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Can our coinage system be improved?

Published online by Cambridge University Press:  18 June 2018

Peter Shiu*
Affiliation:
353 Fulwood Road, Sheffield S10 3BQ e-mail: p.shiu@yahoo.co.uk

Extract

Some forty years ago my wife Christine and I considered the problems in this article, which involves a fair amount of computation. Computing facilities were not good then, so we considered instead the problems in [1] in which we showed, without using computers, that there were 64703 ways to make up £1 using coins; this was before the introduction of the 20p and £1 coins, and the ½p coin was in circulation. If Christine were still with us, this would have been another piece of joint work. I therefore dedicate this article to her memory.

The design of a coinage system depends on considerations we give to various criteria: for example, the number of denominations for the coins, the maximum number of coins required to deliver any given amount in a range, or the required number of coins averaged over the range; see also §3.

Type
Articles
Copyright
Copyright © Mathematical Association 2018 

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References

1. Shiu, C. M. and Shiu, P., Stamps and coins: two partition problems, Mathematical Spectrum 13 (1980) pp. 4955.Google Scholar
2. Shallit, Jeffrey, What this country needs is an 18 cents piece'. The Mathematical Intelligencer, (2) 25 (2003) pp. 2023.Google Scholar
3. Shiu, P., Moment sums associated with binary quadratic forms, Amer. Math. Monthly 113 (2006) pp. 545550.CrossRefGoogle Scholar
4. Tripathi, A., Formulae for the Frobenius number in three variables, J. Number Theory 170 (2017) pp. 368389.Google Scholar
5. Kannan, R., Lattice translates of a polytope and the Frobenius problem, Combinatorica 12 (2) (1992) pp. 161177.Google Scholar
6. Ramírez-Alfonsín, J. L., The Diophantine Frobenius problem, Oxford University Press (2006).Google Scholar