Tower of Hanoi Strategy: The Perfect Solution

1. The smallest disc sets the rhythm

Every second move is the smallest disc. Between two of its moves, there's exactly one legal move that doesn't involve it. Make that one.

2. Which way does the smallest disc go?

The smallest disc always moves in the same direction around the three pegs:

• Odd number of discs: first move it to the goal peg, and keep going left → right → middle → left...
• Even number: first move it to the middle peg, and keep going left → middle → right → left...

3. Think recursively

To move n discs from A to C: move the top n−1 to B, move the biggest to C, then move the n−1 from B to C. Each of those is the same puzzle, smaller.

4. Don't undo

If you ever move a disc back where it just came from, you've wasted two moves. The perfect solution never does.

Last updated 2026-10-20