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• 2004 AIME I Problems
  ...} </math> if <math> i </math> is even. How many snakelike integers between 1000 and 9999 have four distinct digits? ...are two non-similar regular 7-pointed stars. How many non-similar regular 1000-pointed stars are there?
  9 KB (1,434 words) - 13:34, 29 December 2021
• 2004 AIME II Problems/Problem 14
  ...777c = 7000</math>, or dividing by <math>7</math>, <math>a + 11b + 111c = 1000</math>. Then the question is asking for the number of values of <math>n = a ...is the number of multiples of <math>9</math> from <math>0</math> to <math>1000</math>, or <math>112</math>.
  11 KB (1,857 words) - 21:55, 19 June 2023
• 2004 AIME II Problems/Problem 9
  ...a_n </math> be the greatest term in this sequence that is less than <math>1000</math>. Find <math> n+a_n. </math> ...<math>n</math> such that either <math>f(n)^2\, \mathrm{or}\, f(n)f(n-1) < 1000</math>. This happens with <math>f(7)f(8) = 29 \cdot 33 = 957</math>, and th
  3 KB (537 words) - 18:03, 25 May 2024
• 2004 AIME II Problems/Problem 6
  ...l to <math>17z/9</math>. This means there are two possible solutions under 1000: 408 and 816. Trial and error can be done quickly to find the smallest poss
  6 KB (950 words) - 14:18, 15 January 2024
• 2004 AIME II Problems/Problem 5
  In order to complete a large job, <math>1000</math> workers were hired, just enough to complete the job on schedule. All ...1000</math> miles per hour and has one hour to reach its destination <math>1000</math> miles away. After <math>15</math> minutes and <math>250</math> miles
  4 KB (592 words) - 19:02, 26 September 2020
• 2004 AIME II Problems/Problem 1
  ...ind the [[remainder]] when the product <math> abcdef </math> is divided by 1000.
  2 KB (329 words) - 23:20, 4 July 2013
• 2004 AIME II Problems
  ...e. Find the remainder when the product <math> abcdef </math> is divided by 1000. In order to complete a large job, 1000 workers were hired, just enough to complete the job on schedule. All the wo
  9 KB (1,410 words) - 05:05, 20 February 2019
• 1984 AIME Problems
  n-3 & \mbox{if }n\ge 1000 \\ f(f(n+5)) & \mbox{if }n<1000
  6 KB (933 words) - 01:15, 19 June 2022
• 1987 AIME Problems
  ...triples <math>(a,b,c)</math> of positive integers for which <math>[a,b] = 1000</math>, <math>[b,c] = 2000</math>, and <math>[c,a] = 2000</math>. ...e integer]] and <math>r</math> is a positive real number less than <math>1/1000</math>. Find <math>n</math>.
  6 KB (869 words) - 15:34, 22 August 2023
• 1989 AIME Problems
  A sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most fre
  7 KB (1,045 words) - 20:47, 14 December 2023
• 1991 AIME Problems
  Expanding <math>(1+0.2)^{1000}_{}</math> by the binomial theorem and doing no further manipulation gives ...\choose 1}(0.2)^1+{1000 \choose 2}(0.2)^2+\cdots+{1000 \choose 1000}(0.2)^{1000}</math></center>
  7 KB (1,106 words) - 22:05, 7 June 2021
• 1992 AIME Problems
  For how many pairs of consecutive integers in <math>\{1000,1001,1002^{}_{},\ldots,2000\}</math> is no carrying required when the two i
  8 KB (1,117 words) - 05:32, 11 November 2023
• 1993 AIME Problems
  ...rawn randomly and without replacement from the set <math>\{1, 2, 3,\ldots, 1000\}</math>. Three other numbers, <math>b_1, b_2, b_3</math>, are then drawn r
  8 KB (1,275 words) - 06:55, 2 September 2021
• 1994 AIME Problems
  ...What is the remainder when the 1994th term of the sequence is divided by 1000? ...94,\,</math> what is the remainder when <math>f(94)\,</math> is divided by 1000?
  7 KB (1,141 words) - 07:37, 7 September 2018
• 1996 AIME Problems
  ...th>. For how many positive integers <math>n</math> is it true that <math>n<1000</math> and that <math>\lfloor \log_{2} n \rfloor</math> is a positive even
  6 KB (931 words) - 17:49, 21 December 2018
• 1997 AIME Problems
  How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonneg
  7 KB (1,098 words) - 17:08, 25 June 2020
• 1998 AIME Problems
  Except for the first two terms, each term of the sequence <math>1000, x, 1000 - x,\ldots</math> is obtained by subtracting the preceding term from the on
  7 KB (1,084 words) - 02:01, 28 November 2023
• 1999 AIME Problems
  ...whose labels divide the label on the <math>i</math>-th switch. After step 1000 has been completed, how many switches will be in position <math>A</math>?
  7 KB (1,094 words) - 13:39, 16 August 2020
• 2000 AIME I Problems
  ...</math> and <math>b</math> are relatively prime positive divisors of <math>1000.</math> What is the greatest integer that does not exceed <math>\frac{S}{10
  7 KB (1,204 words) - 03:40, 4 January 2023
• 2003 AIME I Problems
  An integer between <math>1000</math> and <math>9999,</math> inclusive, is called balanced if the sum of i ...> m </math> and <math> n </math> are positive integers with <math> m + n < 1000, </math> find <math> m + n. </math>
  6 KB (965 words) - 16:36, 8 September 2019

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