Receiving hats from fellow members
Source: Baltic Way 2010
November 19, 2010
combinatorics proposedcombinatorics
Problem Statement
In a club with members, every member initially had a hat. One day each member sent his hat to a different member (a member could have received more than one hat). Prove that there exists a group of members such that no one in the group has received a hat from another one in the group.