MathDB

2

Part of 2003 AIME Problems

Problems(2)

100 Circles

Source:

5/11/2006
One hundred concentric circles with radii 1,2,3,…,1001, 2, 3, \dots, 100 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 m/nm/n, where mm and nn are relatively prime positive integers. Find m+nm + n.
ratiogeometrynumber theoryrelatively prime
Multiples of 8

Source:

12/26/2006
Let NN be the greatest integer multiple of 8,8, no two of whose digits are the same. What is the remainder when NN is divided by 1000?1000?
AMCAIME