You are given an $m \times n$ chocolate bar divided into $1 \times 1$ squares. You can break a piece of chocolate by splitting it into two pieces along a straight line that does not cut through any of the $1 \times 1$ squares. What is the minimum number of times you have to break the bar in order to separate all the $1 \times 1$ squares?
We note that the number of separate pieces of chocolate increases by 1 at each cut. We begin with 1 piece and end with $m n$ pieces, so we must make $m n-1$ cuts. Thus $m n-1$ is the minimum (and also the maximum) number of cuts necessary to separate all the $1 \times 1$ squares.