Question 66
Given an infinite sheet of square ruled paper. Some of the squares contain a piece. A move consists of a piece jumping over a piece on a neighbouring square (which shares a side) onto an empty square and removing the piece jumped over. Initially, there are no pieces except in an $m \times n$ rectangle ($m, n \gt 1$) which has a piece on each square. What is the smallest number of pieces that can be left after a series of moves?