... but maybe I wouldn't if we had an 18-cent piece! This is why I love computer science -- you can make a lot of discoveries via simulation that might otherwise never be found or considered because they are so counter-intuitive.
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. For the current four-denomination system, he found that, on average, a change-maker must return 4.70 coins with every transaction.
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.
"We would therefore gain about 17 percent efficiency in change-making by switching to either of these four-coin systems," Shallit says. "The first system possesses the notable advantage that we only need make one small alteration in the current system. We could speed up customer service just by replacing the dime with an 18-cent piece."
"The trouble with 18-cent pieces," he admits, "is that it's hard to figure out the best way to make change in your head."
But in my opinion, the best way to simplify our change system would be to eliminate the penny and round everything to the nearest nickel. However, there are powerful political forces that resist the idea, such as the zinc industry which provides much of the metal that's used to make 12 billion pennies a year, and the states of Colorado and Pennsylvania where the pennies are minted.
Just imagine the huge aggregate amount of time that could be saved if people didn't have to dig through their pockets looking for pennies to make change! Many stores already have penny plates that customers can take pennies from when they need them, and this just goes to show that the penny is useless and out-moded. Bills have been proposed to eliminate the penny, but they've died in subcommittee. It's only a matter of time though... the bell tolls for thee, Penny!