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Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 60 | aime24 | [
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... | 6,195 | This is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.
Well, let's tackle this problem step by step. So, Aya walks 9 kilometers every morning, stops at a coffee shop for t minutes, and the time she takes is the walking time plus the coffee shop t... | 6,052 | 143 | 1 | [
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"Let $ABC$ be a triangle inscribed in circle $\\omega$. Let the tangents to $\\omega$ at $B$ and $C$(...TRUNCATED) | 61 | aime24 | [151644,872,198,10061,400,25411,3,387,264,21495,1640,17433,304,12671,57960,32696,12947,6771,279,2187(...TRUNCATED) | 26,425 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 26,309 | 116 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Let $p$ be the least prime number for which there exists a positive integer $n$ such that $n^{4}+1$(...TRUNCATED) | 64 | aime24 | [151644,872,198,10061,400,79,3,387,279,3245,10250,1372,369,892,1052,6724,264,6785,7546,400,77,3,1741(...TRUNCATED) | 22,935 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 22,860 | 75 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$, $AC=BD= \\sqrt{80}$, and $BC=AD= \\sqrt{(...TRUNCATED) | 65 | aime24 | [151644,872,198,10061,400,1867,6484,3,387,264,27853,32507,291,2248,1741,429,400,1867,28,6484,28,1124(...TRUNCATED) | 13,610 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 13,449 | 161 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Let $\\mathcal{B}$ be the set of rectangular boxes with surface area $54$ and volume $23$. Let $r$ (...TRUNCATED) | 66 | aime24 | [151644,872,198,10061,57960,10374,5416,90,33,31716,387,279,738,315,51424,14697,448,7329,3082,400,20,(...TRUNCATED) | 16,066 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 15,960 | 106 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"There exist real numbers $x$ and $y$, both greater than 1, such that $\\log_x\\left(y^x\\right)=\\l(...TRUNCATED) | 67 | aime24 | [151644,872,198,3862,3000,1931,5109,400,87,3,323,400,88,54876,2176,7046,1091,220,16,11,1741,429,5796(...TRUNCATED) | 8,098 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 8,039 | 59 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take tur(...TRUNCATED) | 68 | aime24 | [151644,872,198,61686,323,14261,1486,279,2701,1809,13,362,5611,315,400,77,3,11211,15448,1573,1105,13(...TRUNCATED) | 9,978 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 9,870 | 108 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers(...TRUNCATED) | 69 | aime24 | [151644,872,198,41,268,28833,264,38239,553,21132,400,19,3,12460,5109,504,400,50,34433,90,16,11,17,11(...TRUNCATED) | 6,587 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 6,453 | 134 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Consider the paths of length $16$ that follow the lines from the lower left corner to the upper rig(...TRUNCATED) | 71 | aime24 | [151644,872,198,37175,279,12716,315,3084,400,16,21,3,429,1795,279,5128,504,279,4722,2115,9131,311,27(...TRUNCATED) | 10,180 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 10,116 | 64 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Find the largest possible real part of \\[(75+117i)z+\\frac{96+144i}{z}\\]where $z$ is a complex nu(...TRUNCATED) | 72 | aime24 | [151644,872,198,9885,279,7772,3204,1931,949,315,1124,9697,22,20,10,16,16,22,72,8,89,41715,37018,90,2(...TRUNCATED) | 9,952 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 9,895 | 57 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) |
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