Banking, part III

My Code Card arrived in the mail. Okay, I need to modify what I wrote in the previous post (Banking, part II). This card is not generic. Rather, a portion of the instructions brings a strange clarity: "For security reasons, your Code Card has a limited life- each code can be used just once. But don't worry, you will automatically receive a new code card in the post as you approach the end of each card."

So here's the deal. Whenever I want to make a phone or internet transaction, I will be asked to look at my Code Card and give the long number that is next to the short number that they prompt me with. The card contains 100 possible prompting numbers, and each one can only be used once.

My immediate reaction is to figure out how the short numbers correspond to the long numbers. What I mean is, whenever the operator prompts me for the longer number, how does he/she know I'm giving the correct code? Since each customer of this bank in all of Ireland has 100 code numbers, and these only have only one life, surely they are not keeping some database of all these numbers? Rather, I imagine that there is some system of associating long number to short number so that the operator can tell whether it is a legitimate pair, without actually needing to know the entire number. For example, if she prompts me for a general number "abc", perhaps the number "x" I give should be such that "a+b" is the first digit, "|b-c|" is the second digit, the third digit denotes the sign of "b-c" (1 for positive, 0 for negative), etc. Okay, maybe it's not quite like that, but you get my point? I wonder what the system for generating these codes is...it's certainly not random. Perhaps this will be my entertainment on my bus commute to work each day, to discover the pattern...

No, not really, I've got better things to do and people to watch.