USAMO 2001 Problem 1
Source:
September 30, 2005
USA(J)MOUSAMOcombinatoricsExtremal combinatoricspigeonhole principle
Problem Statement
Each of eight boxes contains six balls. Each ball has been colored with one of colors, such that no two balls in the same box are the same color, and no two colors occur together in more than one box. Determine, with justification, the smallest integer for which this is possible.