Breaking Chocolate Problem There is a large bar of Swiss chocolate laid out in an array of 6×8 squares. Typically, the bars are shared by breaking them along the ridges. If you break the bar initially on a horizontal ridge, the break is of length 6, and if you break on an initial vertical ridge, the break of of length 8. For example, you could start with a vertical break on the second ridge and get a 2 × 8 and a 4 × 8 piece, than then break the 4 × 8 piece on the 4th horizontal ridge and get two 2 × 2, and two 4 × 4 pieces. You cannot stack the pieces, you can only break one piece at a time. If you want to end up with the bar completely broken up, what is the method of breaking which has the fewest breaks.

Initially, there is one piece of chocolate. When you have finished, there will be 48. Observe that each break splits a piece into two pieces, and so increases the total number of pieces by 1. To reach 48 pieces, you therefore need 47 breaks, and all methods require this number.