Euro coins Euro coins There are eight euro coin denominations, ranging from one cent to two euros (the euro is divided into a hundred cents). The coins first came into use in 2002. They have a common reverse, portraying a map of Europe, but each country in the eurozone has its own design on the obverse, which means that each coin has a variety of different designs in circulation at once. Four European microstates which use the euro as their currency also have the right to mint coins with their own designs on the obverse side. The coins, and various commemorative coins,
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