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Tower of Hanoi

Move the whole stack of disks from the left rod to the right rod. Move one disk at a time, and never put a larger disk on a smaller one. Can you solve it in the minimum number of moves?

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Tap the rod with the disk you want to move, then tap the rod to put it on. You can also drag a disk with your finger (or mouse) to another rod, or use the 1, 2 and 3 keys. Close anytime and choose the same number of disks to continue.

How to play Tower of Hanoi →

Tower of Hanoi rules

  • There are three rods. Disks of different sizes are stacked on the left rod, largest at the bottom and smallest at the top.
  • Move only one disk at a time. Each move takes the top disk from one of the rods.
  • A disk can go on an empty rod or on top of a larger disk. You can never place a larger disk on a smaller one.
  • Move the whole stack, in the same order, to the right rod to solve the puzzle.
  • The minimum number of moves is 7 for 3 disks, 15 for 4, 31 for 5, 63 for 6, 127 for 7 and 255 for 8. Each extra disk roughly doubles it.

Tips for solving it in the minimum moves

To move the largest disk to the right rod, every disk above it must first be moved to the middle rod. Think of a big puzzle as solving the puzzle with one fewer disk twice.

Move the smallest disk on every other move. With an odd number of disks, cycle it left → right → middle → left; with an even number, left → middle → right → left. That gives the minimum solution.

On the moves in between, there is only one legal move that doesn't touch the smallest disk: between the two other rods, move the smaller top disk onto the other rod.

Stuck? Press Hint to see the next move of the shortest solution from where you are now, even after a mistake.

FAQ

Is the Tower of Hanoi free to play?

Yes, and there's no sign-up. Play right in your browser on a phone, tablet or computer.

What is the minimum number of moves?

With n disks, the minimum is 2 to the power of n, minus 1: 7 moves for 3 disks, 15 for 4, 31 for 5, 63 for 6, 127 for 7 and 255 for 8.

How many disks should I start with?

Start with 3 disks. Once you can solve it in 7 moves, add one disk at a time.

Can I undo a move?

Yes. Undo takes back one move at a time, and the move counter goes back too.

What does the hint show?

It shows the next move of the shortest solution from your current position: which disk to move and which rod to move it to.

Can I continue later?

Yes. On the same device and browser, you can pick up where you left off for each number of disks.

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