In Algorithm Design, the phrase “total number of moves” is commonly associated with the Tower of Hanoi problem. The problem consists of three rods and (n) disks of different sizes. Initially, all disks are placed on the source rod in decreasing order of size, with the largest disk at the bottom. The objective is to move all the disks from the source rod to the destination rod using the auxiliary rod, while following two rules: only one disk can be moved at a time, and a larger disk cannot be placed on a smaller disk. To calculate the total number of moves, consider the problem for (n) disks. To move all (n) disks from the source rod to the destination rod, the top (n-1) disks must first be moved from the source rod to the auxiliary rod. This requires (T(n-1)) moves. After that, the largest, (n)-th disk is moved from the source rod to the destination rod, requiring exactly one move. Finally, the (n-1) disks placed on the auxiliary rod must be moved to the destination rod over the largest disk. This again requires (T(n-1)) moves. Therefore, the recurrence relation for the number of moves is [ T(n)=T(n-1)+1+T(n-1) ] or [ T(n)=2T(n-1)+1 ] The base case is [ T(1)=1 ] because only one disk requires one move. Using this recurrence, the number of moves for different numbers of disks can be calculated. For one disk, the total