This is question 10 from section 52 of Discrete Mathematics

This is question 10 from section 5.2 of Discrete Mathematics and Its Applications, Seventh Edition, by Kenneth Rosen.

10. Assume that a chocolate bar consists of n squares ar- ranged in a rectangular pattern. The entire bar, a smaller rectangular piece of the bar, can be broken along a vertical or a horizontal line separating the squares. Assuming that only one piece can be broken at a time, determine how many breaks you must successively make to break the bar into n separate squares. Use strong induction to prove your answer.

Solution

WHEN WE HAVE A BIG SQUARE OF M UNITS SIZE, ORIGINAL SQUARE ADDITION WE CAN MAKE M * M = M^2 ,SMALL SQUARES OF 1 2 3