Tower of Hanoi: Play the Classic Disc Puzzle Free Online

What is Tower of Hanoi?

Tower of Hanoi is the classic disc puzzle, free to play online here on your phone, tablet or computer. A tower of discs sits on the first of three pegs, largest at the bottom. Your job is to rebuild it on the last peg.

There are only two rules. You move one disc at a time, and a larger disc may never rest on a smaller one. That is all, and it is enough to keep people busy since 1883.

Start with 3 discs and seven moves, or build up to 12 discs and 4,095. A counter shows your moves against the fewest possible, worked out by the game's own solver. Match it for three stars.

When the classic tower feels easy, try Four Pegs, a scrambled start, Adjacent moves only, or the Daily Tower that is the same for everyone. Stuck? Press Watch and see it solved.

How to play Tower of Hanoi

1. 

   1Meet the board

   Three pegs, one tower. Every disc starts on peg A, and you rebuild the tower on the glowing goal peg. Pick a mode and a size at the top.

2. 

   2Move the top disc

   Drag the top disc to another peg, or tap one peg and then another. On a keyboard, press 1 and then 3.

3. 

   3Bigger never sits on smaller

   That is the one rule. Try to put disc 2 on disc 1 and the game says Not there, and nothing is counted.

4. 

   4Chase the fewest moves

   The counter shows your moves beside the fewest possible. Match it for three stars. Undo and Redo are free, so try things.

5. 

   5Ask for a hint

   With 3 or 4 discs you get two hints per board. A gold arc shows the best next move. You still make it yourself.

6. 

   6Watch it solved

   Press Watch and the game plays the shortest answer, naming what each move is for. Pause, step or change speed. It never counts as a win.

7. 

   7Try the other towers

   Four Pegs adds a spare peg, Scramble scatters the start, Adjacent only allows the peg next door, and the Daily Tower is new each day.

The rules in full

1. The goal: move every disc from peg A to the last peg, so the tower stands there in the same order, largest at the bottom. The goal peg glows green and is labelled Goal.
2. Move one disc at a time. Only the top disc of a peg can move.
3. A disc may land on an empty peg or on a larger disc, never on a smaller one. The game stops an illegal move and tells you why.
4. With a mouse or finger, drag the top disc to another peg and let go. Or tap a peg to lift its top disc, then tap the peg where it should go.
5. On a keyboard, press 1, 2 or 3 (or A, B, C) to lift from that peg, then the number of the peg to drop on. The arrow keys and Space work too.
6. The counter shows your moves next to the fewest possible. Three stars for matching it, two for staying within half as many again, one for any solve.
7. Undo takes back a move, as many times as you like. Redo puts it back. Restart resets the board and the clock.
8. The plus and minus buttons add or remove a disc. The mode button switches between Classic, Four Pegs, Scramble and Adjacent.
9. Boards with 3 or 4 discs give two hints. A hint points at the best next move and leaves you to make it.
10. Press Watch to see any board solved in the fewest moves. A watched solve never counts as yours.

Tower of Hanoi tips and strategy

• Count the discs before you start. With an odd number, the smallest disc goes to the goal peg first. With an even number, it goes to the middle peg first.
• Look for the biggest disc that is not home yet. It can only cross when every smaller disc is stacked on the spare peg, so build that stack first.
• On three pegs, never move the same disc twice in a row. If you just did, one of those moves was wasted, so press Undo.
• In Four Pegs, park more than one disc. With 6 discs, set the top three aside on a spare peg, move the other three, then bring the parked ones home.
• In Adjacent, the smallest disc moves twice, then another disc moves once, over and over. The big disc reaches the goal in two short steps.
• Stuck on a size? Press Watch, slow it to 1×, and follow a single disc. Then stop the demo and try the same board yourself.

What is the Tower of Hanoi?

The Tower of Hanoi is a puzzle with three pegs and a stack of discs, each one smaller than the disc below it. You move the stack to another peg, one disc at a time, without ever putting a larger disc on a smaller one.

It was invented by the French mathematician Édouard Lucas, who sold it as a toy in 1883. It is also called the Towers of Hanoi and Lucas' Tower.

Lucas wrapped it in a legend: temple priests move 64 golden discs between three needles, and when the last one lands the world ends. No hurry. That takes 18,446,744,073,709,551,615 moves, about 585 billion years at one move a second.

Tower of Hanoi rules

This game plays by the exact rules: one disc at a time, only from the top of a peg, and never onto a smaller disc.

You win when the whole tower stands on the last peg. Rebuilding it on the middle peg does not count. Every board can be solved, and you can always undo.

How many moves does it take? The 2ⁿ − 1 formula

The fewest moves for a tower of n discs is 2ⁿ − 1. Every extra disc doubles the work and adds one move.

That gives 7 moves for 3 discs, 15 for 4, 31 for 5, 63 for 6, 127 for 7 and 255 for 8. Then 511 for 9 discs, 1,023 for 10, 2,047 for 11 and 4,095 for 12.

The counter shows this number beside your own moves. It comes from the game's own solver and is checked by a full search, so it is always the true minimum.

How to solve the Tower of Hanoi

Think in towers, not discs. To move a tower, first move everything except the biggest disc to the spare peg. Then move the biggest disc to the goal. Then move the smaller tower on top of it.

The smaller tower is moved in the very same way, and so is the tower inside that. This is why the puzzle is a favourite first lesson in recursion for programmers.

You do not have to hold all of that in your head. Move the smallest disc every other turn, always in the same direction, and make the only other legal move in between. Open The trick in the menu for pictures of both ideas.

Four Pegs: the Reve's puzzle

Add a fourth peg and the puzzle gets shorter and much deeper. The English puzzle maker Henry Dudeney published it in 1907 as the Reve's puzzle.

The spare peg lets you park several small discs out of the way. The fewest moves are 5 for 3 discs, 9 for 4, 13 for 5, 17 for 6, 25 for 7, 33 for 8, 41 for 9 and 49 for 10. Then 65 for 11 and 81 for 12.

The method behind those numbers dates from 1941, yet a full proof that nothing beats it only arrived in 2014. Here every one of those counts is confirmed by the game's own search.

Scramble and Adjacent modes

Scramble starts with the discs already spread over the three pegs, so the moves you know by heart no longer fit. The game finds the fewest moves for each scramble, and New deals another.

Adjacent allows a disc to move only to the peg next door: A to B, or B to C, and back. The tower still has to travel from A to C.

That one small rule triples the work with each disc. The fewest moves are 3ⁿ − 1: 26 for 3 discs, 80 for 4, 242 for 5, 728 for 6 and 2,186 for 7. A perfect solve passes through every possible position once.

The Daily Tower

Every day brings one new board, the same for every player. It starts scrambled, and the kind changes with the weekday: three pegs on some days, four pegs or adjacent moves on others.

Your first solve of the day is the one that counts. Solve it day after day to build a streak.

Missed a day? The last week of Daily Towers stays open to play for fun. The demo cannot be watched on today's board until you have solved it yourself.

Made to feel good on any screen

Discs follow your finger or mouse the moment you touch them, and tap-tap and the keyboard are just as quick. Each disc lands with a clack whose pitch matches its size.

Pick from five looks, Neon, Temple, Aurora, Ember and Ice, and switch on numbered discs if you like to count. Sound can be muted with one tap.

The board saves itself as you play, so you can close the page and pick up the same tower later. Nothing to download.

Tower of Hanoi FAQ