I devised designs for Quatloo tokens. Neither notes nor coins, Quatloo tokens are made from a flexible material printed with distinctive designs front and rear. Each Quatloo token has electrical contacts on both sides and the obverse shows a number denoting the value of the token. Quatloo coins contain RFID circuitry which enables them to be authenticated and recognised by automatic machinery.
Front of 1 Quatloo token and back of all low value tokens
Front of 3, 9 and 27 Quatloo tokens
The values of the tokens are consecutive powers of three. It is possible to pay amounts up to 200 quatloos if you have one of each token. To pay 10 quatloos you pay a 9 and a 1. To pay 100, you pay a 1, a 27 and an 81 and you receive a 9 in change. Even for a decimal system, this set of denominations is more efficient than the usual 1, 2, 5 and 10.
The masses of the tokens are small prime numbers. This means that the weight of any heap of quatloos can be made up in only one way, and the values of the coins in the heap can be found by solving a diophantine equation. For example if 1 Q weighs 7 g, 3 Q weighs 11 g, 9 Q weighs 17 g, 27 Q weighs 23 g, then a heap of quatloos weighing 64 g is made up of one 1 Q coin, two 9 Q coins and one 23 Q coin and its value is 64 Q. Although the masses can be small prime numbers only in one specified set of units, the diophantine equation can be cast in any set of units since the masses of the tokens will have no factors in common.
Front and back of the two high value Quatloo tokens, 81 and 243 Quatloos
The purpose of the electrical contacts is unknown. They may be for authentication checking, for temporarily disabling the tokens as a precaution against theft, or possibly for making them light up in the dark.