We want to place 2012 pockets, including variously colored balls, into k 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 k for which we can always do this placement whatever the number of balls in the pockets and whatever the colors of balls. inequalitiesinductionpigeonhole principlegeometrygeometric transformationcombinatorics proposedcombinatorics