Question 42
In a finite group some pairs are friends. Call the group k-indivisible if every partition into $k$ subgroups leaves a pair of friends in at least one subgroup. Suppose $A$ is 3-indivisible and contains no four pairwise friends. Prove that $A$ can be partitioned into $B,C$ with $B$ 2-indivisible and $C$ 1-indivisible. (V. Dol'nikov)