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%I #41 Aug 12 2023 00:23:54
%S 1,5,10,18,25,50
%N Amounts (in cents) of coins in denominations suggested by Shallit.
%C The following is quoted (with minor changes) from Alan Burdick's article: "Jeffrey Shallit analyzed the average handful of change, and devised a clever way to reduce its size. Getting rid of the 1-cent coin, a plot advocated by numerous antipennyists, would certainly help, he says. But Shallit's own scheme for reducing loose change involves the creation of an entirely new coin. What the United States needs, he says, is an 18-cent piece. Shallit reached this conclusion by a linear Diophantine equation. Shallit calculated that the average U.S. transaction produces 4.7 coins in change. If we got rid of the dime and replaced it with an 18-cent coin, the 'cost' of the average transaction would drop from 4.7 to 3.89 coins. A system of coins worth 1¢, 5¢, 18¢, and 29¢ would have the same effect. Should we wish to keep the dime and simply add a fifth denomination, the best coin to add would be 32¢, for an efficiency of 3.46. Even better, if we kept the dime and actually used the half-dollar, then added an 18-cent coin to that mix, we'd gain maximum efficiency: You'd get back a mere 3.18 coins per transaction."
%H Alan Burdick, <a href="https://www.discovermagazine.com/the-sciences/the-physics-of-pocket-change">The Physics of ... Pocket Change</a>, Discover, October 2003 issue; published online October 1, 2003.
%H Thomas Young, <a href="/A208953/a208953.pdf">Change the Dime not the Dollar!</a>, preprint, 1995.
%Y Cf. A212773, A212774.
%Y See A364607 for another version. - _N. J. A. Sloane_, Aug 12 2023
%K nonn,fini,full
%O 1,2
%A _Jonathan Vos Post_, May 31 2012