Perhaps a good measure of whether or not the general populous can perform mental math based on the value of the coins is to check and see whether or not a singl

Perhaps a good measure of whether or not the general populous can perform mental math based on the value of the coins is to check and see whether or not a single dollar is divisible by the value of the coins (as you hinted with the 15 cent coin). It allows for many mental paths to arrive at the correct answer for what amount of coins are needed to make a certain sum. Take the nickel for example, to make 50 cents you might think to yourself, "I just need to divide 50 by 5, which is obviously 10." Alternately one might think, "I know there are 20 nickels in a dollar, if I halve this I'll have half a dollar, which is 50 cents. That means I need 10 nickels." I'd say that the pool of coin values we can choose from then are 50, 25, 20, 10, 5, 2, 1. The two cent piece is already in use in Europe, and many economists have suggested adding it to the coinage in the united states (usually in replacement for the penny altogether). It'd be interesting to see if the 20 cent coin would be a viable addition though.