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• User:Rowechen
  ...ding order by means of one or more "bubble passes". A bubble pass through a given sequence consists of comparing the second term with the first term, a ...of the form <math>r+si^{}_{}</math>, where <math>r^{}_{}</math> and <math>s^{}_{}</math> are integers, can be uniquely expressed in the base <math>-n+i
  22 KB (3,778 words) - 19:29, 2 June 2020
• Congruent (geometry)
  '''Congruency''' is a property of multiple geometric figures. Two [[geometry | geometric]] [[figure]]s are congruent if one of them can be turned and/or flipped and placed exactl
  10 KB (1,655 words) - 21:43, 24 March 2022
• 1970 Canadian MO Problems
  Find all number triples <math>(x,y,z)</math> such that when any of these numbers is added to the product of th ...prove that <math>a+h\ge b+k</math>. Find under what conditions <math>a+h=b+k</math>.
  4 KB (604 words) - 04:32, 8 October 2014
• 2007 iTest Problems
  A twin prime pair is a set of two primes <math>(p, q)</math> such that <math>q</math> is <math>2</ <math>\mathrm{(A)}\, 4</math>
  30 KB (4,794 words) - 23:00, 8 May 2024
• Euler line
  ...fact of Euclidean [[geometry]]. Certain fixed orders and distance [[ratio]]s hold among these points. In particular, <math>\overline{OGNH}</math> and < ...s examine what else this transformation, which we denote as <math>\mathcal{S}</math>, will do.
  59 KB (10,203 words) - 04:47, 30 August 2023
• 2003 AMC 10A Problems/Problem 22
  ...gle <math>ABCD</math>, we have <math>AB=8</math>, <math>BC=9</math>, <math>H</math> is on <math>BC</math> with <math>BH=6</math>, <math>E</math> is on < pair D=(0,0), Ep=(4,0), A=(9,0), B=(9,8), H=(3,8), C=(0,8), G=(-6,20), F=(-6,0);
  9 KB (1,446 words) - 22:48, 8 May 2024
• 1987 IMO Problems/Problem 4
  ...h> must be even. If <math>k = 2h</math>, then we may take <math>f(n) = n + h</math>. ...m + k(s + 2)</math>. But <math>f(m + k) = n + k</math>, so <math>n = m + k(s + 1) > n</math>. Contradiction.
  5 KB (923 words) - 19:51, 21 January 2024
• 2020 AMC 10A Problems
  {{AMC10 Problems|year=2020|ab=A}} <math>\textbf{(A)}\ {-}\frac{2}{3}\qquad\textbf{(B)}\ \frac{7}{36}\qquad\textbf{(C)}\ \frac{
  13 KB (1,968 words) - 18:32, 29 February 2024
• 2007 AIME I Problems/Problem 9
  .../math> and <math>q</math> are [[relatively prime]] [[positive]] [[integer]]s. Find <math>p+q</math>. ...th>x = AD = AF</math> and <math>y = EB = BG</math>. We know that <math>x + y + 2r = 34</math>.
  11 KB (1,851 words) - 12:31, 21 December 2021
• 2007 AIME II Problems/Problem 15
  .../math>, and <math>\omega</math> is [[externally tangent]] to <math>\omega_{A},</math> <math>\omega_{B},</math> and <math>\omega_{C}</math>. If the sides pair A,B,C,X,Y,Z,P,Q,R;
  11 KB (2,099 words) - 17:51, 4 January 2024
• 2006 AIME II Problems/Problem 7
  ...th> a+b=1000 </math> and neither <math> a </math> nor <math> b </math> has a zero digit. ...(notice that the only time both <math>a</math> and <math>b</math> can have a 0 in the tens digit is when they are divisible by 100, which falls into the
  7 KB (1,114 words) - 03:41, 12 September 2021
• User:Temperal/The Problem Solver's Resource4
  ...usly, there is '''''WAY''''' too much to cover here, but we'll try to give a good overview. *A polynomial is a function of the form
  4 KB (828 words) - 21:45, 27 February 2020
• 2000 PMWC Problems
  ...r <math>1</math> and itself). What is the smallest possible value of <math>y</math>? Given that <math>A^4=75600\times B</math>. If <math>A</math> and <math>B</math> are positive integers, find the smallest value of
  11 KB (1,713 words) - 22:47, 13 July 2023
• De Longchamps point
  label("H",(24,0),(1,1)); ...hamps <br />point (<math>L</math>) is the the <br />[[orthocenter]] (<math>H</math>) reflected <br /> through the [[circumcenter]]<br /> (<math>C</math>
  10 KB (1,780 words) - 09:23, 17 November 2022
• 2007 AMC 10A Problems
  {{AMC10 Problems|year=2007|ab=A}} ...ath>25\%</math> discount. Pam buys 5 tickets using a coupon that gives her a <math>30\%</math> discount. How many more dollars does Pam pay than Susan?
  13 KB (2,058 words) - 17:54, 29 March 2024
• 1959 AHSME Problems
  Each edge of a cube is increased by <math>50</math>%. The percent of increase of the surfa <math>\textbf{(A)}\ 50 \qquad\textbf{(B)}\ 125\qquad\textbf{(C)}\ 150\qquad\textbf{(D)}\ 300
  22 KB (3,345 words) - 20:12, 15 February 2023
• 1966 AHSME Problems
  ...constant, and <math>y = 3</math> when <math>x = 2</math>, then, when <math>y = 12</math>, <math>x</math> equals: <math>\text{(A)} \ \frac 18 \qquad \text{(B)} \ \frac 73 \qquad \text{(C)} \ \frac78 \qqua
  19 KB (3,159 words) - 22:10, 11 March 2024
• Isogonal conjugate
  ...nal conjugates''' are pairs of [[point]]s in the [[plane]] with respect to a certain [[triangle]]. ...ll</math> and a point <math>O</math> lying on <math>\ell</math> be given. A pair of lines symmetric with respect to <math>\ell</math> and containing t
  54 KB (9,416 words) - 08:40, 18 April 2024
• Mock AIME 5 Pre 2005 Problems
  Function <math>g(y)</math> is given such way that for all <math>y</math>, <cmath>6g(1 + (1/y)) + 12g(y + 1) = \log_{10} y</cmath>
  6 KB (909 words) - 07:27, 12 October 2022
• 2008 AIME II Problems/Problem 14
  ...math>. Let <math>\rho</math> be the maximum possible value of <math>\frac {a}{b}</math> for which the system of equations a^2 + y^2 = b^2 + x^2 = (a - x)^2 + (b - y)^2
  8 KB (1,387 words) - 11:56, 29 January 2024

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