1. (5.2.10) Suppose that a rectangular chocolate bar consists of n individual squares. Further suppose that the bar or any smaller, rectangular, piece of the bar can only be broken into two pieces along the horizontal or vertical lines separating its squares. For example, one possible rectangular bar of 32 squares is that with dimensions 8 x 4. One possible way to break this bar 4 times is as follows: 1: 2: ! 3: 4: i that is, ...producing two bars of 4 squares, one bar of 18, and one bar of 6. (a) How many breaks must be made in order to break the bar into its n constituent squares into n bars of 1 square each? (b) Using a proof by induction, prove the above