Tower of Hanoi with 6 Disks
The shortest solution is 63 moves. Play them on the board, or read every one in the list under it.
Optimal solution
63moves2⁶ − 1
- First move
- Disk 1, A → B
- At one move a second
- 1 minute
- Difficulty
- Medium
6 disks on tower A. 63 moves to go.Step 0 of 63
| Move | Disk | From | To |
|---|---|---|---|
| 1 | 1 | A | B |
| 2 | 2 | A | C |
| 3 | 1 | B | C |
| 4 | 3 | A | B |
| 5 | 1 | C | A |
| 6 | 2 | C | B |
| 7 | 1 | A | B |
| 8 | 4 | A | C |
| 9 | 1 | B | C |
| 10 | 2 | B | A |
| 11 | 1 | C | A |
| 12 | 3 | B | C |
| 13 | 1 | A | B |
| 14 | 2 | A | C |
| 15 | 1 | B | C |
| 16 | 5 | A | B |
| 17 | 1 | C | A |
| 18 | 2 | C | B |
| 19 | 1 | A | B |
| 20 | 3 | C | A |
| 21 | 1 | B | C |
| 22 | 2 | B | A |
| 23 | 1 | C | A |
| 24 | 4 | C | B |
| 25 | 1 | A | B |
| 26 | 2 | A | C |
| 27 | 1 | B | C |
| 28 | 3 | A | B |
| 29 | 1 | C | A |
| 30 | 2 | C | B |
| 31 | 1 | A | B |
| 32 | 6 | A | C |
| 33 | 1 | B | C |
| 34 | 2 | B | A |
| 35 | 1 | C | A |
| 36 | 3 | B | C |
| 37 | 1 | A | B |
| 38 | 2 | A | C |
| 39 | 1 | B | C |
| 40 | 4 | B | A |
| 41 | 1 | C | A |
| 42 | 2 | C | B |
| 43 | 1 | A | B |
| 44 | 3 | C | A |
| 45 | 1 | B | C |
| 46 | 2 | B | A |
| 47 | 1 | C | A |
| 48 | 5 | B | C |
| 49 | 1 | A | B |
| 50 | 2 | A | C |
| 51 | 1 | B | C |
| 52 | 3 | A | B |
| 53 | 1 | C | A |
| 54 | 2 | C | B |
| 55 | 1 | A | B |
| 56 | 4 | A | C |
| 57 | 1 | B | C |
| 58 | 2 | B | A |
| 59 | 1 | C | A |
| 60 | 3 | B | C |
| 61 | 1 | A | B |
| 62 | 2 | A | C |
| 63 | 1 | B | C |
On this page
The shape of the solution
There are never 63 separate moves to remember — only three stages:
- Moves 1 to 31: build a tower of 5 disks on B.
- Move 32: disk 6 crosses to C — the only time it moves.
- Moves 33 to 63: rebuild the 5-disk tower on top of it.
Stages 1 and 3 are each the 5-disk solution, with two towers' names swapped.
Which disk moves when
Disk 1 makes half of all the moves — 32 of them, on every odd-numbered move. Each larger disk moves half as often as the one above it, which is the binary counter hiding inside the puzzle: the disk that moves is one more than the number of times you can halve the move number and still get a whole number. Move 6 halves once, to 3, so move 6 is disk 2. There is more on that in Tower of Hanoi and binary.
| Disk | Moves | First moves on | Then every |
|---|---|---|---|
| 1 | 32 | move 1 | 2 moves |
| 2 | 16 | move 2 | 4 moves |
| 3 | 8 | move 4 | 8 moves |
| 4 | 4 | move 8 | 16 moves |
| 5 | 2 | move 16 | 32 moves |
| 6 | 1 | move 32 | — |
The smallest disk's circuit
With 6 disks — an even number — disk 1 travels A → B → C → A for the whole game, never reversing. Every move in between is the only legal move that leaves disk 1 alone. Those two rules alone reproduce the list above move for move; the iterative solution explains why, and strategies turns it into something to play by.
About the 6-disk puzzle
Sixty-three moves is where a game stops being something you finish in one breath and starts needing checkpoints. Halves are too coarse to catch a slip in time, so hold six disks in your head by quarters instead:
- After move 15: disks 1 to 4 are on C.
- After move 31: disks 1 to 5 are on B, and disk 6 is alone on A. Move 32 carries it to C.
- After move 47: disks 1 to 4 are alone on A, disk 5 is on B and disk 6 is on C. Move 48 puts disk 5 on disk 6.
- Moves 49 to 63: disks 1 to 4 come home.
Each checkpoint is a finished four- or five-disk tower, which is easy to see at a glance — and if the board does not match, you have found your mistake within fifteen moves of making it.
Six is even, so the smallest disk starts toward B. It makes thirty-two of the sixty-three moves, and every one of them is forced. Sixty-three is 3 × 3 × 7 — the first move count that is divisible by both earlier primes, seven and three.
Other sizes
- 5 disks31 moves — the solution that makes up each half of this one.
- 7 disks127 moves — this solution twice, with one move between.
- Solve 6 disks from a position you are stuck inThe solver finishes a half-played game in the fewest moves left, rather than starting again.
- Every solution, from 3 to 10 disksMove counts, first moves and timings side by side.
Frequently asked questions
How many moves does it take to solve Tower of Hanoi with 6 disks?
63 moves is the minimum: 2⁶ − 1 = 63. No solution with fewer moves exists, and any solution with more has wasted some.
What is the first move in 6-disk Tower of Hanoi?
Move disk 1, the smallest, from tower A to tower B. With an even number of disks the smallest disk travels A → B → C → A for the whole game, so its first stop is B. Sending it to C first still lets you finish, but it costs one extra move.
How long does 6-disk Tower of Hanoi take to solve?
A perfect game is 63 moves, which at one move a second is 1 minute and at three moves a second — about as fast as anyone plays by hand — 21 seconds.
How can I check I am on track in a 6-disk game?
Look at the board after moves 15, 31 and 47. After move 15, disks 1 to 4 should be stacked on C. After move 31, disks 1 to 5 should be on B, with disk 6 alone on A. After move 47, disks 1 to 4 should be on A, with disk 6 on C and disk 5 on B. If the board matches at each of those moves, you are still on the shortest path.