Tower of Hanoi

Move the tower disk by disk, never placing a disk on a smaller one.

The legendary puzzle, from 3 to 10 lacquered wooden disks, on 3 or 4 rods. The minimum number of moves is displayed and the AI can solve the tower before your eyes.

Players: 1 player
Length: 1 to 30 min

Solo

Play Tower of Hanoi

15 days of full access, no account · No download

How to play

Goal of the game

Carry the whole tower of disks over to the goal rod (on the right), following two rules.

Rules

Only one disk may be moved at a time: the one on top of a rod.
A disk can never rest on a smaller disk.

Controls

Tap a rod to lift its top disk, then tap the destination rod.
You can also drag a disk from one rod to another.
With the keyboard: keys 1 to 4 (source then destination), or the left and right arrows then Space.

Minimum moves

With 3 rods, you need at least 2ⁿ − 1 moves for n disks (7 for 3 disks, 1,023 for 10). With 4 rods, the Frame-Stewart algorithm cuts this number dramatically: 49 moves are enough for 10 disks.

The “Scattered disks” option starts from a random position where the disks are spread across the rods: the minimum specific to that position is computed and displayed.

Tip (3 rods): the smallest disk moves every other move, always in the same direction of rotation; in between, there is only one other legal move.

About the AI

The AI explores every possible position with a breadth-first search (up to 4¹⁰, which is over a million for 10 disks and 4 rods): from any position, it therefore knows the exact number of moves left and the best move. From the classic tower, it applies the recursive Frame-Stewart algorithm, whose optimality it checks with that same search.

Records are only registered in a classic game, with no hints and no help from the AI.

Difficulty levels

Easy3 disks: 7 moves with 3 rods.
Medium5 disks: 31 moves with 3 rods.
Hard7 disks: 127 moves with 3 rods.
Expert8 disks: 255 moves with 3 rods.
Diabolical10 disks: 1,023 moves with 3 rods, for the most patient.