A mathematician at the Waterloo was kind of bored and decided to do a pocket change analysis. I guess Canada isn’t too bad, despite having such big coins.
The average Canadian transaction generates 5.9 coins in change. The best way to lower that average, to 4.578, he found, would be for Canada to adopt an 83-cent coin.
He found that the US should have an 18 cent coin and that more than $10 billion sits around in jars and drawers in people’s homes. And the math isn’t really that hard, just linear systems. Although, he did show the problem (like putting stamps on an envelope) to be NP hard.