The cyclic multi-peg Tower of Hanoi

Abstract

Variants of the classical Tower of Hanoi problem evolved in various directions. Allowing more than 3 pegs, and imposing limitations on the possible moves among the pegs, are two of these. Here, we deal with the case of h ≥3 pegs arranged on a circle, where moves are allowed only from a peg to the next peg (in the clockwise direction). Unlike the multi-peg problem without restrictions on moves between pegs, the complexity of this variant as a function of the number of disks is exponential. We find explicit lower and upper bounds for its complexity for any h , and show how this complexity can be estimated arbitrarily well for any specific h .