"Change" Management, Part I

There's a fascinating little article in October 2003 issue of Discover magazine (not yet available on line) under the category of "The Mathematics of ... Pocket Change." In it, a mathematitian named Jeffrey Shallit has a suggestion for helping us deal with all that loose change we keep collecting that goes beyond the simple idea of eliminating the penny. His solution: Create an 18 cent coin. An EIGHTEEN cent coin?! Yes, that's right.

It seems that Dr. Shallit, through the use of a mathematical equation, was able to calculate that if we added an 18 cent coin to American currency, we'd be able to lessen the amount of change we receive, per transaction, from 4.7 coins to 3.89 coins.

Fascinated by this notion, I thought I'd monitor some of my own results:

Purchase: Two medium pizzas (one cheese, one barbeque chicken) and a large salad. Change: 30 cents; 2 coins (a quarter and a nickel). With the new coin: 4 coins (an eighteen, a dime, and 2 pennies). Net: +2. Not much of an improvement so far!

Purchase: Yarn for some scarves my wife and daughter are knitting. Change: 19 cents; 6 coins (a dime, a nickel, and 4 pennies). With the new coin: 2 coins (an eighteen, and a penny). Net: -4. Cumulative Net: -2. Okay, this is good.

Purchase: Some picture hooks and lightbulbs from the local hardware store. Change: 35 cents; 2 coins (a quarter and a dime). With the new coin: 5 coins (an eighteen, a dime, a nickel, and 2 pennies.) Net: +3. Cumulative Net: +1. I'm losing ground again.

Purchase: Gas for my car. Change: 68 cents; 7 coins (2 quarters, a dime, a nickel, and 3 pennies). With the new coin: 8 coins (3 eighteens, a dime, and 4 pennies). Net: +1; Cumulative Net: +2.

Purchase:Office Supplies. Change: 52 cents: 4 coins (2 quarters, and 2 pennies). With new coin: 7 coins (an eighteen, a quarter, a nickel, and 4 pennies). Net: +3. Cumulative net: +5.

Thank you anyway, Dr. Shallit.