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completions_OlympiadBench_hintgen-qwen3-4b-sft-5e-7init-star_Qwen3-1.7B

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problem stringlengths 73 1.17k	hint stringclasses 8 values	completions sequencelengths 16 16	corrects sequencelengths 16 16	acc float64 0 1	answer stringlengths 1 45
Quadrilateral $A R M L$ is a kite with $A R=R M=5, A M=8$, and $R L=11$. Compute $A L$.		["<think>\nOkay, so I need to find the length of AL in this kite ARML. Let me first recall what a ki(...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	$4 \sqrt{5}$
"Triangle $A B C$ is inscribed in circle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ meet at(...TRUNCATED)		["<think>\nOkay, so I need to find the area of triangle PBC, given some information about triangle A(...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	$\frac{800}{3}$
"Given quadrilateral $A R M L$ with $A R=20, R M=23, M L=25$, and $A M=32$, compute the number of di(...TRUNCATED)	"No hint.ช่ว беременнuser\nGiven the following math problem, generate a list of insigh(...TRUNCATED)	["<think>\nOkay, I'm ready to solve the problem. Let's start by creating a list of insightful hints (...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	49
"Compute the value of\n\n$$\n\\sin \\left(6^{\\circ}\\right) \\cdot \\sin \\left(12^{\\circ}\\right)(...TRUNCATED)		["<think>\nOkay, so I need to compute the value of this expression:\n\n$$\n\\sin \\left(6^{\\circ}\\(...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	$\frac{1}{16}$
"Tanner has two identical dice. Each die has six faces which are numbered 2, 3, 5, $7,11,13$. When T(...TRUNCATED)	"No hint.糖ขนส่งuser\nGiven the following math problem, generate a list of insightful hin(...TRUNCATED)	["</think>\n\n</think>\n\n</think>\n\n</think>\n\n</think>\n\n</think>\n\n</think>\n\n</think>\n\n</(...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	$\frac{1}{6}$
If $\frac{1}{\cos x}-\tan x=3$, what is the numerical value of $\sin x$ ?		["<think>\nOkay, so I need to solve the equation $\\frac{1}{\\cos x} - \\tan x = 3$ and find the num(...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	$-\frac{4}{5}$
"Let $T=2030$. Given that $\\mathrm{A}, \\mathrm{D}, \\mathrm{E}, \\mathrm{H}, \\mathrm{S}$, and $\\(...TRUNCATED)		["<think>\nOkay, let me try to figure out this problem. So, we have T = 2030. The digits A, D, E, H,(...TRUNCATED)	[ true, true, false, true, false, false, false, true, true, true, false, false, true, false, true, true ]	0.5625	9
"Let $\\mathbb{Z}_{\\geqslant 0}$ be the set of non-negative integers, and let $f: \\mathbb{Z}_{\\ge(...TRUNCATED)	"No hint.สำเร็𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯𬜯(...TRUNCATED)	["<think>\nOkay, let's try to tackle this problem. So, we have a function f that's a bijection from (...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	2500,7500
"If $x$ and $y$ are real numbers, determine all solutions $(x, y)$ of the system of equations\n\n$$\(...TRUNCATED)		["<think>\nOkay, so I need to solve this system of equations:\n\n$$\n\\begin{aligned}\n& x^{2} - x y(...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	$(-1,-9),(4+2 \sqrt{2}, 8),(4-2 \sqrt{2}, 8)$
"Let $\\mathbb{Z}_{>0}$ be the set of positive integers. Find all functions $f: \\mathbb{Z}_{>0} \\r(...TRUNCATED)		["<think>\nOkay, so I need to find all functions $ f: \\mathbb{Z}_{>0} \\rightarrow \\mathbb{Z}_{>0}(...TRUNCATED)	[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]	0	$f(n)=n$

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