Tower of Hanoi: the classic puzzle, made of clay

About Tower of Hanoi

Granny Quelonia stacked a tower of clay disks at Challenge Square and threw down the oldest challenge in town: move the tower. Only the top disk can move, one at a time, and no disk can ever sit on a smaller one. The first tower has 3 disks and takes 7 moves; the last one has 8 and needs at least 255. Every extra disk doubles the trip, so plan ahead: to free the bottom disk, all the others have to be stacked on the spare peg. Took a wrong turn? UNDO takes back the move. Stuck? HINT shows the next right move.

In Selminha's words

“The Tower of Hanoi was invented in 1883 by French mathematician Édouard Lucas, who spread it along with the legend of a temple where monks move 64 golden disks from peg to peg. It's one of the go-to puzzles for teaching how to plan and break a big problem into smaller ones. I wanted the classic done the Backyard Town way: clay disks, Granny Quelonia cheering you on, an undo that never scolds and a hint for when you get stuck.”

How to play Tower of Hanoi and tips for the fewest moves

1. Tap or click the peg the disk comes from, and the top disk lifts up. Then tap or click the peg it goes to. You can also drag a disk from one peg to another. Tap the same peg again to put the disk back.
2. Green rings at the foot of the pegs show where the disk you're holding can go. A big disk never goes on a small one.
3. UNDO takes back your last move, and your move count goes back too. HINT lights up the right disk and the peg it should go to; with a hint, the level is worth 2 stars at most.
4. On a computer, ← → or A D pick a peg, Enter or Space pick up and drop a disk, Z undoes and H shows a hint. On a controller: D-pad, A to pick up and drop, X to undo and B for a hint.
5. Tip: with an odd number of disks, the smallest one moves straight to the last peg first; with an even number, to the middle peg. After that, the smallest disk always travels in the same direction, every other move.

The rules

One disk at a time

Only the top disk on a peg can move, and each move takes a single disk.

Never a bigger one on top

A disk can only go on an empty peg or on top of a bigger disk.

The goal

Move the whole tower from the first peg to the last, in the same order: biggest at the bottom, smallest on top.

Undo and hint

UNDO takes back the last move and the move count. HINT shows the next move on the shortest path from wherever the tower is; with a hint, the level is worth 2 stars at most.

Saved game

The game remembers which level you are on. When you come back, you can keep going or start over.

The towers and the fewest moves

6 towers

The first one has 3 disks; each level adds one, up to 8, just like the original toy.

The fewest moves

The minimum doubles with every disk, plus one: 7 moves with 3 disks, 15 with 4, 31 with 5, 63 with 6, 127 with 7 and 255 with 8.

The legend

With the 64 disks of the legend, it would take over 18 quintillion moves: at one per second, about 585 billion years.

Controls on phone and computer

Computer

Tap or click the starting peg and then the target peg, or drag the disk · ← → or A D pick a peg · Enter or Space pick up and drop · Z undo · H hint · P or Esc pause · M sound · F full screen · supported controllers: D-pad picks, A picks up and drops, X undoes, B hint, Start pauses, Back toggles sound.

Touch

Phone held upright, in full screen; on a tablet, the game follows the way you're holding it; on a computer, it's landscape. Tap the pegs directly or drag a disk with your finger. Your game is saved on your device, so you can close it and pick up later.

Stars and points

Stars

Fewest possible moves: 3 stars. Up to one and a half times the minimum: 2. More than that: 1. With a hint, 2 at most.

Points

Each star is worth 100 points on the 3-disk tower, 200 on the 4-disk tower and so on, up to 600 on the 8-disk tower; speed adds up to 100 more on each level.

Leaderboard

After the sixth tower, your points for the whole game go to the site TOP 5.