# Chocolate Bar Quiz Puzzle Answer

Friday's puzzle was another one that is very simple to state, but needs a bit more thought than first appears.

Typically, chocolate bars have a number of small squares, that allow you to break the bar into smaller pieces more easily. The number of squares varying with the size of the bar.

Now say you have a chocolate bar that is m x n squares, and you want to break it into single-square pieces. Is there a generalised optimum solution for the fewest number of "snaps"?

Each "snap" must involve only one piece; you can't stack up the pieces and break more than one piece in a single "snap"

At first it seems that there must be a way to produce a short solution by snapping down the middle of a big piece and so on. A sort of binary chop, or "wolf fencing" solution.

However . . .

If you snap one piece, you end up with two pieces. So if you start with one piece and snap it, you have two pieces. Take one of those and snap it, and now you have three pieces. And every snap increases the number of pieces by one - nothing more and nothing less.

To break an m x n bar into single squares will always need m x n - 1 snaps!