The Cyclic Towers of Antwerpen problem—A challenging Hanoi variant

The Cyclic Towers of Antwerpen problem consists of three variations on the Cyclic Towers of Hanoi problem, involving the exchange or rotation of three stacks of rings (red, white, blue), subject to the usual Hanoi rules plus the additional constraint that rings can only move clockwise. An optimal algorithm (minimal number of ring moves) is presented for one of the three variations, along with formulas for how many moves are needed for solution and how many optimal algorithms exist; (non-optimal) solutions for the other two variants are presented, with the formation of provably optimal algorithms remaining an open issue.