Console App
Odds are you have a credit card in your wallet. That card has a number, both printed on its face and embedded (perhaps with some other data) in the magnetic stripe on back. That number is also stored in a database somewhere, so that when your card is used to buy something, the creditor knows whom to bill. There are a lot of people with credit cards in this world, so those numbers are pretty long: American Express uses 15-digit numbers, MasterCard uses 16-digit numbers, and Visa uses 13- and 16-digit numbers. And those are decimal numbers (0 through 9), not binary, which means, for instance, that American Express could print as many as 10^(15) = 1,000,000,000,000,000 unique cards! (That’s, ahem, a quadrillion.) Now that’s a bit of an exaggeration, because credit card numbers actually have some structure to them.
- American Express numbers all start with 34 or 37;
- MasterCard numbers all start with 51, 52, 53, 54, or 55;
- Visa numbers all start with 4.
But credit card numbers also have a "checksum" built into them, a mathematical relationship between at least one number and others. That checksum enables computers to detect typos (e.g., transpositions), if not fraudulent numbers, without having to query a database, which can be slow.
- Multiply every other digit by 2, starting with the number’s second-to-last digit, and then add those products'digits together.
- Add the sum to the sum of the digits that weren’t multiplied by 2.
- If the total’s last digit is 0 (or, put more formally, if the total modulo 10 is congruent to 0), the number is valid!
- Let’s try an example with American Express: 378282246310005.
- For the sake of discussion, let’s first underline every other digit, starting with the number’s second-to-last digit: 378282246310005 Okay, let’s multiply each of the underlined digits by 2: 7•2 + 2•2 + 2•2 + 4•2 + 3•2 + 0•2 + 0•2 That gives us: 14 + 4 + 4 + 8 + 6 + 0 + 0 Now let’s add those products' digits (i.e., not the products themselves) together: 1 + 4 + 4 + 4 + 8 + 6 + 0 + 0 = 27
- Now let’s add that sum (27) to the sum of the digits that weren’t multiplied by 2: 27 + 3 + 8 + 8 + 2 + 6 + 1 + 0 + 5 = 60
- Yup, the last digit in that sum (60) is a 0, so the card is legit!
So, validating credit card numbers isn’t hard, but it does get a bit tedious by hand. Let’s write a program. Write a program that prompts the user for a credit card number and then reports whether it is a valid American Express, MasterCard, or Visa card number, per the definitions of each’s format herein.