Exercise 2.6. Let us introduce a modified version of the Tower of Hanoi game. We place the three poles in a straight line and make a new rule: A disk can be moved only from one pole to an adjacent pole. Suppose the goal of the modified game is to move the usual stack of n disks from a pole at one end to the pole at the other end. 1. Solve the modified puzzle for small values of n, and determine how many moves are required. 2. From these examples, guess a general formula for the number of moves needed to solve the puzzle. 3. Use induction to prove that the puzzle can be solved in the guessed number of moves