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yoonholee

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completions_AIME2024_hintgen-qwen3-4b-sft-5e-7init-star_Qwen3-1.7B

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"Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations: \n\\[\\l(...TRUNCATED)

"Let $O(0,0), A(\\tfrac{1}{2}, 0),$ and $B(0, \\tfrac{\\sqrt{3}}{2})$ be points in the coordinate pl(...TRUNCATED)

"Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers(...TRUNCATED)

"Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take tur(...TRUNCATED)

"<notes>\n <note>\n <description>When a game involves removing one or a fixed number of tokens, (...TRUNCATED)

"Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ a(...TRUNCATED)

"Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$. Find the number of intersection(...TRUNCATED)

"Each vertex of a regular octagon is independently colored either red or blue with equal probability(...TRUNCATED)

"Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and \\[a^(...TRUNCATED)

"There exist real numbers $x$ and $y$, both greater than 1, such that $\\log_x\\left(y^x\\right)=\\l(...TRUNCATED)

"Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positi(...TRUNCATED)