Answer within 20 mins please Assume that a chocolate bar con

Answer within 20 mins please

Assume that a chocolate bar consists of n squares arranged in a rectangular pattern. The entire bar, a smaller rectangularpieceofthebar,canbebrokenalongavertical or a horizontal line separating the squares.Assuming that only one piece can be broken at a time, determine how manybreaksyoumustsuccessivelymaketobreakthebar into n separate squares. Use strong induction to prove your answer.

Solution

If the rectangle is of dimension mx n

let us divide that into two halves.

Now keep one half of piece on another and cut again. We get 4 pieces

Now all 4 pieces one on the other and cut into 8 equal pieces.

Thus for 8 pieces, we have to cut 3 times

4 pieces we have to cut 2 times.

Let k times for 2^k

Then if we cut one time more we get 2^k+1 pieces equal in k+1 cuts

Hence for n squares, n cut one on the other every time is required.