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The mathematics of a mechanical puzzle

Published online by Cambridge University Press:  22 September 2016

G. C. Shephard
G. C. Shephard*
Affiliation:
University of Toronto, Toronto M5S 1A1, Canadaand , University of East Anglia, Norwich NR4 7TJ
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Extract

For some mechanical puzzles there exists a complete mathematical analysis. The purpose of this note is to describe one such puzzle, together with a number of variations of it. In the classroom the puzzle could be used as a teaching aid to introduce children to binary notation, mathematical induction, congruences, as well as some of the concepts of group theory. My own ten-year-old son was delighted to find that counting in binary notation, an idea to which he had been introduced in a purely theoretical way, leads to an easy method of solving the puzzle.

Type
Research Article
Information
The Mathematical Gazette , Volume 61 , Issue 417 , October 1977 , pp. 174 - 178
Copyright
Copyright © Mathematical Association 1977

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References

page no 176 note † See, for example, W. W. Rouse Ball, Mathematical recreations and essays, 11th edition revised by H. S. M. Coxeter (1939), pp. 307-310; H. E. Dudeney, Amusements in mathematics (1917), pp. 247-248; or M. Kraitchik, Mathematical recreations, pp. 89-91. See also Lucas, E., Récréations mathématiques (1891), Vol. 1, pp. 161–186 Google Scholar, where it is called “Le jeu du Baguenaudier”. This is a better name than “Chinese rings”, for the puzzle appears to be of an occidental rather than an oriental origin.