The cyclic multi-peg Tower of Hanoi

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.