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Defining sets for magic squares

  • A. D. Keedwell (a1)


A topic of current interest is that of finding defining sets (preferably smallest defining sets) for various combinatorial structures such as latin squares and block designs, so it seemed interesting (though of no practical use) to try to solve the same problem for magic squares of small size. (The germ of this idea was suggested in the Gazette Note [1] of 1988 under the sub-heading ‘Squares from clues’.)



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1. Cornelius, M., Magic squares, Math. Gaz. 72 (March 1988) p. 43.
2. Trump, W., Notes on magic squares and cubes,
3. Berlekamp, E.R., Conway, J.H., Guy, R.K., Winning ways for your mathematical plays (2nd edn.), Vol. 4, Chapter 24, Peters, A.K. (2004).
4. Keedwell, A.D., Critical sets in latin squares: an intriguing problem, Math. Gaz. 85 (July 2001) pp. 239244.
5. Andrews, W.S., Magic squares and cubes, Dover Reprint, New York (1960).

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Defining sets for magic squares

  • A. D. Keedwell (a1)


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