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- ...math>40</math> coins in toll to Rabbit after each crossing. The payment is made after the doubling, Fox is excited about his good fortune until he discover {{AMC10 box|year=2016|ab=A|num-b=7|num-a=9}}1 KB (169 words) - 14:59, 8 August 2021
- ...regions is <math>1</math> foot wide on all four sides. What is the length in feet of the inner rectangle? ...x, 2x+6, 2x+14</math> is an arithmetic progression, meaning that the terms in the sequence increase by the same amount each term.2 KB (337 words) - 14:56, 25 June 2023
- ...sted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other communit ...etition. There is no guarantee that community members will make Mock AMCs in any given year, but there probably will be one.51 KB (6,220 words) - 21:22, 17 July 2024
- ...ns have been hosted on the Art of Problem Solving message boards. Some are made by one community member and administered to the AoPS community, while other ...on. There is no guarantee that community members will make Mock MATHCOUNTS in any given year, but it's usually a good bet that someone will.26 KB (3,265 words) - 21:34, 20 March 2024
- There is an unlimited supply of [[congruent]] [[equilateral triangle]]s made of colored paper. Each [[triangle]] is a solid color with the same color on ...wo triangles distinct, they must differ either in their center triangle or in the collection of colors which make up their outer three triangles.4 KB (695 words) - 10:37, 4 November 2023
- ...s, and is helpful in solving complex geometry problems involving lengths. In essence, it involves using a local [[coordinate system]] to identify [[poin ...hnique did not catch on until the 1960s when New York high school students made it popular. The technique greatly simplifies certain problems.5 KB (849 words) - 13:32, 3 July 2024
- ...sted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other communit ...etition. There is no guarantee that community members will make Mock AMCs in any given year, but there probably will be one.18 KB (2,206 words) - 19:41, 24 December 2020
- {{AMC10 Problems|year=2016|ab=A}} ...ss. Ben paid <math>\$12.50</math> more than David. How much did they spend in the bagel store together?13 KB (1,979 words) - 23:56, 2 July 2024
- ...region has been eliminated in 2015. It is uncertain about their existence in the future. *2016: Vincent Li (Whittier Middle School)4 KB (452 words) - 19:17, 9 February 2024
- Three numbers in the interval <math>\left[0,1\right]</math> are chosen independently and at ..., meaning the solution is <math>\boxed{\textbf{(C)}\;1/2}</math>, as shown in the graph below.10 KB (1,700 words) - 16:49, 16 May 2024
- ...rac{m}{n}</math> to study. Let <math>p</math> denote the previous fraction in the list and <math>x_\text{old}</math> (<math>0 \le x_\text{old} < k</math> ...the value <math>\lfloor n \{ x \} \rfloor</math>. Since the overall change in <math>f(x)</math> is positive as fractions <math>m/n</math> increase, we de12 KB (1,951 words) - 18:23, 4 April 2023
- ...0)</math>. Find the area of this circle in the first quadrant. The area is made of a semi-circle with radius of <math>\frac{\sqrt{2}}{2}</math> and a trian Because of symmetry, the area is the same in all four quadrants.1 KB (188 words) - 22:57, 9 January 2024
- In <math>\triangle ABC</math> let <math>I</math> be the center of the inscribe ...th>R+d=DL+LI=5</math>. Euler gives us that <math>d^{2}=R(R-2r)</math>, and in this case, <math>r=LI=2</math>. Thus, <math>d=\sqrt{R^{2}-4R}</math>. Solvi15 KB (2,694 words) - 13:36, 16 July 2024
- ...x^3)P'(x^5)P'(x^7)P'(x^9)</math>, we have made it so that all coefficients in <math>Q'(x)</math> are just the positive/absolute values of the coefficient ...s like this (including <math>P(x)P(x^3)P(x^5)P(x^7)P(x^9)</math>), we plug in <math>-1</math> to get <math>\frac{243}{32} \implies \boxed{275}</math>.2 KB (426 words) - 16:09, 21 July 2023
- The figure below shows a ring made of six small sections which you are to paint on a wall. You have four paint ...proceeding clockwise) such that the last section has color <math>C</math>. In general (except for when we complete the coloring), we see that20 KB (3,327 words) - 16:16, 7 June 2024
- {{AIME Problems|year=2016|n=II}} [[2016 AIME II Problems/Problem 1 | Solution]]8 KB (1,312 words) - 21:16, 3 March 2021
- ...e up. It is now 1,000,000 dollars for one math problem. Gmaas's technician made a mistake and reciprocated the fee," you must pay <math>1,000,000</math> to 4. Gmaas wants every fact to have a pi reference. Gmaas created pi. EDIT: He made it 3.1415926 times.69 KB (11,805 words) - 20:49, 18 December 2019
- ...h>M\in\overline{AB},</math> <math>Q\in\overline{AC},</math> and <math>N, P\in\overline{BC}.</math> Let <math>S</math> be the intersection of lines <math> Since the rotation between the two triangles in 90 degrees, <math>OI\perp MR</math>. However, <math>l</math> is parallel to8 KB (1,449 words) - 00:09, 12 October 2023
- Let us plug in <math>(5 * x)=1</math> into <math>3a-b</math>. Thus it would be <math>3(5)- ...o five. By substitution, we see that <math>5 * x</math> = 5. Solving for x in the equation <math>5(3)-x = 5</math> we get <cmath>x=\boxed{\textbf{(D)}1 KB (217 words) - 11:52, 20 June 2024
- ...th>30</math> minutes. As an old man, he can now walk <math>10</math> miles in <math>4</math> hours. How many minutes longer does it take for him to walk ...tes per mile. Now that he is an old man, he can walk <math>10</math> miles in <math>4</math> hours <math>= 4 \times 60</math> minutes <math>= 240</math>2 KB (274 words) - 11:42, 20 June 2024
