Steven D. Levitt's Freakonomics blog got an interesting submission from Patrick DeJarnette regarding coins.

DeJarnette was curious how efficient our current system of coinage is in handling amounts with the least coins involved. His results are surprising.

The most efficient system was a tie between 1-cent-piece, 3-cent piece, 11-cent piece, 37-cent piece and (1,3,11,38) at 4.10 coins per transaction.

A more palatable combination that's still more efficient than our current system is (1,4,15,40) with 4.14 coins per transaction.

I don't expect our coins to change anytime soon, but it's interesting to see more efficient combinations.