MasterCard uses identification numbers that are 16 digits in length. The 16th digit is the check digit and is calculated using the LUHN formula (see Problem 21 in Section 1.1), which is a weighted mod 10 check-digit scheme. Use the first 15 digits to calculate the check digit. Double each of the digits in the odd-numbered positions and then add all the digits to obtain the weighted sum. Assign a check digit that makes the weighted sum congruent to 0 mod 10.
a. Is 5281 0023 9894 7221 a valid MasterCard number?
b. Find the check digit for the MasterCard number 5590 2723 8100 133.
c. Find the missing digit in the number 54?1 0032 1816 2235.
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