Tower of Hanoi

The rules

• Move the whole tower from peg 1 to the last peg (peg 3, or peg 4 if you choose four pegs).
• Move one disk at a time, and only the top disk of a peg.
• Never put a disk on top of a smaller one.

With n disks the fewest possible moves is 2ⁿ − 1: 7 for three disks, 1,023 for ten. The board shows that number as the minimum, and tells you how many moves are left from wherever you are.

Learn more

• The solver: finish any position with the shortest solution.
• How to solve it: a rule you can follow without thinking.
• The formula: why the minimum is 2ⁿ − 1.
• Four pegs: Reve’s puzzle, with far fewer moves.
• For teachers: embed the board in a course page or slides.

By size: 3 disks4 disks5 disks6 disks