This method catches 100% of all single-digit errors. Furthermore, the only errors of the form ...ai....aj... ...Aj...ai... That go undetected are those where i=1 and j=7 (an unlikely error indeed) and some involving the check digits 0 and 1. Assuming that all transposition errors are equally likely , this method detects 98.2% of such errors. The Vermont scheme is the same as the one used by New Mexico except that when x=0,