Many credit cards use a weighted even/odd code called the LUHN formula. Both MasterCard...

Many credit cards use a weighted even/odd code called the LUHN formula. Both MasterCard and Discover use a 16-digit code. The check digit is the 16th digit and is the number that must be added to the weighted sum to make it divisible by 10. To find the weighted sum, begin with the second digit from the right (the digit next to the check digit) and multiply every other digit by 2. When multiplying by 2, if a two-digit number results, then add the two digits before finding the weighted sum.

For example, the check digit, d, for the Discover card number 6011 2465 0103 721d can be found by calculating the following weighted sum.

Notice that there are three two-digit numbers, namely 12, 12, and 14, that resulted from multiplying by 2. Add the digits in each of those cases.

Because the weighted sum is 35, the check digit must be 5 to yield 35 + 5 = 40, which is divisible by 10.

a. Is the credit card number, 5423 9011 8372 1312, valid under the check-digit scheme we just defined?

b. Use the check-digit scheme we just defined to find the check digit for the credit card number 5532 9014 7389 237.