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• AMC historical results
  ...at a consistent number of students qualify for AIME each year, rather than a fixed percentage. Usually, 6000-7000 competitors from the AMC 10 and 12 qua *Distinguished Honor Roll: 123
  17 KB (1,921 words) - 13:00, 28 April 2024
• Composite number
  A comprehensive video explaining composite numbers: https://youtu.be/SMOGYNYD A '''composite number''' is a [[positive integer]] with at least one [[divisor]] different from 1 and its
  6 KB (350 words) - 12:58, 26 September 2023
• 2006 AIME I Problems/Problem 6
  ...cimal| decimals]] of the form <math> 0.\overline{abc} </math> where <math> a, b, c </math> are distinct [[digit]]s. Find the sum of the elements of <mat ...erline{999}</math>, or, more precisely, 1. As an example, <math>.\overline{123}+.\overline{876}=.\overline{999} \Longrightarrow 1</math>.
  2 KB (237 words) - 19:14, 20 November 2023
• 2004 AMC 12A Problems
  {{AMC12 Problems|year=2004|ab=A}} <math>\text{(A) } 0.0029 \qquad \text{(B) } 0.029 \qquad \text{(C) } 0.29 \qquad \text{(D)
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2003 AMC 12B Problems
  \text {(A) } -1 \qquad \text {(B) } -\frac{2}{3} \qquad \text {(C) } \frac{2}{3} \qqu ...ks. A green pill costs 1 dollar more than a pink pill, and Al's pills cost a total of 546 dollars for the two weeks. How much does one green pill cost?
  13 KB (1,987 words) - 18:53, 10 December 2022
• 1989 AIME Problems
  Ten points are marked on a circle. How many distinct convex polygons of three or more sides can be dra ...ose <math>n_{}^{}</math> is a positive integer and <math>d_{}^{}</math> is a single digit in base 10. Find <math>n_{}^{}</math> if
  7 KB (1,045 words) - 20:47, 14 December 2023
• 1987 AIME Problems/Problem 11
  ...h>m</math> we do indeed have the valid [[expression]] <math>3^{11} = 122 + 123 + \ldots + 607</math>, for which <math>k=\boxed{486}</math>. ...e of the two factors will be a power of three, and the other will be twice a power of three. <math>(2n + m + 1)</math> will represent the greater factor
  3 KB (418 words) - 18:30, 20 January 2024
• 1989 AIME Problems/Problem 8
  9x_1 + 16x_2 + 25x_3 + 36x_4 + 49x_5 + 64x_6 + 81x_7 &= 123. ...tic function of <math>k:</math> <cmath>f(k)=ak^2+bk+c,</cmath> where <math>a,b,</math> and <math>c</math> are linear combinations of <math>x_1,x_2,x_3,x
  8 KB (1,146 words) - 04:15, 20 November 2023
• 1993 AIME Problems/Problem 3
  :(a) the winner caught <math>15</math> fish; ...(9+5+7)=y-21</math> fishers that caught <math>3</math> or more fish caught a total of <math>x - \left(0\cdot(9) + 1\cdot(5) + 2\cdot(7)\right) = x - 19<
  2 KB (364 words) - 00:05, 9 July 2022
• 2005 AMC 10B Problems/Problem 25
  A [[subset]] <math>B</math> of the set of integers from <math>1</math> to <ma <math>\textbf{(A) } 50 \qquad \textbf{(B) } 51 \qquad \textbf{(C) } 62 \qquad \textbf{(D) }
  3 KB (517 words) - 19:15, 15 October 2023
• 2005 AMC 10A Problems/Problem 14
  <math> \textbf{(A) } 41\qquad \textbf{(B) } 42\qquad \textbf{(C) } 43\qquad \textbf{(D) } 44\ If the middle digit is <math>2</math>, possible numbers range from <math>123</math> to <math>420</math>. So there are <math>4</math> numbers in this cas
  4 KB (694 words) - 19:25, 13 December 2021
• Stirling number
  ...<math>n</math>-[[element]] [[set]] with exactly <math>k</math> [[cycle of a permutation | cycles]]. ...mutations <math>\{(1)(234), (1)(243), (134)(2),(143)(2),(124)(3),(142)(3),(123)(4),(132)(4), (12)(34), (13)(24), (14)(23)\}</math>.
  2 KB (253 words) - 00:04, 5 December 2020
• 2004 AMC 10A Problems
  {{AMC10 Problems|year=2004|ab=A}} ...and five friends need to raise <math>1500</math> dollars in donations for a charity, dividing the fundraising equally. How many dollars will each of y
  15 KB (2,092 words) - 20:32, 15 April 2024
• 2007 AMC 12A Problems
  {{AMC12 Problems|year=2007|ab=A}} ...h> discount. Pam buys <math>5</math> tickets using a coupon that gives her a <math>30\%</math> discount. How many more dollars does Pam pay than Susan?
  11 KB (1,750 words) - 13:35, 15 April 2022
• LaTeX:Help
  ...ase consult the AoPS [http://www.artofproblemsolving.com/Forum/index.php?f=123 message board]. ==== I'm using a Macintosh. What do I do? ====
  7 KB (1,109 words) - 20:01, 8 September 2022
• 2007 AMC 12A Problems/Problem 11
  ...ctively, the hundreds and tens digits of the first term. For example, such a sequence might begin with the terms 247, 475, and 756 and end with the term <math>\mathrm{(A)}\ 3\qquad \mathrm{(B)}\ 7\qquad \mathrm{(C)}\ 13\qquad \mathrm{(D)}\ 37\qq
  2 KB (243 words) - 01:15, 27 January 2024
• 2007 AMC 12A Problems/Problem 25
  Call a set of integers ''spacy'' if it contains no more than one out of any three <math>\mathrm{(A)}\ 121 \qquad \mathrm{(B)}\ 123 \qquad \mathrm{(C)}\ 125 \qquad \mathrm{(D)}\ 127 \qquad \mathrm{(E)}\ 129<
  9 KB (1,461 words) - 23:07, 27 January 2024
• 2004 AMC 12A Problems/Problem 22
  ...ually tangent spheres of radius <math>1</math> rest on a horizontal plane. A sphere of radius <math>2</math> rests on them. What is the distance from th ...ext {(B)}\ 3 + \frac {\sqrt {69}}{3} \qquad \text {(C)}\ 3 + \frac {\sqrt {123}}{4}\qquad \text {(D)}\ \frac {52}{9}\qquad \text {(E)}\ 3 + 2\sqrt2</math>
  2 KB (382 words) - 19:59, 29 January 2023
• 2008 AIME I Problems/Problem 4
  Since <math>244</math> is even, one of the factors is even. A [[parity]] check shows that if one of them is even, then both must be even. So <math>y^2-244</math> is a perfect square. Since 244 is even, the difference <math>\sqrt{y^2-244} -y^2
  4 KB (732 words) - 22:17, 28 November 2023
• 1988 AJHSME Problems
  The diagram shows part of a scale of a measuring device. The arrow indicates an approximate reading of <math>\text{(A)}\ 10.05 \qquad \text{(B)}\ 10.15 \qquad \text{(C)}\ 10.25 \qquad \text{(D)
  14 KB (1,872 words) - 15:23, 17 January 2023

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