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• 2019 AIME I Problems/Problem 3
  ==Problem== dot((3,4));
  6 KB (933 words) - 19:30, 29 January 2025
• 2019 AIME II Problems/Problem 3
  ==Problem== ...ons. Similarly, <math>72 = 2^3 \cdot 3^2</math>, so <math>d(72) = 4 \times 3 = 12</math>.
  2 KB (272 words) - 21:05, 23 December 2023

Page text matches

• Mock AMC
  ...ake. Sometimes, the administrator may ask other people to sign up to write problems for the contest. * Look at past [[AMC]]/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.
  51 KB (6,175 words) - 21:41, 27 November 2024
• 2019 AIME I Problems/Problem 2
  ==Problem== ...math>. Bela then randomly chooses a number <math>B</math> from <math>1, 2, 3,\ldots, 19, 20</math> distinct from <math>J</math>. The value of <math>B -
  5 KB (831 words) - 18:47, 29 January 2025
• Chicken McNugget Theorem
  ...n McNugget Theorem''' (or '''Postage Stamp Problem''' or '''Frobenius Coin Problem''') states that for any two [[relatively prime]] [[positive integer]]s <mat ...t Theorem has also been called the Frobenius Coin Problem or the Frobenius Problem, after German mathematician Ferdinand Frobenius inquired about the largest
  17 KB (2,823 words) - 23:06, 15 November 2024
• Mass points
  ...eorems concerning [[polygon]]s, and is helpful in solving complex geometry problems involving lengths. In essence, it involves using a local [[coordinate syst ...school students made it popular. The technique greatly simplifies certain problems.
  5 KB (812 words) - 15:43, 1 March 2025
• Ball-and-urn
  ...<math>3</math> bins. The number of ways to do such is <math>{4+3-1 \choose 3-1} = {6 \choose 2} = 15</math>. ...ach urn, then there would be <math>{n \choose k}</math> possibilities; the problem is that you can repeat urns, so this does not work.<math>n</math> and then
  5 KB (795 words) - 17:39, 31 December 2024
• Gmaas
  ...into anything. Using that fact, you can use the Games theorem to solve any problem. ...e now eats gnats again. He thinks that they taste like pi(e). EDIT: He ate 3,141,592,653,589,793,238,462,643,383 so far.
  69 KB (11,805 words) - 20:49, 18 December 2019
• 2018 AIME II
  ...k contains the full set of test problems. The rest contain each individual problem and its solution. * [[2018 AIME II Problems|Entire Test]]
  1 KB (133 words) - 18:13, 18 March 2020
• 2019 AIME I
  ...k contains the full set of test problems. The rest contain each individual problem and its solution. * [[2019 AIME I Problems|Entire Test]]
  1 KB (133 words) - 17:41, 29 March 2019
• 2019 AIME II
  ...k contains the full set of test problems. The rest contain each individual problem and its solution. * [[2019 AIME II Problems|Entire Test]]
  1 KB (133 words) - 15:43, 22 March 2019
• 2020 AIME I
  ...k contains the full set of test problems. The rest contain each individual problem and its solution. * [[2020 AIME I Problems|Entire Test]]
  1 KB (133 words) - 18:11, 18 March 2020
• 2018 AIME II Problems
  {{AIME Problems|year=2018|n=II}} ==Problem 1==
  9 KB (1,385 words) - 00:26, 21 January 2024
• 2019 AMC 10C Problems
  Here are the problems from the 2019 AMC 10C, a mock contest created by the AoPS user fidgetboss_4000. ==Problem 1==
  12 KB (1,917 words) - 12:14, 29 November 2021
• 2019 AIME II Problems/Problem 7
  ==Problem== ==Solution 3==
  7 KB (1,053 words) - 14:58, 14 January 2024
• 2019 AIME II Problems/Problem 15
  ==Problem== ...c= \frac{(b\cos B)(c\cos C)}{\cos B\cos C}=\frac{16\cdot 21}{(2/\sqrt{35})(3/\sqrt{40})}=560\sqrt{14}.</cmath>
  7 KB (1,129 words) - 16:27, 6 January 2025
• 2019 AIME II Problems/Problem 8
  ==Problem== ...2019</math>, and <math>f\left(\tfrac{1+\sqrt{3}i}{2}\right)=2015+2019\sqrt{3}i</math>. Find the remainder when <math>f(1)</math> is divided by <math>100
  4 KB (706 words) - 22:18, 28 December 2023
• 2019 AIME II Problems/Problem 9
  ==Problem== ...pretty. Let <math>S</math> be the sum of positive integers less than <math>2019</math> that are <math>20</math>-pretty. Find <math>\tfrac{S}{20}</math>.
  3 KB (474 words) - 01:38, 22 December 2024
• 2019 AIME II Problems/Problem 10
  ==Problem== ...heta\right)}</math> is positive when <math>n</math> is a multiple of <math>3</math>, and negative otherwise. The degree measure of <math>\theta</math> i
  8 KB (1,172 words) - 18:21, 8 August 2024
• 2019 AIME II Problems/Problem 11
  ==Problem== == Solution 3 (Death By Trig Bash) ==
  14 KB (2,229 words) - 14:57, 27 December 2024
• 2019 AIME II Problems/Problem 13
  ==Problem== ...l be \(3+2\sqrt2\). Now \(\frac{PU}{\sqrt{2}} + \frac{PV}{\sqrt{2}} + PW = 3+2\sqrt2\) which gives:
  7 KB (1,051 words) - 20:45, 27 January 2024
• 2019 AIME II Problems/Problem 14
  ==Problem== ...guaranteed to not be divisible by one of the numbers <math>2</math>, <math>3</math>, and <math>4</math>.
  9 KB (1,543 words) - 19:48, 3 January 2025

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