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• 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 I Problems/Problem 9
  ==Problem== ...9</math> and <math>10</math>. <math>\boxed{(8,9)}</math> and <math>\boxed{(9,10)}</math> both work.
  7 KB (1,208 words) - 09:21, 4 October 2022

Page text matches

• 2019 AIME I Problems/Problem 2
  ==Problem== ...ty that <math>B-J \ge 2</math> is <math>1-\frac{1}{2}-\frac{1}{20} = \frac{9}{20} \implies \boxed{029}</math>
  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
• Gmaas
  ...into anything. Using that fact, you can use the Games theorem to solve any problem. 9. He hates contemporary music. He only like Renaissance music, Baroque music
  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== draw(J+9/8*(K-J)--K+9/8*(J-K),dashed);
  7 KB (1,053 words) - 14:58, 14 January 2024
• 2019 AIME II Problems/Problem 15
  ==Problem== <cmath>\cos C=\cos\left(\tfrac 12 (\pi-Q)\right)=\sin\tfrac 12 Q=\sqrt{\frac{9}{40}}.</cmath>
  7 KB (1,129 words) - 16:27, 6 January 2025
• 2019 AIME II Problems/Problem 8
  ==Problem== ...ing <math>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 <m
  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== ...nds will converge to such a value (since it is unique, as indicated in the problem). Let's keep track of the lower bound.
  8 KB (1,172 words) - 18:21, 8 August 2024
• 2019 AIME II Problems/Problem 11
  ==Problem== ...e <math>ABC</math> has side lengths <math>AB=7, BC=8, </math> and <math>CA=9.</math> Circle <math>\omega_1</math> passes through <math>B</math> and is t
  14 KB (2,229 words) - 14:57, 27 December 2024
• 2019 AIME II Problems/Problem 13
  ==Problem== ...r arc <math>\widehat{A_3A_4}</math> of the circle has area <math>\tfrac{1}{9}.</math> There is a positive integer <math>n</math> such that the area of t
  7 KB (1,051 words) - 20:45, 27 January 2024
• 2019 AIME I Problems
  {{AIME Problems|year=2019|n=I}} ==Problem 1==
  8 KB (1,331 words) - 06:57, 4 January 2021
• 2019 AIME I Problems/Problem 1
  ==Problem== Consider the integer <cmath>N = 9 + 99 + 999 + 9999 + \cdots + \underbrace{99\ldots 99}_\text{321 digits}.</c
  3 KB (433 words) - 07:57, 9 February 2023
• 2019 AIME I Problems/Problem 6
  ==Problem== ...own above. Note that <math>m\angle KPL = 90^{\circ}</math> as given in the problem. Since <math>\angle KPL \cong \angle KLN</math> and <math>\angle PKL \cong
  11 KB (1,782 words) - 23:29, 29 January 2025
• 2019 AIME II Problems
  {{AIME Problems|year=2019|n=II}} ==Problem 1==
  7 KB (1,254 words) - 14:45, 21 August 2023

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