• Corpus ID: 18183339

# Explorations in 4-peg Tower of Hanoi Ben

@inproceedings{Houston2004ExplorationsI4,
title={Explorations in 4-peg Tower of Hanoi Ben},
author={Ben Houston and Hassan Masum},
year={2004}
}
• Published 2004
• Computer Science
Finding an optimal solution to the 4-peg version of the classic Tower of Hanoi problem has been an open problem since the 19th century, despite the existence of a presumed-optimal solution. We verify that the presumed-optimal Frame-Stewart algorithm for 4-peg Tower of Hanoi is indeed optimal, for up to 20 discs. We also develop a distributed Tower of Hanoi algorithm, and present 2D and 3D representations of the state transition graphs. Finally, two variants (k-out-of-order and k-at-a-time) and…
2 Citations

## Figures and Tables from this paper

• Computer Science
Am. Math. Mon.
• 2022
The space complexity of the Tower of Hanoi puzzle, i.e., how many disks need to be accommodated on the pegs involved in the transfer, is considered for the first time.
• R. Demontis
• Mathematics, Computer Science
Discret. Math. Algorithms Appl.
• 2019
It is proved that the solutions to the Tower of Hanoi problem given by Frame and Stewart are minimal and the maximum number of disks that can be moved using formula is [Formula: see text].

## References

SHOWING 1-10 OF 10 REFERENCES

• Computer Science
SIAM J. Comput.
• 2004
It is proved that FS(n,k) and H(n-k) both have the same order of magnitude of $2^{(1\pm o(1)!)(n(k-2)!)^{1/(k- 2)}}$.
The famous Tower of Hanoi puzzle, invented in 1883 by Edouard Lucas (see [21]), consists of three posts and a set of n, typically 8, pierced disks of differing diameters that can be stacked on the
In this we paper we consider the version of the classical Towers of Hanoi games where the game-board contains more than three pegs. For k pegs we give a 2Ckn1/(k-2) lower bound on the number of steps
• Mathematics
• 2002
Abstract. Several different approaches to the multi-peg Tower of Hanoi problem are equivalent. One of them is Stewart's recursive formula ¶¶\$ S (n, p) = min \{2S (n_1, p) + S (n-n_1, p-1)\mid n_1,
• Philosophy
• 1990
SummaryThe canonical distance of points on the Sierpiński gasket is considered and its expectation deduced. The solution is surprising, both for the value and for the method derived from an analysis

• 1998

### pdf. S. Klavzar. Square-edge graphs, partial cubes and their subclasses

• pdf. S. Klavzar. Square-edge graphs, partial cubes and their subclasses
• 1998

### Results and open problems on the Tower of Hanoi

• In Congressus Numerantium, Volume
• 1999

### Results and open problems on the Tower of Hanoi

• Congressus Numerantium
• 1999