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 12:12, 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 | ||
