Towers

Puzzle · plays in your browser, no download

Move the stack one disc at a time, never a bigger disc on a smaller one. Each extra disc doubles the shortest answer.

Where it comes from

The towers of Hanoi, invented in 1883 by a French mathematician who sold it with a story about a temple where monks had been moving sixty-four discs since the beginning of the world. At one move a second that would take longer than the universe has existed, which is the point he was making.

How to play

Move the whole stack from the first peg to the third. Tap a peg to lift its top disc, tap another to drop it.
Changing your mind is free: tap the same peg again and the disc goes back down, no move counted.
The par is the fewest moves possible: fifteen with four discs, thirty-one with five, sixty-three with six. Each extra disc doubles it.

What makes this one different

The way in is to stop thinking about the big disc: to move six you first have to move five out of the way, and that is the same puzzle one size smaller. The answer is the puzzle itself, repeated, and once you see that the number of discs stops mattering. Each extra disc doubles the fewest moves: fifteen, thirty-one, sixty-three.

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