New variants of the bottleneck tower of Hanoi problems

摘要

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 MB 3 ( n , b ) the minimum number of moves required to solve the new variant of the bottleneck Tower of Hanoi problem, an explicit form of MB 3 ( n , b ) is found. Also, MB 4 ( 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 MB 4 ( n , b ) is derived.