Problem #1
ZIP Code: Given the following ZIP code (4X122Y), which corresponds to an address in the fourth zone.
(a) What is the set of all possible values for the check digit Y? For more details about the zones defined in the US, you may refer to your lectures.
(b) Assume that the USPS office would like to add 4-digit extension to the ZIP code mentioned above. Give three possible sets of such 4-digit extension such that your answer for (a) will not change.
Problem #2
Given a credit card number (5518-X201-2345-6781),
(a) What is the suitable value for X?
(b) If we would like to make the check digit 5, what is the suitable value for X?
Problem #3
The routing number of a bank in the U.S. is (123271978). For some reasons, the bank is asked to eliminate ‘7' from the routing number. Notice that ‘7' appears twice in the routing number.
Provide four possible options to replace ‘7' in the routing number without changing the others digits in the routing number. For example, one option is (4,0). So if we replace the first ‘7' by ‘4'and the second ‘7' by ‘0', the result is (123241908). The later is still a valid routing number and we did no change to other digits to the other digits.
Problem #4
Assume an ISBN (87 - 11 - 07559 - 7) is proposed for a new book. The publisher does not want ‘5' to appear in the ISBN. Without changing other digits in the ISBN, provide four options to replace ‘5', which appears twice in the ISBN. For example, (8,1) is an option. This is because (87 - 11 - 07819 - 7) is a valid ISBN.