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• 2008 iTest Problems
  ...s. Michael is their oldest child, and Wendy their oldest daughter. Tony is the youngest child. Twins Joshua and Alexis are <math>12</math> years old. When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo.
  71 KB (11,749 words) - 01:31, 2 November 2023
• Sierpinski triangle
  ...angle, named after [[Waclaw Sierpinki]], is formed by parity of [[Pascal's triangle]], coloring a cell black if odd and white if even.
  257 bytes (37 words) - 17:08, 9 March 2015
• 2009 USAMO Problems/Problem 5
  ...ath> again at points <math>P</math> and <math>Q</math>, respectively. Let the line through <math>G</math> parallel to <math>\overline{AB}</math> intersec \end{align*}</cmath> depending on the configuration.
  6 KB (973 words) - 19:24, 18 October 2018
• Binomial
  A '''binominal''' is a polynominal with two terms, the sum of two monominals. *The binomial <math>a^2-b^2</math> can be [[factoring|factored]] as a product of
  605 bytes (98 words) - 16:39, 30 June 2021
• 2008 iTest Problems/Problem 77
  ...tion, Wendy looks for something to do. She starts working on a project for the math team. ...e are sixteen students, including Wendy, who are about to be sophomores on the math team. Elected as a math team officer,
  5 KB (788 words) - 05:15, 28 January 2019
• 2011 AMC 10B Problems/Problem 23
  What is the hundreds digit of <math>2011^{2011}?</math> To compute this, we use a clever application of the [[binomial theorem]].
  9 KB (1,287 words) - 20:37, 20 August 2023
• 1993 AHSME Problems/Problem 22
  ...ich it rests. Find the smallest possible number which could be assigned to the top block. ...gate down the block pyramid, its sort of like a three dimensional Pascal's triangle.
  7 KB (780 words) - 08:19, 27 June 2021
• 1971 AHSME Problems
  The number of digits in the number <math>N=2^{12}\times 5^8</math> is ...bricks, then the number of days it will take <math>c</math> men working at the same rate to lay <math>b</math> bricks, is
  18 KB (2,703 words) - 20:50, 11 September 2023
• 2014 IMO Problems/Problem 4
  ...math>BM</math> and <math>CN</math> intersect on the circumcircle of <math>\triangle{ABC}</math>. ...d <math>CN</math>, call it point <math>D</math>, is on the circumcircle of triangle <math>ABC</math>. In other words, we are trying to prove <math>\angle {BDC}
  13 KB (1,803 words) - 12:00, 19 May 2024
• 1986 AHSME Problems/Problem 23
  ...rime factorized as <math>2^5\cdot5^5\cdot7^5</math>. Finally, we can count the number of factors of this number.
  843 bytes (116 words) - 18:52, 1 April 2018
• 2016 AMC 12A Problems/Problem 19
  ...hen he gets tails, he moves <math>1</math> unit in the negative direction. The probability that he reaches <math>4</math> at some time during this process ...to <math>8</math> heads, we are guaranteed to hit <math>4</math> heads, so the sum here is <math>\binom{8}{2}+\binom{8}{1}+\binom{8}{0}=28+8+1=37</math>.
  5 KB (881 words) - 13:34, 7 October 2023
• 2006 iTest Problems
  Find the number of positive integral divisors of 2006. Find the harmonic mean of 10 and 20.
  31 KB (4,811 words) - 00:02, 4 November 2023
• 2016 USAMO Problems/Problem 3
  Let <math>\triangle ABC</math> be an acute triangle, and let <math>I_B, I_C,</math> and <math>O</math> denote its <math>B</math This problem can be proved in the following two steps.
  6 KB (998 words) - 21:36, 17 October 2022
• 2017 USAJMO Problems/Problem 2
  Consider the equation ...e infinitely many pairs <math>(x,y)</math> of positive integers satisfying the equation.
  10 KB (1,657 words) - 19:08, 24 April 2023
• Bill's Triangle
  ...top two. It was found by Bill9000. (If anyone finds someone who found this triangle before, please tell Bill9000.) ==How to Make Bill's Triangle==
  2 KB (307 words) - 20:25, 12 December 2017
• 2018 IMO Problems
  ...lines <math>DE</math> and <math>FG</math> are either parallel or they are the same line. ...numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from <math>1</math> to <math>10
  3 KB (544 words) - 08:34, 27 May 2023
• 2018 IMO Problems/Problem 3
  ...numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from <math>1</math> to <math>10 Does there exist an anti-Pascal triangle with <math>2018</math> rows which contains every integer from <math>1</math
  4 KB (626 words) - 01:45, 19 November 2023
• 2008 iTest Problems/Problem 60
  Consider the Harmonic Table ...emainder when the sum of the reciprocals of the <math>2007</math> terms on the <math>2007^\text{th}</math> row gets divided by <math>2008</math>.
  3 KB (527 words) - 01:29, 2 November 2023
• 2008 iTest Problems/Problem 78
  Feeling excited over her successful explorations into Pascal's Triangle, Wendy formulates a second problem to use during a future Jupiter Falls Hig ''How many of the first 2010 rows of Pascal's Triangle (Rows 0 through 2009) have exactly 256 odd entries?''
  2 KB (234 words) - 15:09, 1 August 2021
• A choose b
  Here is the formula for a choose b: <math>\binom{a}{b}=\frac{a!}{b!(a-b)!}</math>. This a choose b counts the number of ways you can pick b things from a set of a things. For example <m
  3 KB (407 words) - 20:03, 25 July 2021

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