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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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... | 6,486 | 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... | 6,343 | 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) | 25,137 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 25,021 | 116 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Each vertex of a regular octagon is independently colored either red or blue with equal probability(...TRUNCATED) | 62 | aime24 | [151644,872,198,4854,11936,315,264,5792,18491,6113,374,28135,27197,2987,2518,476,6303,448,6144,18927(...TRUNCATED) | 31,864 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 31,778 | 86 | 1 | [-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100(...TRUNCATED) | |
"Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$. Find the number of intersection(...TRUNCATED) | 63 | aime24 | [151644,872,198,35338,400,69,2075,11730,8484,856,91,30529,83,37018,90,16,15170,17,52398,3,323,400,70(...TRUNCATED) | 32,859 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 32,768 | 91 | 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) | 24,104 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 24,029 | 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) | 13,507 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 13,346 | 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) | 18,311 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 18,205 | 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) | 5,939 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 5,880 | 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) | 15,081 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 14,973 | 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) | 7,084 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | 6,950 | 134 | 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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