What is the minimum Tower of Hanoi moves?

 title: 'Figure 13: Detailed results on reasoning effort (measured in inference thinking tokens) versus problem complexity (N) for three LRMs (DeepSeek-R1, Claude-3.7-Sonnet with thinking, and o3-mini) across four puzzle environments.'

The minimum number of moves required to solve the Tower of Hanoi puzzle with N disks is 2^N - 1. This means, for example, with 3 disks, the minimum moves needed would be 7 moves[1].