## Identification numbers with check digit algorithms

### Serial numbers of Euro notes

Surely everyone has already heard about the different security mechanisms of Euro banknotes. They are designed to make life difficult for counterfeiters. There are the holographic band, the watermark and the identifying band, which are well known systems easily visible to everyone. But there is also a less know mechanism used in the generation of the identification numbers of notes. This mechanism serves mainly for detecting errors in the use and transmission of those numbers. Each identification number in Euro banknotes consists of a letter followed by eleven digits. The letter represents the country where the note was issued (for example, Portugal is represented by the letter M) and the eleven digits represent the identification number of the note. Well, this is not quite right because the rightmost digit is just a check digit "similar" to that used, for example, in ID cards. That is, only the first ten digits are used to number the Euro banknotes, the last one is then calculated from those ten. Since there is a genuine banknote with serial number $$T23155172799$$, we can guarantee that, for example, there are not banknotes with serial numbers $$T23155172790$$ or $$T23155172796$$.

 LETTER COUNTRY L Finland M Portugal N Austria P Netherlands R Luxembourg S Italy T Ireland U France V Spain X Germany Y Greece Z Belgium

But after all, how is the check digited computed?