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Bracelets

Published online by Cambridge University Press:  01 August 2016

Paul Green  and
Pamela Liebeck
Paul Green
Affiliation:
Barton Peveril College, Hants
Pamela Liebeck
Affiliation:
Department of Education, University of Keele, ST5 5BG
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Extract

Our original source for this investigation was an Open University video on Secondary classroom practice (OU video no. PM644). Since then, however, we have seen the problem mentioned in [1], [2] and [3]. The investigation as presented to pupils is as follows:

Choose two integers between 0 and 9 (not both 0) and write them down. As an example, we shall choose 0 and 2. Write down their sum, doing the addition modulo 10. Then write down the sum of the last two numbers in the sequence, again doing the addition modulo 10. Repeat this process. Our example gives the sequence

Type
Research Article
Information
The Mathematical Gazette , Volume 74 , Issue 469 , October 1990 , pp. 232 - 239
Copyright
Copyright © The Mathematical Association 1990

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References

1. Dynkin, E.B. and Uspenskii, V.A., Problems in the theory of numbers. (English translation by Whaland, N.D. Jr and Slater, M.B.P., published by Heath and company, 1963.)Google Scholar
2. Engel, A., Elementary mathematics from an algorithmic standpoint. (English translation by Watson, F.R., published by Keele, Mathematical Education Publications, 1984.)Google Scholar
3. Banwell, C.S., Saunders, K.D. and Tahta, D.S., Starting points, Tarquin (1986).Google Scholar