Identification numbers with check digit algorithms 
The check digit of Euro bank notes
Each letter corresponds to one country and has a numerical value (see table below). For example, letter \(M\) has the value \(5\)).
| LETTER | L | M | N | P | R | S | T | U | V | X | Y | Z |
| VALUE | 4 | 5 | 6 | 8 | 1 | 2 | 3 | 4 | 5 | 7 | 8 | 9 |
Then add to that value all the remaining ten digits in the banknote number.
The check digit is the number (\(1\), \(2\), \(3\),... or \(9\)) that added to the previous sum yields a multiple of nine. In mathematical language, the check digit is the solution \(C\) of the equation \[L+x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}+x_{7}+x_{8}+x_{9}+x_{10}+C=0 (\mbox{mod }9),\] where \(L\) denotes the digit represented by the country letter, \(x_{1}\) the first digit, \(x_{2}\) the second digit, etc..
Note that we are taking Modular Arithmetic and not the usual arithmetic.
What is the effectiveness rate of errors detection of this system?
