MathDB

2

Part of 2004 AIME Problems

Problems(2)

Sets and sums.

Source:

11/27/2005
Set AA consists of mm consecutive integers whose sum is 2m2m, and set BB consists of 2m2m consecutive integers whose sum is mm. The absolute value of the difference between the greatest element of AA and the greatest element of BB is 9999. Find mm.
absolute valueP2 catalystwilkinson catalystbirch reduction
Candy

Source:

11/17/2005
A jar has 10 red candies and 10 blue candies. Terry picks two candies at random, then Mary picks two of the remaining candies at random. Given that the probability that they get the same color combination, irrespective of order, is m/nm/n, where mm and nn are relatively prime positive integers, find m+nm+n.
probabilitynumber theoryrelatively prime