Difference between revisions of "2003 AIME I Problems/Problem 2"
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== Problem == | == Problem == | ||
| + | One hundred concentric circles with radii <math> 1, 2, 3, \dots, 100 </math> are drawn in a plane. The interior of the circle of radius 1 is colored red, and each region bounded by consecutive circles is colored either red or green, with no two adjacent regions the same color. The ratio of the total area of the green regions to the area of the circle of radius 100 can be expressed as <math> m/n, </math> where <math> m </math> and <math> n </math> are relatively prime positive integers. Find <math> m + n. </math> | ||
== Solution == | == Solution == | ||
| + | |||
| + | {{solution}} | ||
== See also == | == See also == | ||
* [[2003 AIME I Problems]] | * [[2003 AIME I Problems]] | ||
Revision as of 22:16, 15 July 2006
Problem
One hundred concentric circles with radii 
are drawn in a plane. The interior of the circle of radius 1 is colored red, and each region bounded by consecutive circles is colored either red or green, with no two adjacent regions the same color. The ratio of the total area of the green regions to the area of the circle of radius 100 can be expressed as 
where 
and 
are relatively prime positive integers. Find 
Solution
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