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Rooks inviolate

Published online by Cambridge University Press:  03 November 2016

D. F. Holt
D. F. Holt*
Affiliation:
Mathematisches Institut, Universität Tübingen, Federal Republic of Germany
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Extract

One of the oldest and best known of chessboard problems is to place the largest possible number of similar pieces on the board such that no two of these pieces are attacking each other. In his book Amusements in mathematics [1], Dudeney considered this problem on a generalised square chessboard containing n 2 cells, and proved that for rooks, queens and bishops this maximum number is equal to n, n and 2n – 2 respectively.

Type
Research Article
Information
The Mathematical Gazette , Volume 58 , Issue 404 , June 1974 , pp. 131 - 134
Copyright
Copyright © Mathematical Association 1974

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References

1. Dudeney, H. E., Amusements in mathematics, pp. 76, 88, 96. Nelson (1917).Google Scholar
2. Gardner, Martin, Further mathematical diversions, Chapter 16. Allen and Unwin (1970).Google Scholar
3. Madachy, J. S., Mathematics on vacation, Chapter 2. Nelson (1968).Google Scholar
4. Biggs, Norman, Finite groups of automorphisms (London Mathematical Society Lecture Note Series). Cambridge University Press (1971).Google Scholar