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The four-peg Tower of Hanoi puzzle

Published: 01 September 1991 Publication History

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.

References

[1]
1. N. Dale and C. Weems, Introduction to Pascal and Structured Design, 2nd ed., Heath, Lexington, Mass., 1987.
[2]
2. A. M. Hinz, "The Tower of Hanoi," L'Enseignement Mathématique, t. 35, 1989, pp. 289-321.
[3]
3. R. Johnsonbaugh, Discrete Mathematics, 2nd ed., Macmillan, New York, 1990.
[4]
4. Problem 3918, Amer. Math. Mo., March 1941, pp. 216-219.

Cited By

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  • (2009)Generalized multi-peg tower of hanoi problemThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics10.1017/S033427000000059X38:02(201)Online publication date: 17-Feb-2009
  • (2007)A recursive algorithm for the multi-peg tower of hanoi problemInternational Journal of Computer Mathematics10.1080/0020716950880441257:1-2(67-73)Online publication date: 19-Mar-2007
  • (1995) The Divide-and-Conquer Approach to the Generalized p -Peg Tower of Hanoi Problem Optimization10.1080/0233193950884412134:4(373-378)Online publication date: Jan-1995

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 1991
Published in SIGCSE Volume 23, Issue 3

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Cited By

View all
  • (2009)Generalized multi-peg tower of hanoi problemThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics10.1017/S033427000000059X38:02(201)Online publication date: 17-Feb-2009
  • (2007)A recursive algorithm for the multi-peg tower of hanoi problemInternational Journal of Computer Mathematics10.1080/0020716950880441257:1-2(67-73)Online publication date: 19-Mar-2007
  • (1995) The Divide-and-Conquer Approach to the Generalized p -Peg Tower of Hanoi Problem Optimization10.1080/0233193950884412134:4(373-378)Online publication date: Jan-1995

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