The Tower of Hanoi (ToH) Game is described as follows: l. ToH contains n disks stacked with large at the bottom. 2. The disks are numbered from 1 to n starting from small. 3. A player is supposed to move the entire stack from one pole to another using the third pole. 4. The player will receive dollar k if he/she moves disk k. a. Form a recurrence relation and initial condition for the winning amount W_n for playing n disks a1. Solve your recurrence problem. Solution: W_n = 2^n+1 - n - 2, n greaterthanorequalto 1 b. If the player is allowed to move the disks only to adjacent poles, Formulate and solve the winning amount A_n. Solution: A_n = 3^n+1/2 - n - 3/2, n greaterthanorequalto 1