Question 3
In a mathematical competition some competitors are (mutual) friends. Call a group of competitors a *clique* if each two of them are friends. The size of a clique is its number of members; any group of fewer than two competitors is also a clique. Given that the largest size of a clique is even, prove that the competitors can be arranged into two rooms such that the largest size of a clique contained in one room is the same as the largest size of a clique contained in the other room.