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• The perfect squares from $1$ through $2500,$ inclusive, are printed in a sequence of digits $1491625\ldots2500.$ How many digits are in the sequence?
  961 bytes (143 words) - 16:25, 30 October 2024

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• 2016 AMC 10A Problems/Problem 12
  ...egers are selected at random between <math>1</math> and <math>2016</math>, inclusive. Which of the following is a correct statement about the probability <math>
  2 KB (302 words) - 01:57, 18 October 2024
• American Invitational Mathematics Examination
  ...h USAMTS only is rare, however. Each answer is an integer from 000 to 999, inclusive, making guessing almost futile. Wrong answers receive no credit, while cor
  5 KB (669 words) - 17:19, 11 March 2025
• Pigeonhole Principle
  ...'': Let <math>k</math> be an integer from <math>0</math> to <math>n</math> inclusive. Note that for all of <math>0x, 1x, \ldots, nx</math>, we can write <math>k
  11 KB (1,980 words) - 22:39, 19 February 2025
• Constructive counting
  ...re there such that each entry is between <math>2</math> and <math>9</math> inclusive and no two consecutive entries are equal?'' ...the four integers. They must be between <math>1</math> and <math>9</math> inclusive, and no digit can be repeated, so the combination that describes this is <m
  13 KB (2,018 words) - 15:31, 10 January 2025
• Correspondence
  Consider the task of counting the number of integers between 14 and 103 inclusive. We could simply list those [[integers]] and count them. However, we can ...art our list with <math>n</math> and end with <math>m</math> (i.e. m and n inclusive), the number of integers in the list is
  2 KB (289 words) - 17:17, 13 February 2009
• 2005 USAMO Problems/Problem 4
  ...we note that <math>k_i</math> range from <math>0</math> to <math>n</math>, inclusive. For <math>m=0</math>, each of <math>(k_1,k_4)</math> and <math>(k_2,k_3)</
  7 KB (1,276 words) - 20:51, 6 January 2024
• International Mathematical Olympiad
  Scoring on each problem is done on a 0-7 scale (inclusive and integers only). Full credit is only given for complete, correct soluti
  3 KB (485 words) - 03:31, 3 February 2025
• 2006 AIME I Problems/Problem 9
  .... All that's left is to count the number of odd integers between 1 and 91 (inclusive), which yields <math>\boxed{046}</math>.
  4 KB (651 words) - 18:27, 22 May 2021
• 2006 AIME I Problems/Problem 8
  ...</math> can be any [[integer]] between <math>1</math> and <math>89</math>, inclusive, so the number of positive values for <math>K</math> is <math>\boxed{089}</
  5 KB (735 words) - 16:15, 3 February 2025
• 2000 AMC 12 Problems
  ...pick six different integers from <math>1</math> through <math>46</math>, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his s
  13 KB (1,948 words) - 10:35, 16 June 2024
• 2006 AMC 12B Problems/Problem 19
  ...iscard one number from the integers <math>1</math> through <math>9</math>, inclusive (<math>8</math> children, oldest is <math>9</math>), and there's always goi
  4 KB (696 words) - 09:47, 10 August 2015
• 2006 AMC 10A Problems
  Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers has a difference
  13 KB (2,028 words) - 16:32, 22 March 2022
• 2006 AMC 10A Problems/Problem 20
  ...integers are randomly chosen between <math>1</math> and <math>2006</math>, inclusive. What is the probability that some pair of these integers has a difference
  1 KB (187 words) - 08:21, 17 March 2023
• 2005 AIME I Problems/Problem 12
  ...for the difference between <math>2005</math> and <math>44^2 = 1936</math>, inclusive. Notice that if we align the two and subtract, we get that each difference
  4 KB (647 words) - 02:29, 4 May 2021
• 2004 AIME I Problems/Problem 2
  ...find the number of integers between <math>-98</math> and <math>102</math>, inclusive, and it is <math>m = \boxed{201}</math>.
  8 KB (1,431 words) - 17:50, 29 December 2024
• 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 frequent valu
  7 KB (1,045 words) - 10:33, 12 March 2025
• 1992 AIME Problems
  ...and imaginary parts between <math>0^{}_{}</math> and <math>1^{}_{}</math>, inclusive. What is the integer that is nearest the area of <math>A^{}_{}</math>?
  8 KB (1,117 words) - 05:32, 11 November 2023
• 1997 AIME Problems
  How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integ
  7 KB (1,098 words) - 17:08, 25 June 2020
• 2000 AIME I Problems
  ...every integer <math>k</math> between <math>1</math> and <math>100,</math> inclusive, the number <math>x_{k}</math> is <math>k</math> less than the sum of the o
  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 its two leftmost digits equals the sum of
  6 KB (965 words) - 16:36, 8 September 2019

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