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Waterloo, Ontario (pte038/19.05.2003/14:09) - Canadian mathematician Jeffrey O. Shallit has conducted a study to find out which coins could be introduced to optimise the circulation of dollars and euros http://www.math.uwaterloo.ca/~shallit/Papers/change2.ps .
In his study carried out at the University of Waterloo http://www.cs.uwaterloo.ca , Shallit found that US and Canadian currencies lacked a 32-cent coin, while Europe would benefit from a 133-cent or 137-cent coin. If these coins were introduced, Shallit believes they would greatly reduce the time and cost involved in currency exchange and payment. The goal of his study was to find out how to save time and cost without greatly increasing the number of available coins.
In Europe, where 1, 5, 10, 20, and 50 cent and 1 and 2 euro coins are common, an average of 4.6 separate pieces of money are required during an exchange. According to Shallit, the introduction of a 133-cent or 137-cent coin could reduce this average to 3.92.
Shallit based his calculations on the assumption that post-comma sums are distributed evenly between 1 and 99, but he admits that this may not be the case in reality. The assumption could be inexact for various reasons, writes Shallit, one of them being that the prices for many items end with a 9. Benford's Law, which says that more sums beginning with a 1 appear in real life than one would assume, could also qualify Shallit's findings.
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