Are those coins in your pocket a burden? Do you wish you didn’t have to carry so many? Mathematicians have discovered that we’d have to carry fewer if the dime were replaced by an eighteen-cent piece.

Most businesses in the United States make change using just four different types of coins: 1 cent (penny), 5 cents (nickel), 10 cents (dime), and 25 cents (quarter). This distribution of coinage suggests an interesting question: Is it the most efficient way to make change? In other words, is this the optimal choice of coin values for minimizing the number of coins required to handle typical transactions? Computer scientist Jeffrey Shallit of the University of Waterloo has worked out an answer. In the current issue of the Mathematical Intelligencer, he contends that “what the U.S. needs is an 18-cent piece.”

In 1995, a group of high-schoolers and their teacher came to the same conclusion. You can read their analysis (with fun charts) in this PDF: Change the Dime not the Dollar! Replacing the dime with an eighteen-cent piece would reduce the number of coins required to make change for a transaction from an average of 4.70 to an average of 3.89.

Change-making could apparently be made even more efficient not by replacing the dime, but by adding a fifth coin: a 32-cent piece.

Finally, here’s a bit of trivia:

The United States has experimented briefly with extra coin denominations. At one time or another in the distant past, the U.S. mint issued half-cent, two-cent, three-cent, and 20-cent pieces

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