I have a bunch of serial numbers and their corresponding activation keys for some old software. Since installing them originally I have lost a number of the activation keys (but still have the serial number). I still have a data set of about 20 keys and even eyeballing it I can tell there is a method to the madness in determining the the activation keys. Given my large data set is there a way I can backsolve to figure out the activation keys for the information I lost.

example of serial #: 14051 Activation Key: E9E9F-9993432-45543