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• 2022 AIME II Problems/Problem 8
  ...we can also say that if <math>60k+l</math> is a solution, then <math>60k-l-1</math> is a solution! Therefore, one doesn't have to go as far as determi ...and <math>20</math> possibilities for cases 2 and 4 each. However, we over-counted the cases where
  13 KB (2,136 words) - 22:39, 31 December 2023
• 2022 AIME II Problems/Problem 9
  ...mula of this recursion: <math>f(n+1)=f(n)+N_a+\frac{n\cdot (N_a) \cdot (N_a-1)}{2}</math>, where <math>N_a</math> is the number of points on <math>\ell_ ...>, it crosses <math>m*(n-2)</math> lines, thus making additional <math>m*(n-2)+1</math> bounded regions; etc. By simple algebra/recursion methods, we se
  12 KB (2,025 words) - 14:56, 25 January 2024
• 2023 IOQM Problems
  Let <math>x, y</math> be positive integers such that<cmath>x^{4}=(x-1)(y^{3}-23)-1</cmath> ...n^2-5n+16</math>, where n is an integer. Find the maximum value of <math>|m-n|</math>.
  7 KB (1,225 words) - 03:05, 4 May 2024
• 1981 AHSME Problems/Problem 22
  413 bytes (62 words) - 23:45, 12 November 2023
• G285 2021 Summer Problem Set
  ...o the Birthday Problem Set! In this set, there are multiple choice AND free-response questions. Feel free to look at the solutions if you are stuck: ...rs <math>P=\{a,b,c \cdots \}</math> from the set <math>S=\{1,2,3,4 \cdots k-1,k \}</math> such that the sum of all elements in <math>P</math> is <math>k
  9 KB (1,577 words) - 23:28, 28 June 2021
• 2022 AMC 10B Problems
  Define <math>x\diamond y</math> to be <math>|x-y|</math> for all real numbers <math>x</math> and <math>y.</math> What is th How many three-digit positive integers have an odd number of even digits?
  15 KB (2,224 words) - 13:10, 20 February 2024
• PaperMath’s sum
  3 KB (549 words) - 17:22, 27 March 2024
• 2021 IMO Problems/Problem 4
  ...,XA=XF-AM;ZC=ZJ-CN</math> Same reason, we can get that <math>DT=TN-DM;DY=YM-DM</math> <cmath>AD + DT + XA = AN+ND + TM – MD +XP-PA =</cmath>
  7 KB (1,196 words) - 10:30, 18 June 2023
• 2022 AMC 8 Problems/Problem 24
  pair E = F + r * dir(- 45 - theta/2), D = I+E-F; pair H = J + r * dir(135 + theta/2), A = B+H-J;
  3 KB (527 words) - 15:03, 23 November 2023
• 2021 IMO Problems/Problem 2
  <cmath>\sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i-x_j|} \le \sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i+x_j|}</cmath> \sum_{i=1}^{n}\sum_{j=1}^{n}(\sqrt{x_i-x_j}^4)\leq \sum_{i=1}^{n}\sum_{j=1}^{n}(\sqrt{x_i+x_j}^4)</cmath>
  1 KB (238 words) - 06:11, 24 April 2024
• 2021 Fall AMC 12B Problems/Problem 12
  ...isors of <math>384</math> is <cmath>\sum_{k=2}^{9}2^k = \frac{2^{10}-2^2}{2-1} = 1020,</cmath> from which <math>f(384) = \frac{1020}{384}.</math> Simila ...}\left(\sum_{j=0}^{e_i}p_i^j\right)=\prod_{i=1}^{k}\frac{p_i^{e_i+1}-1}{p_i-1}</cmath> by geometric series.
  6 KB (901 words) - 13:48, 4 April 2024
• 2021 Fall AMC 12A Problems/Problem 20
  ...f <math>n</math>, and for <math>j \ge 2</math>, let <math>f_j(n) = f_1(f_{j-1}(n))</math>. For how many values of <math>n \le 50</math> is <math>f_{50}( {{AMC12 box|year=2021 Fall|ab=A|num-b=19|num-a=21}}
  10 KB (1,622 words) - 16:56, 5 June 2024
• 2021 Fall AMC 10B Problems/Problem 22
  {{AMC10 box|year=2021 Fall|ab=B|num-b=21|num-a=23}}
  5 KB (901 words) - 18:36, 13 November 2023
• 2021 Fall AMC 10B Problems/Problem 13
  ...> of <math>C</math> is <math>0</math>. Using this, we find that the <math>y-value</math> is <math>9</math>. So the coordinates of <math>C</math> are <ma We know that the <math>y-value</math> is <math>0</math>. Plugging this in, we find <math>0 = -4x +9</
  6 KB (881 words) - 22:41, 10 November 2023
• 2021 Fall AMC 12A Problems
  What is the value of <math>\frac{(2112-2021)^2}{169}</math>? The six-digit number <math>\underline{2}\,\underline{0}\,\underline{2}\,\underline{1
  15 KB (2,452 words) - 19:37, 7 June 2023
• 2021 WSMO Team Round Problems
  How many ways are there to pick a three-letter word using only letters from "Winter Solstice" such that the word is .../math>, where <math>A_nB_nC_n</math> is outside of <math>A_{n-1}B_{n-1}C_{n-1}</math>. Find the value of <cmath>\left(\sum_{i=1}^{\infty}[A_iB_iC_i]\rig
  7 KB (1,137 words) - 12:40, 6 June 2022
• 2022 AMC 8 Problems
  ...gned a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches? int mod12(int i) {if (i<13) {return i;} else {return i-12;}}
  20 KB (2,805 words) - 14:53, 6 July 2024
• 2022 AMC 8 Problems/Problem 10
  int mod12(int i) {if (i<13) {return i;} else {return i-12;}} <ul style="list-style-type:square;">
  5 KB (774 words) - 04:59, 22 January 2024
• 2021 WSMO Team Round/Problem 2
  960 bytes (160 words) - 14:45, 6 July 2023
• 1994 IMO Problems
  3 KB (545 words) - 14:01, 19 April 2024

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