "976",
"style": "rule"
} | {
"index": 605,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Compute the third least positive integer $n$ such that each of $n, n+1$, and $n+2... | math | {
"ground_truth": "93",
"style": "rule"
} | {
"index": 606,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The points $(1,2,3)$ and $(3,3,2)$ are vertices of a cube. Compute the product of... | math | {
"ground_truth": "216",
"style": "rule"
} | {
"index": 607,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Eight students attend a Harper Valley ARML practice. At the end of the practice, ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 608,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "$\\quad$ Compute the least positive value of $t$ such that\n\n$$\n\\operatorname{... | math | {
"ground_truth": "$\\frac{3 \\pi}{4}$",
"style": "rule"
} | {
"index": 609,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In non-right triangle $A B C$, distinct points $P, Q, R$, and $S$ lie on $\\overl... | math | {
"ground_truth": "$\\frac{45}{2}$",
"style": "rule"
} | {
"index": 610,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Consider the system of equations\n\n$$\n\\begin{aligned}\n& \\log _{4} x+\\log _{... | math | {
"ground_truth": "$\\frac{66}{7}$",
"style": "rule"
} | {
"index": 611,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A complex number $z$ is selected uniformly at random such that $|z|=1$. Compute t... | math | {
"ground_truth": "$\\frac{505}{8076}$",
"style": "rule"
} | {
"index": 612,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Compute the least positive integer $n$ such that the sum of the digits of $n$ is ... | math | {
"ground_truth": "7986",
"style": "rule"
} | {
"index": 613,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "$\\quad$ Compute the greatest real number $K$ for which the graphs of\n\n$$\n(|x|... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"index": 614,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "To morph a sequence means to replace two terms $a$ and $b$ with $a+1$ and $b-1$ i... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"index": 615,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Triangle $A B C$ is inscribed in circle $\\omega$. The tangents to $\\omega$ at $... | math | {
"ground_truth": "$\\frac{800}{3}$",
"style": "rule"
} | {
"index": 616,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Given that $a, b, c$, and $d$ are integers such that $a+b c=20$ and $-a+c d=19$, ... | math | {
"ground_truth": "39",
"style": "rule"
} | {
"index": 617,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T$ = 39. Emile randomly chooses a set of $T$ cards from a standard deck of 5... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 618,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=1$. In parallelogram $A B C D, \\frac{A B}{B C}=T$. Given that $M$ is the ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 619,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=6$. Compute the value of $x$ such that $\\log _{T} \\sqrt{x-7}+\\log _{T^{... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 620,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=11$. Let $p$ be an odd prime and let $x, y$, and $z$ be positive integers ... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"index": 621,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=55$. Compute the value of $K$ such that $20, T-5, K$ is an increasing geom... | math | {
"ground_truth": "125",
"style": "rule"
} | {
"index": 622,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=125$. Cube $\\mathcal{C}_{1}$ has volume $T$ and sphere $\\mathcal{S}_{1}$... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 623,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Square $K E N T$ has side length 20 . Point $M$ lies in the interior of $K E N T$... | math | {
"ground_truth": "400",
"style": "rule"
} | {
"index": 624,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T$ be a rational number. Let $a, b$, and $c$ be the three solutions of the e... | math | {
"ground_truth": "362",
"style": "rule"
} | {
"index": 625,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=362$ and let $K=\\sqrt{T-1}$. Compute $\\left|(K-20)(K+1)+19 K-K^{2}\\righ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 626,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=20$. In $\\triangle L E O, \\sin \\angle L E O=\\frac{1}{T}$. If $L E=\\fr... | math | {
"ground_truth": "$\\frac{1}{40}$",
"style": "rule"
} | {
"index": 627,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=\\frac{1}{40}$. Given that $x, y$, and $z$ are real numbers such that $x+y... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 628,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=20$. The product of all positive divisors of $2^{T}$ can be written in the... | math | {
"ground_truth": "210",
"style": "rule"
} | {
"index": 629,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=210$. At the Westward House of Supper (\"WHS\"), a dinner special consists... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 630,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $S=15$ and let $M=10$ . Sam and Marty each ride a bicycle at a constant speed... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"index": 631,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Compute the $2011^{\\text {th }}$ smallest positive integer $N$ that gains an ext... | math | {
"ground_truth": "6455",
"style": "rule"
} | {
"index": 632,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In triangle $A B C, C$ is a right angle and $M$ is on $\\overline{A C}$. A circle... | math | {
"ground_truth": "$\\frac{12}{5}$",
"style": "rule"
} | {
"index": 633,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The product of the first five terms of a geometric progression is 32 . If the fou... | math | {
"ground_truth": "$\\frac{4}{17}$",
"style": "rule"
} | {
"index": 634,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Polygon $A_{1} A_{2} \\ldots A_{n}$ is a regular $n$-gon. For some integer $k<n$,... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 635,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A bag contains 20 lavender marbles, 12 emerald marbles, and some number of orange... | math | {
"ground_truth": "69",
"style": "rule"
} | {
"index": 636,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Compute the number of ordered quadruples of integers $(a, b, c, d)$ satisfying th... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 637,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer such that $\\frac{3+4+\\cdots+3 n}{5+6+\\cdots+5 n}... | math | {
"ground_truth": "$\\frac{27}{106}$",
"style": "rule"
} | {
"index": 638,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The quadratic polynomial $f(x)$ has a zero at $x=2$. The polynomial $f(f(x))$ has... | math | {
"ground_truth": "$-\\frac{32}{9}$",
"style": "rule"
} | {
"index": 639,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The Local Area Inspirational Math Exam comprises 15 questions. All answers are in... | math | {
"ground_truth": "7530",
"style": "rule"
} | {
"index": 640,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Circle $\\omega_{1}$ has center $O$, which is on circle $\\omega_{2}$. The circle... | math | {
"ground_truth": "$548 \\pi$",
"style": "rule"
} | {
"index": 641,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Compute the number of integers $n$ for which $2^{4}<8^{n}<16^{32}$.",
"role":... | math | {
"ground_truth": "41",
"style": "rule"
} | {
"index": 642,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=41$. Compute the number of positive integers $b$ such that the number $T$ ... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"index": 643,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=35$. Triangle $A B C$ has a right angle at $C$, and $A B=40$. If $A C-B C=... | math | {
"ground_truth": "111",
"style": "rule"
} | {
"index": 644,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $x$ be a positive real number such that $\\log _{\\sqrt{2}} x=20$. Compute $\... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 645,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=5$. Hannah flips two fair coins, while Otto flips $T$ fair coins. Let $p$ ... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"index": 646,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=17$. In ARMLovia, the unit of currency is the edwah. Janet's wallet contai... | math | {
"ground_truth": "1020",
"style": "rule"
} | {
"index": 647,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Spheres centered at points $P, Q, R$ are externally tangent to each other, and ar... | math | {
"ground_truth": "$18 \\sqrt{6}$",
"style": "rule"
} | {
"index": 648,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $f(x)=x^{1}+x^{2}+x^{4}+x^{8}+x^{16}+x^{32}+\\cdots$. Compute the coefficient... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 649,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Compute $\\left\\lfloor 100000(1.002)^{10}\\right\\rfloor$.",
"role": "user"
... | math | {
"ground_truth": "102018",
"style": "rule"
} | {
"index": 650,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $1, x, y$ is a geometric sequence and $x, y, 3$ is an arithmetic sequence, com... | math | {
"ground_truth": "$\\frac{15}{4}$",
"style": "rule"
} | {
"index": 651,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Define the sequence of positive integers $\\left\\{a_{n}\\right\\}$ as follows:\n... | math | {
"ground_truth": "253",
"style": "rule"
} | {
"index": 652,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Compute the base $b$ for which $253_{b} \\cdot 341_{b}=\\underline{7} \\underline... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 653,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Some portions of the line $y=4 x$ lie below the curve $y=10 \\pi \\sin ^{2} x$, a... | math | {
"ground_truth": "$\\frac{5 \\pi}{4} \\sqrt{17}$",
"style": "rule"
} | {
"index": 654,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In equilateral hexagon $A B C D E F, \\mathrm{~m} \\angle A=2 \\mathrm{~m} \\angl... | math | {
"ground_truth": "$\\frac{9}{2}$",
"style": "rule"
} | {
"index": 655,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The taxicab distance between points $A=\\left(x_{A}, y_{A}\\right)$ and $B=\\left... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"index": 656,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The function $f$ satisfies the relation $f(n)=f(n-1) f(n-2)$ for all integers $n$... | math | {
"ground_truth": "4096",
"style": "rule"
} | {
"index": 657,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Frank Narf accidentally read a degree $n$ polynomial with integer coefficients ba... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"index": 658,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Given a regular 16-gon, extend three of its sides to form a triangle none of whos... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 659,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Two square tiles of area 9 are placed with one directly on top of the other. The ... | math | {
"ground_truth": "$\\frac{5}{4}$",
"style": "rule"
} | {
"index": 660,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that neither of the three-digit numbers $M=\\underline{4} \\underline{A} ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 661,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=12$. Each interior angle of a regular $T$-gon has measure $d^{\\circ}$. Co... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"index": 662,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that $r$ and $s$ are the two roots of the equation $F_{k} x^{2}+F_{k+1} x... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 663,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=2$. Compute the product of $-T-i$ and $i-T$, where $i=\\sqrt{-1}$.",
"... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 664,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=5$. Compute the number of positive divisors of the number $20^{4} \\cdot 1... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 665,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=72 \\sqrt{2}$, and let $K=\\left(\\frac{T}{12}\\right)^{2}$. In the sequen... | math | {
"ground_truth": "414",
"style": "rule"
} | {
"index": 666,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $A$ be the sum of the digits of the number you will receive from position 7 ,... | math | {
"ground_truth": "$\\frac{79}{128}$",
"style": "rule"
} | {
"index": 667,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=9.5$. If $\\log _{2} x^{T}-\\log _{4} x=\\log _{8} x^{k}$ is an identity f... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"index": 668,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=16$. An isosceles trapezoid has an area of $T+1$, a height of 2 , and the ... | math | {
"ground_truth": "9.5",
"style": "rule"
} | {
"index": 669,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=10$. Susan flips a fair coin $T$ times. Leo has an unfair coin such that t... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"index": 670,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=1$. Dennis and Edward each take 48 minutes to mow a lawn, and Shawn takes ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 671,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let T be a rational number. Compute $\\sin ^{2} \\frac{T \\pi}{2}+\\sin ^{2} \\fr... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 672,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $T=11$. Compute the value of $x$ that satisfies $\\sqrt{20+\\sqrt{T+x}}=5$.",... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 673,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The sum of the interior angles of an $n$-gon equals the sum of the interior angle... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 674,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Each of the two Magellan telescopes has a diameter of $6.5 \\mathrm{~m}$. In one ... | math | {
"ground_truth": "1.6",
"style": "rule"
} | {
"index": 0,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A white dwarf star has an effective temperature, $T_{e}=50,000$ degrees Kelvin, b... | math | {
"ground_truth": "4.5e33",
"style": "rule"
} | {
"index": 1,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Preamble: A prism is constructed from glass and has sides that form a right trian... | math | {
"ground_truth": "41.8",
"style": "rule"
} | {
"index": 2,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A particular star has an absolute magnitude $M=-7$. If this star is observed in a... | math | {
"ground_truth": "20.39",
"style": "rule"
} | {
"index": 3,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Find the gravitational acceleration due to the Sun at the location of the Earth's... | math | {
"ground_truth": "0.006",
"style": "rule"
} | {
"index": 4,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Preamble: A collimated light beam propagating in water is incident on the surface... | math | {
"ground_truth": "np.arcsin(10/13)",
"style": "rule"
} | {
"index": 5,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Find the theoretical limiting angular resolution (in arcsec) of a commercial 8-in... | math | {
"ground_truth": "0.49",
"style": "rule"
} | {
"index": 6,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A star has a measured parallax of $0.01^{\\prime \\prime}$, that is, $0.01$ arcse... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"index": 7,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "An extrasolar planet has been observed which passes in front of (i.e., transits) ... | math | {
"ground_truth": "0.022",
"style": "rule"
} | {
"index": 8,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If the Bohr energy levels scale as $Z^{2}$, where $Z$ is the atomic number of the... | math | {
"ground_truth": "9.6",
"style": "rule"
} | {
"index": 9,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If the Sun's absolute magnitude is $+5$, find the luminosity of a star of magnitu... | math | {
"ground_truth": "3.83e35",
"style": "rule"
} | {
"index": 10,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Preamble: A spectrum is taken of a single star (i.e., one not in a binary). Among... | math | {
"ground_truth": "300",
"style": "rule"
} | {
"index": 11,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The differential luminosity from a star, $\\Delta L$, with an approximate blackbo... | math | {
"ground_truth": "\\frac{2 \\pi c^{2} R^{2}}{\\lambda^{5}\\left[e^{h c /(\\lambda k T)}-1\\right] d^{2}}",
"style": "rule"
} | {
"index": 12,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of ... | math | {
"ground_truth": "8.7e8",
"style": "rule"
} | {
"index": 13,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A star is at a distance from the Earth of $300 \\mathrm{pc}$. Find its parallax a... | math | {
"ground_truth": "0.003",
"style": "rule"
} | {
"index": 14,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The Sun's effective temperature, $T_{e}$, is 5800 Kelvin, and its radius is $7 \\... | math | {
"ground_truth": "4e33",
"style": "rule"
} | {
"index": 15,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Use the Bohr model of the atom to compute the wavelength of the transition from t... | math | {
"ground_truth": "4.49",
"style": "rule"
} | {
"index": 16,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Preamble: A radio interferometer, operating at a wavelength of $1 \\mathrm{~cm}$,... | math | {
"ground_truth": "0.01",
"style": "rule"
} | {
"index": 17,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Preamble: Orbital Dynamics: A binary system consists of two stars in circular orb... | math | {
"ground_truth": "3.3e12",
"style": "rule"
} | {
"index": 18,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If a star cluster is made up of $10^{4}$ stars, each of whose absolute magnitude ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 19,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A galaxy moves directly away from us with a speed of $3000 \\mathrm{~km} \\mathrm... | math | {
"ground_truth": "6630",
"style": "rule"
} | {
"index": 20,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The Spitzer Space Telescope has an effective diameter of $85 \\mathrm{cm}$, and a... | math | {
"ground_truth": "1.2",
"style": "rule"
} | {
"index": 21,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "It has long been suspected that there is a massive black hole near the center of ... | math | {
"ground_truth": "3e6",
"style": "rule"
} | {
"index": 22,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of ... | math | {
"ground_truth": "7e37",
"style": "rule"
} | {
"index": 23,
"split": "default"
} |
minerva | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A large ground-based telescope has an effective focal length of 10 meters. Two as... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"index": 24,
"split": "default"
} |
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