Difference between revisions of "1997 AIME Problems"

(Problem 2)
(Problem 2)
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== Problem 2 ==
 
== Problem 2 ==
 
The nine horizontal and nine vertical lines on an <math>8\times8</math> checkeboard form <math>r</math> rectangles, of which <math>s</math> are squares.  The number <math>s/r</math> can be written in the form <math>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers.  Find <math>m + n.</math>
 
The nine horizontal and nine vertical lines on an <math>8\times8</math> checkeboard form <math>r</math> rectangles, of which <math>s</math> are squares.  The number <math>s/r</math> can be written in the form <math>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers.  Find <math>m + n.</math>
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[[1997 AIME Problems/Problem 2|Solution]]
 
[[1997 AIME Problems/Problem 2|Solution]]
  

Revision as of 11:18, 11 October 2007

Problem 1

How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers?

Solution

Problem 2

The nine horizontal and nine vertical lines on an $8\times8$ checkeboard form $r$ rectangles, of which $s$ are squares. The number $s/r$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

See also

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