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• 1985 AIME Problems/Problem 10
  ~[[User:N828335|N828335]] Finally, looking back at the original expression, we plug in <math>k</math> to get a multiple of <math>10</math>
  12 KB (1,859 words) - 18:16, 28 March 2022
• 1989 AIME Problems/Problem 10
  So now we can simplify our original expression: ~[[User: Yiyj1|Yiyj1]]
  8 KB (1,401 words) - 21:41, 20 January 2024
• 2000 AMC 12 Problems/Problem 8
  ...econd differences are constant and all equal to <math>4</math>. Thus, the original sequence can be generated from a quadratic function. ...n = 5050</math> squares. <math>4 \cdot 5050 = 20200</math>. Adding in the original center box we have <math> 20200 + 1 = \boxed{\textbf{(C) }20201}</math>.
  8 KB (1,202 words) - 16:17, 10 May 2024
• Mock MathCounts
  * <b>Make sure the problems are original.</b> The AoPS community does not want to waste time seeing a collection of Note that "author" is the user(s) who started the mock competition, not their helpers.
  26 KB (3,265 words) - 21:34, 20 March 2024
• Asymptote: CSE5
  ...ttp://www.artofproblemsolving.com/Forum/viewtopic.php?t=149650 here]. The original idea for writing CSE5 was to enable writing terse codes for complicated pic ...h function; a function with a full name and a function with an abbreviated name.
  4 KB (607 words) - 15:09, 30 June 2020
• 2009 AMC 10B Problems/Problem 15
  -[[User:Sweetmango77|SweetMango77]] I restored the original video solution that was deleted by Whitelisted and replaced with a Rick Rol
  3 KB (545 words) - 13:37, 3 September 2023
• Pascal (language)
  ...p. Pascal also draws programming components from ALGOL 68 and ALGOL-W. The original published definition for the Pascal language appeared in 1971 with latter r User defined Data Types - Has the ability to define scalar types as well as subr
  2 KB (296 words) - 15:37, 1 December 2015
• Python reference
  .... The function itself takes two parameters. The first is a string with the name of the file. ...o min() except it returns the largest element. If we were working with the original value of ls (which is [1,2,3,4,5]) then this would return 5.
  28 KB (4,762 words) - 21:20, 12 June 2023
• 2002 AMC 10B Problems/Problem 23
  ~[[User:emerald_block|emerald_block]] ...aren't given anything that has odd numbers ( without substitution into the original equation), we need to find two numbers that add up to 12, which result from
  5 KB (781 words) - 06:38, 23 October 2023
• 2010 AMC 8 Problems/Problem 22
  ...the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result? ...101c+10b+2</math>. Subtracting this expression from the expression for the original number, we get <math>(101c+10b+200) - (101c+10b+2) = 198</math>. Thus, the
  2 KB (338 words) - 09:06, 10 March 2023
• CSS
  Rephrased by some AoPS user, CSS is a language that a webpage can be styled with. In Art of Problem Solving, CSS of AoPS user's blogs can be modified by the respective owner.
  5 KB (846 words) - 22:23, 13 July 2022
• 2013 IMO Problems/Problem 4
  //Original diagram by suli, August 2014. Feel free to make edits, but please leave thi --[[User:Suli|Suli]] 13:51, 25 August 2014 (EDT)
  11 KB (1,991 words) - 01:31, 19 November 2023
• 2015 AMC 12B Problems/Problem 17
  ...text so that the answer would make sense. [[User:Adihaya|— @adihaya]] ([[User talk:Adihaya|talk]]) 15:23, 19 February 2016 (EST)
  3 KB (399 words) - 21:24, 13 February 2021
• Searching the community
  ...mple, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted | Posted By User
  21 KB (3,334 words) - 23:53, 23 March 2022
• 2016 AMC 12B Problems/Problem 4
  since the larger the original angle, the smaller the complement. ...sures is <math>5x + 4x = 9x = 9(15) = \boxed{\textbf{(C)}\ 135}</math>. ~[[User:emerald_block|emerald_block]]
  2 KB (254 words) - 20:49, 6 November 2021
• 2016 AMC 8 Problems/Problem 22
  ~[[User:Bloggish|Bloggish]] // Original drawing code
  8 KB (1,157 words) - 16:12, 18 January 2024
• 2017 AMC 10A Problems/Problem 24
  ~[[User: Yiyj1|Yiyj1]] ...-a} = 10</math>, <cmath>\therefore c=10(1-a)=10*90=900</cmath> Solving the original problem, <math>f(1)=1 + 1 + b + 100 + c = 102+b+c=102+900-8009=\boxed{\text
  10 KB (1,708 words) - 23:16, 7 October 2023
• 2018 AIME II Problems/Problem 5
  Written by [[User:A1b2|a1b2]] ...z=240(5+3i).</math> Dividing this by each of the equations provided in the original problem, we get <math>x=20+12i,y=-10-10i,</math> and <math>z=-3+3i</math>.
  11 KB (2,077 words) - 20:15, 12 January 2024
• 2019 AIME II Problems/Problem 7
  ..., 22.5, and 27.5 into a equilateral triangle with side length 1. Then, the original triangle gets turned into a equilateral triangle with side length 8. Since ~ [[User:Afly|Afly]] ([[User talk:Afly|talk]])
  7 KB (1,053 words) - 14:58, 14 January 2024
• 2019 USAJMO Problems/Problem 4
  ...Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */ Returning to our original problem:
  10 KB (1,536 words) - 20:27, 12 April 2021
• 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