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- ...etitions</td><td>2006-2007</td><td>2007-2008</td><td>2008-2009</td><td>2009-2010</td></tr>2 KB (383 words) - 22:32, 21 April 2010
- Which of the five "T-like shapes" would be symmetric to the one shown with respect to the dashed ...per is then cut in half along the dashed line. Three rectangles are formed-a large one and two small ones. What is the ratio of the perimeter of one o13 KB (1,765 words) - 11:55, 22 November 2023
- ascending chain of (two-sided) [[ideal]]s of <math>A[x]</math>. <math>\mathfrak{c}_{i,j}</math> is a two-sided ideal of <math>A</math>; furthermore,4 KB (617 words) - 19:59, 23 April 2023
- ...n\times n</math> determinant can be written in terms of <math>(n-1)\times(n-1)</math> determinants: where <math>m_i</math> is the <math>(n-1)\times(n-1)</math> matrix formed by removing the <math>1</math>st row and <math>i</ma8 KB (1,345 words) - 00:31, 9 May 2020
- By Schur's theorem (a generalization of the more well-known Chicken McNugget theorem), every integer greater than some integer <ma {{USAMO newbox|year=2004|num-b=1|num-a=3}}3 KB (508 words) - 14:23, 17 July 2014
- {{AHSME 35p box|year=1968|num-b=34|after=Last Problem}}3 KB (597 words) - 01:52, 16 August 2023
- <cmath>4.8-2.2=2.6\approx 2.5 \rightarrow \boxed{\text{B}}</cmath> {{AJHSME box|year=1989|num-b=18|num-a=20}}2 KB (255 words) - 03:28, 28 November 2019
- {{AJHSME box|year=1989|num-b=21|num-a=23}}1 KB (177 words) - 16:03, 19 April 2021
- **2010 - 65-67, qualified for CMOQR **2011 - 40-50, qualified for CMO6 KB (796 words) - 17:48, 26 December 2017
- ...= 1-P \Longleftrightarrow x_i = 1 \pm t</math> where <math>t = \pm \sqrt{1-P} \in \mathbb{R}</math>. Which has no non-zero solutions for <math>t</math>.2 KB (382 words) - 12:51, 29 January 2021
- ...Test.] When considering problem difficulty, '''put more emphasis on problem-solving aspects and less so on technical skill requirements'''. ...iple choice tests like AMC are rated as though they are free-response. Test-takers can use the answer choices as hints, and so correctly answer more AMC41 KB (6,751 words) - 11:02, 7 June 2024
- ...ile a chessboard polygon by dominoes is to exactly cover the polygon by non-overlapping <math>1 \times 2</math> rectangles. Finally, a ''tasteful tiling4 KB (718 words) - 18:16, 17 September 2012
- {{USAMO newbox|year=2009|num-b=5|after=Last question}}2 KB (463 words) - 12:19, 21 August 2020
- ...h> be distinct positive integers and let <math>M</math> be a set of <math>n-1</math> positive integers not containing <math>s=a_1+a_2+\ldots+a_n</math>. ...ts are identical, we can treat them as one and use induction on <math>n = k-1</math>. We now consider four cases:5 KB (1,055 words) - 01:18, 19 November 2023
- By AM-GM, {{USAMO newbox|year=1998|num-b=2|num-a=4}}2 KB (322 words) - 13:31, 23 August 2023
- Let us take a well-ordering on <math>I</math> (such an ordering exists by the [[well-ordering theorem]], a consequence of the [[axiom of choice]]),6 KB (1,183 words) - 15:02, 18 August 2009
- 3 KB (567 words) - 08:42, 21 August 2009
- For space-time saving we say that a positive integer is a T-number or simply is T if it has exactly three 1s in his base two representat * <math>f(2^n) = \tbinom n2 = \sum_{i=1}^{n-1} i</math> whence7 KB (1,298 words) - 19:59, 9 February 2024
- ...\sum_{x \in \mathbb{U}} (1-I_{(1,3)}(x))(1-I_{(3,1)}(x))(1-I_{(2,4)}(x))(1-I_{(4,2)}(x))</math> So there are <math>2 \times 2 = 4</math> non-zero pairs. Each pair however has 2 ways to rearrange. So the third sum equa11 KB (1,928 words) - 12:26, 26 July 2023
- *[[Mock AIME 3 2006-2007/Problem 2 | Next Problem]] *[[Mock AIME 3 2006-2007]]862 bytes (151 words) - 01:35, 30 December 2009
