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• 2005 AIME I Problems
  ...> A(0,12), B(10,9), C(8,0), </math> and <math> D(-4,7). </math> There is a unique square <math> S </math> such that each of the four points is on a different
  6 KB (983 words) - 05:06, 20 February 2019
• 2005 AIME I Problems/Problem 14
  ...h> A(0,12), B(10,9), C(8,0),</math> and <math> D(-4,7). </math> There is a unique [[square]] <math> S </math> such that each of the four points is on a diffe
  3 KB (561 words) - 14:11, 18 February 2018
• 2004 AIME II Problems/Problem 4
  ...digit, there are <math>9</math> possibilities. When <math>n</math> has two unique digits there are two cases. Case 1: two digits are the same with each other
  3 KB (508 words) - 01:16, 19 January 2024
• 1983 AIME Problems
  For <math>\{1, 2, 3, \ldots, n\}</math> and each of its nonempty subsets a unique '''alternating sum''' is defined as follows. Arrange the numbers in the sub
  7 KB (1,104 words) - 12:53, 6 July 2022
• 1987 AIME Problems
  What is the largest positive integer <math>n</math> for which there is a unique integer <math>k</math> such that <math>\frac{8}{15} < \frac{n}{n + k} < \fr
  6 KB (869 words) - 15:34, 22 August 2023
• 1988 AIME Problems
  ..., <math>w_4 = 1 + 27i</math>, and <math>w_5 = -14 + 43i</math>, there is a unique mean line with y-intercept <math>3</math>. Find the slope of this mean line
  6 KB (902 words) - 08:57, 19 June 2021
• 1989 AIME Problems
  ...h between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let <math>D^{}_{}</math> be the difference betw is true for a unique choice of non-negative integer <math>m^{}_{}</math> and digits <math>a_0,a_
  7 KB (1,045 words) - 20:47, 14 December 2023
• 1991 AIME Problems
  ...\ldots,a_n^{}</math> are positive real numbers whose sum is 17. There is a unique positive integer <math>n^{}_{}</math> for which <math>S_n^{}</math> is also
  7 KB (1,106 words) - 22:05, 7 June 2021
• 1997 AIME Problems
  ...f(f(x))=x</math> for all values except <math>\frac{-d}{c}</math>. Find the unique number that is not in the range of <math>f</math>.
  7 KB (1,098 words) - 17:08, 25 June 2020
• 2000 AIME II Problems
  Every positive integer <math>k</math> has a unique factorial base expansion <math>(f_1,f_2,f_3,\ldots,f_m)</math>, meaning tha
  6 KB (947 words) - 21:11, 19 February 2019
• 1983 AIME Problems/Problem 13
  ...or <math>\{1, 2, 3, \ldots, n\}</math> and each of its non-empty subsets a unique '''alternating sum''' is defined as follows. Arrange the numbers in the sub
  5 KB (894 words) - 22:02, 5 April 2024
• 1983 AIME Problems/Problem 15
  ...assume that the answer is unique, but would need to prove that this is the unique solution. This can be proven as follows.
  19 KB (3,221 words) - 01:05, 7 February 2023
• 1984 AIME Problems/Problem 11
  ...remove <math>4</math> trees that aren't birch. What you are left with is a unique arrangement of <math>5</math> birch trees and <math>3</math> other trees th ...ve <math>4</math> trees. Adding a tree between each pair of people gives a unique arrangement of <math>5</math> nonadjacent birch trees.
  7 KB (1,115 words) - 00:52, 7 September 2023
• 1987 AIME Problems/Problem 8
  What is the largest positive integer <math>n</math> for which there is a unique integer <math>k</math> such that <math>\frac{8}{15} < \frac{n}{n + k} < \fr ...\frac{7n}{8}</math>. Thus, <math>48n < 56k < 49n</math>. <math>k</math> is unique if it is within a maximum [[range]] of <math>112</math>, so <math>n = 112</
  2 KB (393 words) - 16:59, 16 December 2020
• 1988 AIME Problems/Problem 11
  ...<math>w_4 = 1 + 27i</math>, and <math>w_5 = - 14 + 43i</math>, there is a unique mean line with <math>y</math>-intercept 3. Find the [[slope]] of this mean
  2 KB (422 words) - 00:22, 6 September 2020
• 1989 AIME Problems/Problem 14
  is true for a unique choice of non-negative integer <math>m</math> and digits <math>a_0,a_1,\ldo
  2 KB (408 words) - 17:28, 16 September 2023
• 1989 AIME Problems/Problem 11
  ...h between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique [[mode]] (most frequent value). Let <math>D</math> be the difference betwee
  5 KB (851 words) - 18:01, 28 December 2022
• 1991 AIME Problems/Problem 15
  ...\ldots,a_n^{}</math> are positive real numbers whose sum is 17. There is a unique positive integer <math>n^{}_{}</math> for which <math>S_n^{}</math> is also
  4 KB (658 words) - 16:58, 10 November 2023
• 1992 AIME Problems/Problem 10
  ...he area outside the two circles but inside the square, we want to find the unique area of the two circles. We can do this by adding the area of the two circl
  2 KB (323 words) - 12:05, 16 July 2019
• 1994 AIME Problems/Problem 7
  ...of <math>\frac{12}{2}=6</math> lines. Finally, we add the <math>12</math> unique tangent lines to the circle at each of the lattice points.
  3 KB (442 words) - 19:51, 8 January 2024

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