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An unexpected use of primes: solving sudokus by calculator

Published online by Cambridge University Press:  23 January 2015

Mark Spahn ,
Ron Lancaster ,
Deborah Moore-Russo  and
Gerald Rising
Mark Spahn
Affiliation:
Independent Japanese-to-English technical translator, West Seneca, New York
Ron Lancaster
Affiliation:
Ontario Institute for Studies in Education, University of Toronto
Deborah Moore-Russo
Affiliation:
Department of Learning and Instruction, University at Buffalo, e-mail:[email protected]
Gerald Rising
Affiliation:
Department of Learning and Instruction, University at Buffalo, e-mail:[email protected]
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Extract

This essay demonstrates an application of prime numbers to the development of a calculator program that solves sudoku puzzles. Among the positive integers, the primes—numbers with exactly two divisors, the numbers themselves and 1—are central to our thinking about numbers. They give us a basis for factoring and divisibility and they contribute to the solution of many problems in the mathematical field of number theory. More important for the purposes of this paper, they provide a way of representing numbers uniquely by prime factors. For example, 6221592 = 23 × 32 × 13 × 172 × 23, any other factorisation differing only in the order of factors.

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 530 , July 2010 , pp. 224 - 232
Copyright
Copyright © The Mathematical Association 2010

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References

1. Keedwell, A. D., Two remarks about Sudoku squares, Math. Gaz., 90 (November 2006) pp. 424–430.CrossRefGoogle Scholar
2. Rising, G. R., Calculator programs for Sudoku puzzles, http://www.buffalo.edu/~insrisg/LINKS/Sudoku.htm Google Scholar
3. Rising, G. R., Inside your calculator, http://www.buffalo.edu/~insrisg/InsideYourCalculator.htm Google Scholar
4. [Author unknown], Sudoku, http://en.wikipedia.org/wiki/Sudoku Google Scholar