Euro coins edge of the €2 coin also protects it from counterfeiting. Euro coins were designed in cooperation with organisations representing blind persons, and as a result they incorporate many features allowing them to be distinguished by touch alone. In addition, their visual appearance is designed to make them easy to tell apart for persons who cannot read the inscriptions on the coins. The coins increase in size and weight with value. Of the eight denominations of euro coins, the three lowest denominations are small, resemble copper in colour and are quite thin and light. The next three denominations resemble gold in
Coin problem 1. There is an explicit formula for the Frobenius number when there are only two different coin denominations, "x" and "y" : "xy" − "x" − "y". If the number of coin denominations is three or more, no explicit formula is known; but, for any fixed number of coin denominations, there is an algorithm computing the Frobenius number in polynomial time (in the logarithms of the coin denominations forming an input). No known algorithm is polynomial time in the "number" of coin denominations, and the general problem, where the number of coin denominations may be as large as desired, is