Question 65
A poker set contains three chips of each of $2n$ different colours for a complete set of $6n$ chips. Let $p_n$ be the number of ways in which the chips can be partitioned into two piles of $3n$ chips each in such a way that no pile contains three chips of the same colour. Prove that $p_n$ is odd if and only if $n$ is a power of 2.