A carpenter has a rectangular board, $x$ feet long and $y$ feet wide, with total area $n = xy $square feet. The board is to be divided into n squares (each 1 foot x 1 foot) by successively cutting a rectangle into two smaller rectangles whose sides are each a whole number of feet. Using strong induction, show that exactly $n -1$ cuts are needed, no matter how the carpenter decides to perform the cuts.
Any help please? I was thinking of maybe trying to write down the possible number of arrangements he can do it but I think it is pointless since it states no matter how it is done.