Difference between revisions of "1997 AIME Problems/Problem 2"
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== Problem == | == Problem == | ||
− | The nine horizontal and nine vertical lines on an <math>8\times8</math> | + | The nine horizontal and nine vertical lines on an <math>8\times8</math> checkerboard 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> |
== Solution == | == Solution == |
Revision as of 13:12, 21 November 2007
Problem
The nine horizontal and nine vertical lines on an checkerboard form rectangles, of which are squares. The number can be written in the form where and are relatively prime positive integers. Find
Solution
For r, we can choose two out of 9 lines, and 2 out of nine lines again, to get
For s, there are 8^2 unit squares, 7^2 2*2 squares, .... 1^1 8*8 squares. That gives us
See also
1997 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |