ID stringlengths 8 10 | Year int64 2.01k 2.02k | Problem Number int64 1 15 | Part stringclasses 2
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2012-I-13 | 2,012 | 13 | I | "Three concentric circles have radii $3,$ $4,$ and $5.$ An equilateral triangle with one vertex on e(...TRUNCATED) | 41 | ["</think>\n\nAlright, let's tackle this problem step by step. We have three concentric circles with(...TRUNCATED) | ["59","106",",not","32","a + \\frac{b}{c} \\sqrt{d}","33","49\\sqrt{3} - \\tfrac{125}{4}","a + b + c(...TRUNCATED) | [
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2012-I-14 | 2,012 | 14 | I | "Complex numbers $a,$ $b,$ and $c$ are zeros of a polynomial $P(z) = z^3 + qz + r,$ and $|a|^2 + |b|(...TRUNCATED) | 375 | ["</think>\n\nLet's solve the problem step by step.\n\n**Given:**\n- Complex numbers \\( a \\), \\( (...TRUNCATED) | ["250"," - + +"," + wait=","375","125","375","500","500"," +something"," is is is +not","250","500",(...TRUNCATED) | [
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2012-II-1 | 2,012 | 1 | II | "Find the number of ordered pairs of positive integer solutions $(m, n)$ to the equation $20m + 12n (...TRUNCATED) | 34 | ["Okay, so I have this problem: Find the number of ordered pairs of positive integer solutions (m, n(...TRUNCATED) | [
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2012-II-2 | 2,012 | 2 | II | "Two geometric sequences $a_1, a_2, a_3, \\ldots$ and $b_1, b_2, b_3, \\ldots$ have the same common (...TRUNCATED) | 363 | ["Okay, so I have this problem about two geometric sequences. Let me try to understand it step by st(...TRUNCATED) | [
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2012-II-3 | 2,012 | 3 | II | "At a certain university, the division of mathematical sciences consists of the departments of mathe(...TRUNCATED) | 88 | ["Okay, so I need to solve this problem about forming a committee at a university's mathematical sci(...TRUNCATED) | [
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2012-II-4 | 2,012 | 4 | II | "Ana, Bob, and Cao bike at constant rates of $8.6$ meters per second, $6.2$ meters per second, and $(...TRUNCATED) | 61 | ["Okay, so I have this problem about Ana, Bob, and Cao biking around a rectangular field. The field (...TRUNCATED) | ["?. wait"," is.","."," is,?.,",")."," something."," is is is"," is,0? is",",),,,0,?,0,0? is ising i(...TRUNCATED) | [
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2012-II-6 | 2,012 | 6 | II | "Let $z=a+bi$ be the complex number with $\\vert z \\vert = 5$ and $b > 0$ such that the distance be(...TRUNCATED) | 125 | ["Okay, let's try to solve this problem step by step. The problem says:\n\nLet \\( z = a + bi \\) be(...TRUNCATED) | ["125","\\ \\ \\ \\\\Wait is \\. \\.?Wait compute\\\\ \\/\\ Waited \\\n\n \\ \\.\n\n \\.\n\n \\.\n\n(...TRUNCATED) | [
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2012-II-7 | 2,012 | 7 | II | "Let $S$ be the increasing sequence of positive integers whose binary representation has exactly $8$(...TRUNCATED) | 32 | ["Okay, so I have this problem where I need to find the 1000th number in a sequence S. The sequence (...TRUNCATED) | ["."," butBut perhaps,","376"," that=6 combination"," the",", n of is the","33",". of","376","376","(...TRUNCATED) | [
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2012-II-8 | 2,012 | 8 | II | "The complex numbers $z$ and $w$ satisfy the system \\[z + \\frac{20i}w = 5+i\\] \\[w+\\frac{12i}z =(...TRUNCATED) | 40 | ["Okay, so I need to solve this problem where we have two complex numbers z and w that satisfy the s(...TRUNCATED) | ["."," is.","100","40","40","40",".","..","40",",","40"," &检查 ensure说明.,? warehouse","40","{(...TRUNCATED) | [
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2012-II-9 | 2,012 | 9 | II | "Let $x$ and $y$ be real numbers such that $\\frac{\\sin x}{\\sin y} = 3$ and $\\frac{\\cos x}{\\cos(...TRUNCATED) | 107 | ["<think>\nOkay, let's tackle this problem step by step. So, we have two equations involving sine an(...TRUNCATED) | [
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