17% more efficient with 18 cent coins

May 16, 2003 22:14 · 208 words · 1 minute read

In the “err, yeah” department we have this dandy Science News article: Coins for Making Change Efficiently, in which Jeffrey Shallit, a Computer Science person:

He discovered two sets of four denominations that minimize the transaction cost. The combination of 1 cent, 5 cents, 18 cents, and 25 cents requires only 3.89 coins in change per transaction, as does the combination of 1 cent, 5 cents, 18 cents, and 29 cents.

Yep… We can gain 17% in change-making efficiency by replacing our dimes with 18 cent coins. But, not only do 18 cent coins seem somewhat unpleasant, since most people are used to thinking in base 10, but Shallit made an assumption that I don’t think is correct…

In finding coin denominations that minimize the average cost of making change, Shallit assumed that every amount of change between 0 and 99 cents is equally likely.

The thing is that many prices here end in $0.99 or $0.95, and then when you add sales tax (which, of course, varies from place to place) you end up with some numbers that will certainly come up more frequently than others. Thankfully, I don’t think the Treasury Department will likely start minting new coins on the basis of this Science News article.