An alternative definition of efficiency is total number of coins you need to carry in your pocket to cover a single transaction of 1..99 cents. Interestingly al

An alternative definition of efficiency is total number of coins you need to carry in your pocket to cover a single transaction of 1..99 cents. Interestingly all the good 4-coin solutions in the article, including (1, 3, 11, 37) as well as our current (1, 5, 10, 25), require a total of 10 coins. There are 12 other 4-coin solutions, (1, 3, 9, 25) being the most reasonable looking, that only require a total of 9 coins.