The Starting Point of Payment Efficiency

When ensuring payment efficiency, the goal is to minimise the number of coins and notes required to make and settle a payment. There are many ways to achieve this. Perhaps the simplest methodology to achieve an optimal currency structure for coins and banknotes is the principle of least effort, ie. the settlement of cash transactions using, on average, as few coins and/or banknotes as possible. Least effort points to a denominational structure of 1,2,4 etc ¹. 

There is an approach based on a famous problem in number theory, the problem of Bâchet ² which follow the powers of three (ie., 1, 3, 9, 27, 81, 243…) (see Appendix 1). However, in the real world, the structures based on the power of three are not used.