5. [20 points ] The Tower of Hanoi is a mathematical puzzle. It consists of three stacks, A, B, C and a number of disks of different sizes stacked in ascending order of size on one stack, the smallest at the top. Problem is to move the entire discs from one stack to another obeying the following simple rules: 1. Only one disk can be moved at a time II. A disk can only be moved if it is the top disk on a stack III. No bigger disk may be placed on top of a smaller disk. Your task is to (No programming implementation needed) a. Write the steps(decompose the problem using recursion) to move all 4 discs, as in the above figure, from stack A to stack C using stack B satisfying all the above rules with minimum number of movement. b. What is your minimum number of movements for 4 discs? Show each movement sequentially as follows