4 disks15 moves minimum
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How to play Tower of Hanoi
Move the whole tower from the left rod onto either of the others. Click a rod (or press 1, 2 or 3) to lift its top disk, then click another rod to set it down. Only one disk moves at a time, and a disk can never sit on a smaller one. Solve it in the fewest possible moves for a perfect game. Pick a taller tower from the New Game menu, and undo as often as you like (Ctrl+Z or U).
The fewest moves
A tower of n disks needs at least 2ⁿ − 1 moves: 7 for 3 disks, 15 for 4, 31 for 5, 63 for 6, 127 for 7 and 255 for 8. Each extra disk doubles the work, plus one. The legend of the puzzle tells of 64 golden disks; at one move a second, moving them would take about 585 billion years.
Tips and strategy
- Think recursively. To move a tower, first move everything above its biggest disk to the spare rod, then move the biggest disk, then move the smaller tower back on top of it.
- Move the smallest disk on every other turn, always round the rods in the same direction. In between, make the only legal move that doesn't touch the smallest disk. Following these two rules solves any tower in the fewest moves.
- With an odd number of disks, the smallest disk's first move goes to the rod you want to finish on; with an even number, it goes to the other one.