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• 2019 AIME I Problems/Problem 4
  ...layer on the field to sub out and one player on the bench that was not the original player subbed out. This gives us a total of <math>11\cdot 11\cdot 11\cdot 1 ~minor mistake fixed by [[User:Prism_melody|Prism Melody]]
  4 KB (551 words) - 10:32, 5 February 2022
• 2019 AIME II Problems/Problem 5
  ...520</math> is divided by <math>1000</math> is <math>\boxed{520}</math>. ~[[User:emerald_block|emerald_block]] Now, we are ready to tackle the original problem. If we forget about the numbers and the uniqueness of people, we wi
  8 KB (1,329 words) - 17:00, 27 January 2024
• 2019 IMO Problems/Problem 5
  We claim that this process is symmetrical to the original process on <math>n-1</math> coins, and thus it terminates and has the expec ...th>n-1</math> coins does, and has the same expected number of moves as the original. Thus, the claim is proven.
  10 KB (1,760 words) - 01:51, 19 November 2023
• 2020 AMC 10A Problems/Problem 14
  ...^2} + \frac{y^3}{x^2} + y = (88)(5) = \boxed{\textbf{(D)}\ 440}.</math> ~[[User:emerald_block|emerald_block]] We first change the original expression to <math>4 + \frac{x^5 + y^5}{x^2 y^2}</math>, because <math>x +
  13 KB (2,236 words) - 18:18, 1 April 2024
• 2020 AMC 10B Problems/Problem 25
  ...<math>3</math> somewhere in it, either by placing it somewhere next to the original numbers (in one of <math>n+1</math> ways, where <math>n</math> is the numbe ...+ 7 \cdot 6 + 9 \cdot 4 + 11 \cdot 1 = \boxed{\textbf{(A) }112}</math>. ~[[User:emerald_block|emerald_block]]
  16 KB (2,560 words) - 20:26, 11 November 2023
• 2021 AMC 10A Problems/Problem 15
  ...ction (we could flip <math>B</math> and <math>D</math> again to obtain the original choice (injectivity) and we could flip <math>B</math> and <math>D</math> fr ~[[User:emerald_block|emerald_block]]
  4 KB (577 words) - 19:18, 28 October 2022
• 2021 AMC 12A Problems/Problem 14
  Using these results, we evaluate the original expression: ~[[User:PowerQualimit|PowerQualimit]]
  6 KB (805 words) - 22:48, 23 November 2023
• 2021 AMC 10B Problems/Problem 22
  ~[[User:emerald_block|emerald_block]] ...elements, i.e. the number of permutations where no element appears in its original position. Recall the recursive formula <math>!0 = 1, !1 = 0, !n = (n-1)(!(n
  10 KB (1,448 words) - 21:49, 24 July 2023
• 2022 AIME II Problems/Problem 8
  ~[https://artofproblemsolving.com/wiki/index.php/User:Isabelchen isabelchen] ...th>n</math>, let <math>a</math>, <math>b</math>, and <math>c</math> be the original values of <math>\lfloor\frac{n}{4}\rfloor</math>, <math>\lfloor\frac{n}{5}\
  13 KB (2,136 words) - 22:39, 31 December 2023
• 1976 AHSME Problems/Problem 15
  ...>r=164</math>. Then, <math>d-r=179-164= \boxed{\textbf{(B) }15}</math>. ~[[User:Jiang147369|jiang147369]]
  1 KB (198 words) - 14:46, 20 July 2021
• 1981 AHSME Problems/Problem 25
  ...th>, thus <math>b^2=216</math>. So, <math>c<b</math> and the answer to the original problem is <math>c=\sqrt{40}=\boxed{2\sqrt{10}~\textbf{(A)}}</math>. ~ [[User:Aops-g5-gethsemanea2|Aops-g5-gethsemanea2]]
  2 KB (304 words) - 21:01, 9 August 2023
• 2022 USAMO Problems
  // Original polygon ...exist so that every user could eventually become friends with every other user?
  4 KB (762 words) - 13:45, 22 November 2023
• 2016 Mathcounts State Sprint Problems
  ...AisAdy23mKZZCGIGU_feUePztOco3QuUmNf3fIodik=?authuser=0&nonce=ial8h6qa099ic&user=110546807795006377675&hash=gkkuvej9jksp1bf0oq2dbuur2bk0nbhp| here] (Don't h value. The product of this new integer and the original integer is <math>91567</math>. What is
  11 KB (1,672 words) - 21:18, 12 March 2023
• Xarcade! (c)
  ...throughout 2023, and continues throughout 2024 to reign as the most active user-created game forum to today. ...w months, AlienGirl05, rct2021, ElectricWolverine, and NSAoPS are the only original forum staff members that remains staff, but the others have returned.
  6 KB (929 words) - 14:54, 5 March 2024
• Know the Facts: Gmaas
  ...Gmaas. This was made possible by the discovery of the missing pages of the original manuscript in Pompeii. ...Gmaas real name is Grayson Maas. He is the CEO of AoPS. EDIT: Gmaas's real name is Gmaas. He is not the CEO of AoPS. EDIT: Gmaas has always been the master
  88 KB (14,928 words) - 13:54, 29 April 2024
• Proofs of trig identities
  Pythagorean identities are easy and there's no algebra involved. In fact, the name Pythagorean is a giveaway of what we should do! This time we can't get it from our diagram. We need to go back to the original definition of tangent. This is the summary of my algebra: <math>\tan (\alph
  16 KB (2,796 words) - 13:12, 21 January 2024

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