Cyclic Tower of Hanoi

Put the three pegs in a circle. A disk may only move to the next peg round, never backwards.

The rules

• Move the whole tower from the first peg to the last.
• Pegs 1, 2 and 3 form a ring: a disk goes from peg 1 to peg 2, from peg 2 to peg 3, or from peg 3 back to peg 1.
• One disk at a time, only the top disk, never a larger disk on a smaller one.

Why it takes longer

The last peg is two stops round the circle from the first, so even the smallest disk needs two moves to get there, and a disk can never step back to undo a mistake. With the same number of disks the cyclic puzzle takes at least three times as many moves as the classic one, and each extra disk multiplies the count by about 2.7 instead of 2.

How many moves

Getting started

The first move is forced: the smallest disk goes to the second peg. After that, think one stop ahead, because a disk can only be moved on to the next peg round. The Cyclic solver shows a shortest solution for any size.