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• 1994 USAMO Problems
  Let <math>\, k_1 < k_2 < k_3 < \cdots \,</math> be positive integers, no two consecutive, and let <math>\, s_m = k_1 + k_2 + \cdots + k_m \,</math> ...e of the three given colors (red, blue, yellow), under the constraint that no two adjacent sides may be the same color. By making a sequence of such modi
  2 KB (391 words) - 07:58, 19 July 2016
• 2007 AMC 12B Problems/Problem 24
  Let <math>u = \frac{a}{b}</math>. Then the given equation becomes <math>u + \frac{14}{9u} = \frac{9u^2 + 14}{9u}</math>. ...ring the denominator and simplifying, we get a quadratic in terms of <math>u</math>:
  9 KB (1,522 words) - 22:46, 12 May 2022
• 1984 IMO Problems/Problem 4
  ...ath>, and with all conditions satisfied. We shall prove that there exists no point <math>T</math> on <math>CD</math> such that <math>T</math> is a midpo ...the circle with diameter <math>CD</math> touching <math>AB</math> at <math>U</math>(as well as the circle with diameter <math>AB</math> touching <math>C
  4 KB (750 words) - 23:49, 29 January 2021
• 1991 IMO Problems/Problem 4
  ...ge joining <math>v_i</math> and <math>v_{i+1}</math> with the number <math>u+i-1</math>. ...that vertex will be sorrounded by edges whose greates common factor is 1, no matter how the other edges sorrounding it are labelled. Notice that from o
  4 KB (668 words) - 17:45, 30 January 2021
• 2002 AMC 10B Problems
  ...<math>A</math>, <math>M</math>, <math>O</math>, <math>S</math>, and <math>U</math>, we can form five-letter "words". If these "words" are arranged in a ...ath> does the equation <math>\frac{x-1}{x-2} = \frac{x-k}{x-6}</math> have no solution for <math>x</math>?
  10 KB (1,540 words) - 22:53, 19 December 2023
• 1974 USAMO Problems
  ...her and son hold a family tournament, playing a two person board game with no ties. The tournament rules are: ...ngle ADB = \angle BDC = \angle CDA = 120^\circ</math>. Prove that <math>x=u+v+w</math>.
  3 KB (427 words) - 18:55, 3 July 2013
• 2007 AMC 10B Problems/Problem 25
  ...th>(a,b)</math> are there such that <math>a</math> and <math>b</math> have no common factors greater than <math>1</math> and: Let <math>u = \frac{a}{b}</math>. Then the given equation becomes <math>u + \frac{14}{9u} = \frac{9u^2 + 14}{9u}</math>.
  8 KB (1,425 words) - 23:05, 21 June 2023
• 2010 AIME I Problems/Problem 13
  ...ath>, and segment <math>CD</math> at distinct points <math>N</math>, <math>U</math>, and <math>T</math>, respectively. Line <math>\ell</math> divides re label("$U$",(87.13819,5.00321),NE/2);
  10 KB (1,418 words) - 23:05, 20 October 2021
• 2011 AIME I Problems/Problem 8
  ...math> on <math> \overline{CY} </math>, and points <math>Z</math> and <math>U</math> are on <math> \overline{AB} </math> with <math>Z</math> on <math> \o pair[] A, B, C, U, V, W, X, Y, Z;
  6 KB (1,077 words) - 21:47, 12 April 2022
• 1999 AMC 8 Problems
  label("U",(10,-2),S); The ratio of the number of games won to the number of games lost (no ties) by the Middle School Middies is <math>11/4</math>. To the nearest who
  17 KB (2,394 words) - 19:51, 8 May 2023
• 2011 USAMO Problems/Problem 3
  In hexagon <math>ABCDEF</math>, which is nonconvex but not self-intersecting, no pair of opposite sides are parallel. The internal angles satisfy <math>\ang ...}</cmath> <cmath>\vec{w} = \vec{CD} + \vec{FA}</cmath> Clearly, <math>\vec{u}+\vec{v}+\vec{w}=\textbf{0}</math>.
  11 KB (1,925 words) - 12:07, 31 August 2023
• Mock Amc 12
  ...ular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMCs in any given year, but ! scope="row" | '''Mock AMC U'''
  18 KB (2,206 words) - 19:41, 24 December 2020
• 2000 AMC 8 Problems/Problem 11
  Casework by the units digit <math>u</math> will help organize the answer. <math>u=0</math> gives no solutions, since no real numbers are divisible by <math>0</math>
  2 KB (382 words) - 15:59, 1 January 2024
• 2011 IMO Problems/Problem 2
  ...S}</math> be a finite set of at least two points in the plane. Assume that no three points of <math>\mathcal S</math> are collinear. A ''windmill'' is a (By u/basuboss on reddit)
  3 KB (577 words) - 23:19, 26 November 2023
• 1950 AHSME Problems
  ...igit number whose tens' digit is <math>t</math>, and units' digit is <math>u</math>, the new number is: ...extbf{(B)}\ 100t+10u+1\qquad\textbf{(C)}\ 1000t+10u+1\qquad\textbf{(D)}\ t+u+1\qquad\\ \textbf{(E)}\ \text{None of these answers} </math>
  22 KB (3,306 words) - 19:50, 3 May 2023
• BBCode:Tutorial
  ...utton is for underlining text. When you click on it, the symbols [u] and [/u] appear. Then you can type in whatever you want to be underlined: ...tags (not implemented on the top BBCode bar in the forums). There will be no grey box that there is when using [code][/code], and it will not automatica
  10 KB (1,680 words) - 19:26, 5 April 2023
• 2002 Romanian NMO Problems
  has no positive integer solutions. ...tarrow\mathbb{R}</math> be a function that has limits at any point and has no local extrema. Show that:
  10 KB (1,695 words) - 10:03, 10 May 2012
• 1955 AHSME Problems
  <math> \textbf{(A)}\ \text{no real values of }x\qquad\textbf{(B)}\ \text{either }x=1\text{ or }x=2\qquad\ The negation of the statement "No slow learners attend this school" is:
  22 KB (3,509 words) - 21:29, 31 December 2023
• 2020 Mock Combo AMC 10
  How many permutations of the string <math>AABBCC</math> are there such that no two identical letters are adjacent to each other? ...positive integers <math>s, t, u, v, w, x, y, z</math> where <math>s > t > u > v > w > x > y > z</math>.
  15 KB (2,452 words) - 03:03, 4 July 2020
• 2013 AMC 12A Problems/Problem 25
  ...part of a radical of a complex number: <math>\sqrt{u}</math>, where <math>u = v+wi = r e^{i\theta}</math>. <math>\operatorname{Im}(\sqrt{u}) = \operatorname{Im}(\pm \sqrt{r} e^{i\theta/2}) = \pm \sqrt{r} \sin(\thet
  4 KB (766 words) - 14:22, 8 October 2023

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