The United States Postal Service (USPS) uses 11-digit serialnumbers on its money orders. The first ten digits identify thedocument, and the last digit is the check digit. The check digit isobtained by a11 = a1 + · · · + a10 (mod 9). For example, one of themoney order has serial number 16094004377. (a) The first ten digitsof the serial number on a USPS money order are 7306125986. Find thelast digit (the check digit). (b) Will this scheme detect allsingle-digit errors? Prove your statement. (c) Will this schemedetect all transposition error? Why?
