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• 2005 AMC 8 Problems
  ...clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same p
  13 KB (1,821 words) - 22:18, 5 December 2023
• 2006 AMC 8 Problems
  ...h> of positive integers for which <math> w </math> is the width and <math> l </math> is the length of a rectangle with area 12. What should his graph lo label("$l$", (0,6), W);
  16 KB (2,215 words) - 19:18, 10 April 2024
• 2003 AMC 8 Problems
  ...ildren riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there? pair i=(534, 342), j=(442,432), k=(374,484), l=(278,501);
  16 KB (2,236 words) - 12:02, 19 February 2024
• 2012 AIME II Problems/Problem 4
  ...e field. Cao arrives at point <math>D</math> at the same time that Ana and Bob arrive at <math>D</math> for the first time. The ratio of the field's lengt We have a system of equations: <cmath>\left\{\begin{array}{l}b+c=6.2\\ b^2+c^2=25\end{array}\right.</cmath>
  5 KB (796 words) - 00:17, 20 January 2024
• 2013 AMC 8 Problems
  Abe holds 1 green and 1 red jelly bean in his hand. Bob holds 1 green, 1 yellow, and 2 red jelly beans in his hand. Each randomly p triple A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P;
  15 KB (2,162 words) - 20:05, 8 May 2023
• 1981 AHSME Problems
  ...th respect to the line <math>y=x</math>. If the equation of the line <math>L</math> is <math>y=ax+b</math> with <math>a\neq 0</math> and <math>b\neq 0</ ...ossing a die. Alice begins; Bob always follows Alice; Carol always follows Bob; and Alice always follows Carol. Find the probability that Carol will be th
  17 KB (2,633 words) - 15:44, 16 September 2023
• Mock AIME 3 2010 Problems
  where e, f, g, h, j, k, l are positive integers such that g, j, k and l are not divisible by any prime and e is no greater than 2 + l
  14 KB (2,904 words) - 18:24, 16 May 2017
• 2017 AMC 10A Problems/Problem 19
  Alice refuses to sit next to either Bob or Carla. Derek refuses to sit next to Eric. How many ways are there for th Let Alice be A, Bob be B, Carla be C, Derek be D, and Eric be E.
  7 KB (1,196 words) - 01:31, 31 January 2023
• 2024 AIME I Problems/Problem 3
  ...2024</math> for which there exists a strategy for Bob that guarantees that Bob will win the game regardless of Alice's play. ...if there are <math>1</math>, <math>3</math>, or <math>4</math> coins left. Bob wins if there are <math>2</math> or <math>5</math> coins left.
  10 KB (1,628 words) - 18:50, 7 February 2024
• Sharygin Olympiads, the best
  Let <math>K</math> and <math>L</math> be the midpoints of the arcs <math>\overset{\Large\frown}{CB'}</math Let <math>K'</math> and <math>L'</math> be the midpoints of the arcs <math>\overset{\Large\frown}{CA'}</mat
  29 KB (4,997 words) - 18:06, 16 May 2024