The four-peg Tower of Hanoi puzzle

Abstract

We discuss a version of the Tower of Hanoi puzzle in which there are four pegs rather than three. The fourpeg puzzle provides a rich source of exercises (samples of which are included) for students after the familiar three-peg version has been presented. We give an algorithm that solves the four-peg puzzle in the claimed minimum number of moves (see [2, 4]). Our algorithm solves the four-peg puzzle in O -(4 √n ) moves whereas the best algorithm for the three-peg puzzle requires 2 n - 1 moves. As far as we know, the minimum number of moves required to solve the four-peg puzzle is an open question.

Generalized multi-peg tower of hanoi problem

“…The Dynamic Programming (DP) technique has been employed by Wood [30], Roth [24], Hinz [8][9][10], van de Liefvoort [13,14], Chu and Johnsonbaugh [4] and Majumdar [16]. Wood considers only the 3-peg problem, and the remaining papers deal with the 4-peg problem.…”