2013 Team #7: Children and their Toy orderings
Source:
February 22, 2013
Problem Statement
There are are children and toys such that each child has a strict preference ordering on the toys. We want to distribute the toys: say a distribution dominates a distribution if in , each child receives at least as preferable of a toy as in . Prove that if some distribution is not dominated by any other, then at least one child gets his/her favorite toy in that distribution.