MathDB
Receiving hats from fellow members

Source: Baltic Way 2010

November 19, 2010
combinatorics proposedcombinatorics

Problem Statement

In a club with 3030 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 1010 members such that no one in the group has received a hat from another one in the group.