The Tower of Hanoi problem is a classic example of a problem that can be…

Concept

The Tower of Hanoi puzzle has a well-known recurrence for the minimum number of moves: T(n) = 2·T(n-1) + 1, with base case T(1) = 1. Solving this recurrence gives the closed-form formula: Moves = 2n − 1, where n is the number of disks.

Application

1. Identify the number of disks: n = 3.

2. Write the closed-form formula: Moves = 2n − 1.

3. Substitute n = 3: Moves = 23 − 1.

4. Evaluate the power: 23 = 8.

5. Subtract: 8 − 1 = 7.

Cross-check

Verify independently using the recurrence itself, building up from the base case: T(1) = 1. T(2) = 2·T(1) + 1 = 2·1 + 1 = 3. T(3) = 2·T(2) + 1 = 2·3 + 1 = 7. This matches the closed-form result exactly.

Result

Therefore, the minimum number of moves required to solve the Tower of Hanoi problem with 3 disks is 7.