Difference between revisions of "1997 AIME Problems/Problem 2"
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== Solution == | == Solution == | ||
| + | For r, we can choose two out of 9 lines, and 2 out of nine lines again, to get <math>r=(\binom{9}{2})^2=36^2=1296</math> | ||
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| + | For s, there are 8^2 unit squares, 7^2 2*2 squares, .... 1^1 8*8 squares. That gives us <math>s=1^2+2^2+\cdots+8^2=\dfrac{8*9*17}{6}=12*17=204</math> | ||
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| + | <math>\dfrac{204}{1296}=\dfrac{17}{108}</math> | ||
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| + | <math>m+n=125</math> | ||
== See also == | == See also == | ||
* [[1997 AIME Problems]] | * [[1997 AIME Problems]] | ||
Revision as of 11:21, 11 October 2007
Problem
The nine horizontal and nine vertical lines on an 
checkeboard 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 
