Move the disks

• Click a peg to pick up the top disk, then click another peg to place it.
• You can only move one disk at a time.
• A larger disk cannot sit on a smaller disk.

Try the solver

• Use Step to see the next move in the optimal solution.
• Use Auto solve to watch the full solution.
• Change the disk count to explore how the optimal move count grows.

Why the minimum is 2ⁿ − 1

To move the largest disk, you must first move the top n − 1 disks away, then move the largest disk, then move those n − 1 disks back onto it. That leads to a recursion:

Moves(n) = 2 × Moves(n − 1) + 1, which simplifies to 2ⁿ − 1.