Tower of Hanoi with 6 Disks

Six disks need 63 moves. Someone who solves it by rule rather than by feel finds it no harder than five disks, only twice as long.

Quick facts

Six is even, so the smallest disk goes to peg 2 first. Move 32 is the single move of the largest disk. Everything before it is a five-disk puzzle onto peg 2; everything after it is the same five-disk puzzle onto peg 3.

How often each disk moves

The smallest disk does half of all the work. Each disk moves half as often as the one below it, and the largest disk moves exactly once.

A pattern worth remembering

Count how many times 2 divides the move number, and add one: that is the disk to move. Move 1 is odd, so it moves disk 1. Move 2 is divisible by 2 once, so it moves disk 2. Move 4 is divisible by 2 twice, so it moves disk 3. Move 32 is divisible by 2 exactly 5 times, so it is the one move of disk 6. You can check every line of the list below against it.

The complete solution

All 63 moves, in order. Peg numbers are 1 (left), 2 (middle) and 3 (right).

1. Disk 1: peg 1 → 2
2. Disk 2: peg 1 → 3
3. Disk 1: peg 2 → 3
4. Disk 3: peg 1 → 2
5. Disk 1: peg 3 → 1
6. Disk 2: peg 3 → 2
7. Disk 1: peg 1 → 2
8. Disk 4: peg 1 → 3
9. Disk 1: peg 2 → 3
10. Disk 2: peg 2 → 1
11. Disk 1: peg 3 → 1
12. Disk 3: peg 2 → 3
13. Disk 1: peg 1 → 2
14. Disk 2: peg 1 → 3
15. Disk 1: peg 2 → 3
16. Disk 5: peg 1 → 2
17. Disk 1: peg 3 → 1
18. Disk 2: peg 3 → 2
19. Disk 1: peg 1 → 2
20. Disk 3: peg 3 → 1
21. Disk 1: peg 2 → 3
22. Disk 2: peg 2 → 1
23. Disk 1: peg 3 → 1
24. Disk 4: peg 3 → 2
25. Disk 1: peg 1 → 2
26. Disk 2: peg 1 → 3
27. Disk 1: peg 2 → 3
28. Disk 3: peg 1 → 2
29. Disk 1: peg 3 → 1
30. Disk 2: peg 3 → 2
31. Disk 1: peg 1 → 2
32. Disk 6: peg 1 → 3
33. Disk 1: peg 2 → 3
34. Disk 2: peg 2 → 1
35. Disk 1: peg 3 → 1
36. Disk 3: peg 2 → 3
37. Disk 1: peg 1 → 2
38. Disk 2: peg 1 → 3
39. Disk 1: peg 2 → 3
40. Disk 4: peg 2 → 1
41. Disk 1: peg 3 → 1
42. Disk 2: peg 3 → 2
43. Disk 1: peg 1 → 2
44. Disk 3: peg 3 → 1
45. Disk 1: peg 2 → 3
46. Disk 2: peg 2 → 1
47. Disk 1: peg 3 → 1
48. Disk 5: peg 2 → 3
49. Disk 1: peg 1 → 2
50. Disk 2: peg 1 → 3
51. Disk 1: peg 2 → 3
52. Disk 3: peg 1 → 2
53. Disk 1: peg 3 → 1
54. Disk 2: peg 3 → 2
55. Disk 1: peg 1 → 2
56. Disk 4: peg 1 → 3
57. Disk 1: peg 2 → 3
58. Disk 2: peg 2 → 1
59. Disk 1: peg 3 → 1
60. Disk 3: peg 2 → 3
61. Disk 1: peg 1 → 2
62. Disk 2: peg 1 → 3
63. Disk 1: peg 2 → 3

Other sizes

3 disks4 disks5 disks For the rule behind these lists see how to solve the Tower of Hanoi; for why 6 disks need 63 moves see the formula; to finish a position that has gone wrong, use the solver.