# Which Rectangular Chessboards Have a Knight's Tour?

@article{Schwenk1991WhichRC, title={Which Rectangular Chessboards Have a Knight's Tour?}, author={Allen J. Schwenk}, journal={Mathematics Magazine}, year={1991}, volume={64}, pages={325-332} }

(1991). Which Rectangular Chessboards Have a Knight's Tour? Mathematics Magazine: Vol. 64, No. 5, pp. 325-332.

## 71 Citations

### Which Chessboards have a Closed Knight's Tour within the Rectangular Prism?

- MathematicsElectron. J. Comb.
- 2011

In honor of the upcoming twentieth anniversary of the publication of Schwenk's paper, this article extends his result by classifying thei\times j\times k$ rectangular prisms that admit a closed knight's tour.

### Single Square Removed

- Mathematics
- 2013

The following theorem is proved: A knight’s tour exists on all chessboards with one square removed unless: n is even, the removed square is (i, j) with i + j odd, n = 3 when any square other than…

### Which Chessboards have a Closed Knight's Tour within the Cube?

- MathematicsElectron. J. Comb.
- 2007

In this paper necessary and sufficient conditions for the existence of a closed knight's tour for the cube are proven.

### Domination and Independence on a Triangular Honeycomb Chessboard

- Philosophy
- 2013

Summary We define moves for king, queen, rook, bishop, and knight on a triangular honeycomb chessboard. Domination and independence numbers on this board for each piece are analyzed.

### The Closed Knight Tour Problem in Higher Dimensions

- MathematicsElectron. J. Comb.
- 2012

The solution of existence of closed knight tours for rectangular chessboards for rectangular boards for n-dimensional rectangular boards is given.

### Knight’s Tours

- MathematicsOpt Art
- 2019

In this paper we discuss the knight’s tour, a chess puzzle related to graph theory. We explore the history of the problem, the connection to Hamiltonian paths and circuits, and some techniques for…

### Mathematical Chess Problems

- Education
- 2018

The Pawn Timmy had just been promoted to a Rook, and was being apprenticed to the King’s Rook; he was instructed to move slowly and cautiously, one square at a time.

### Knight's Tours on a Torus

- Mathematics
- 1997

The knight is the only piece in chess that does not move in a straight line. Instead, it moves in an "L"-two squares in either a vertical or horizontal direction and then one square in a…

### Knight’s Tours on Rectangular Chessboards Using External Squares

- Mathematics
- 2014

The classic puzzle of finding a closed knight’s tour on a chessboard consists of moving a knight from square to square in such a way that it lands on every square once and returns to its starting…

## References

SHOWING 1-7 OF 7 REFERENCES

### Graphs an Introductory Approach

- Mathematics
- 1990

a marvellous introduction to graph theory, covering the basic ideas and showing how can be to in traffic cycles,

### Amusements in Mathematics

- HistoryNature
- 1917

MR. DUDENEY is famous as a composer of puzzles of a semi-mathematical character, and for some years questions by him of this kind have appeared regularly in several English periodicals. He has now…

### Mathematical Recreations and Essays

- MathematicsNature
- 1905

THIS edition differs from the third by containing chapters on the history of the mathematical tripos at Cambridge, Mersenne's numbers, and cryptography and ciphers, besides descriptions of some…

### Knight's circuits and tours, Ars Combinatoria 17A

- 1984

### and H

- S. M. Coxeter, Mathematical Recreations and Essays, University of Toronto Press, Toronto,
- 1974