CH✦OSCHEMY

Potion stacking puzzle · 6 levels Tower of Hanoi.

Move the whole potion stack to peg C. One disk at a time, never a bigger disk on a smaller one.

Stacking the potion disks…

How to play Tower of Hanoi

Move every disk from peg A on the left to peg C on the right. Only the top disk of a peg can move, and a disk may never sit on a smaller one.

Tap a peg to lift its top disk, then tap another peg to drop it, or drag the disk across. The fewest possible moves for n disks is 2 to the power n, minus 1: 7 for 3 disks, 255 for 8.

A trick: move the smallest disk every other turn, always the same way round. With an odd number of disks it goes A, C, B, A; with an even number A, B, C, A. In between, make the only other legal move.

How to play the Tower of Hanoi game online

The Tower of Hanoi is a stack of disks on the first of three pegs, smallest on top. Move the whole stack to the last peg, one disk at a time, without ever putting a bigger disk on a smaller one. Here the disks are alchemy potion disks on glass pegs, and the game has six levels, from 3 disks (7 moves at best) to 8 disks (255 moves).

How are stars earned?

Finish in the fewest possible moves, 2 to the power of the number of disks minus 1, for 3 stars. Finish within half as many moves again for 2 stars, and any finish earns 1. Hint shows the best next move from any position, and caps the round at 2 stars.

What is the trick?

To move n disks, move the top n − 1 to the spare peg, move the biggest disk across, then move the n − 1 disks back on top. By hand, move the smallest disk every other turn, always in the same direction round the pegs.

For the recursive idea and a step-by-step routine, read the Tower of Hanoi game guide. Want to watch the shortest solution from where you are? Open the Tower of Hanoi solver.