I-Ping Chu
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 2n - 1 moves. As far as we know, the minimum number of moves required to solve the four-peg puzzle is an open question.
- 1. N. Dale and C. Weems, Introduction to Pascal and Structured Design, 2nd ed., Heath, Lexington, Mass., 1987. Google Scholar
Digital Library
- 2. A. M. Hinz, "The Tower of Hanoi," L'Enseignement Mathématique, t. 35, 1989, pp. 289-321.Google Scholar
- 3. R. Johnsonbaugh, Discrete Mathematics, 2nd ed., Macmillan, New York, 1990. Google ScholarDigital Library
- 4. Problem 3918, Amer. Math. Mo., March 1941, pp. 216-219.Google Scholar
Index Terms
- The four-peg Tower of Hanoi puzzle
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