The towers of Hanoi problem consists of three pegs A, B, and C, and n squares of varying sizes. Initially the squares are stacked on peg A in order of decreasing size, the largest square on the bottom. The problem is to move the squares from peg A to peg B one at a time in such a way that no square is ever placed on a smaller square. Peg C may be used for temporary storage of squares.

A. Write a recursive algorithm to solve this problem.

B. Write a recurrence relation of the number of moves M(n) and solve it.