New variants of the bottleneck tower of Hanoi problems

Abstract

This paper considers two variants of the bottleneck Tower of Hanoi problems with n (≥1) discs and the bottleneck size b (≥2), which allows violation of the “divine rule” (at most) once. Denoting by MB3(n, b) the minimum number of moves required to solve the new variant of the bottleneck Tower of Hanoi problem, an explicit form of MB3(n, b) is found. Also, MB4(n, b) denotes the minimum number of moves required to solve the new variant of the bottleneck Reve’s puzzle, a closed-form expression of MB4(n, b) is derived.
 Journal of Bangladesh Academy of Sciences, Vol. 44, No. 2, 197-200, 2020

The Reve’s Puzzle with single relaxation of the Divine rule

“…An immediate generalization is the Reve's puzzle with r(2) relaxations of the "divine rule". Another problem of interest is the bottleneck Reve's puzzle, introduced by Majumdar (1996) and Majumdar et al (1996), which is still open, though a conjecture about the solution is given in Majumdar (2013). A third generalization of the Reve's puzzle has been treated recently by Majumdar (2016).…”