Balls inside pockets which are inside boxes
Source: Turkey Junior National Olympiad 2012 P4
December 12, 2012
inequalitiesinductionpigeonhole principlegeometrygeometric transformationcombinatorics proposedcombinatorics
Problem Statement
We want to place pockets, including variously colored balls, into boxes such thati) For any box, all pockets in this box must include a ball with the same color
or
ii) For any box, all pockets in this box must include a ball having a color which is not included in any other pocket in this boxFind the smallest value of for which we can always do this placement whatever the number of balls in the pockets and whatever the colors of balls.