kochlyfe / tp-validator

Howdy partner, hey dude, cheers mate, good morning comrade,...

or wherever you are in the world and what people use there to wish a good morning

Here is your toyproblem: The credit card validator!!!

How are credit cards checked if they are valid and what company they belong to? It is all about the numbers. And you will write a function that checks if a credit card is valid an what company it is from.

First some theory (you will need it).

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 a bit of an exaggeration, because credit card numbers actually have some structure to them. All American Express numbers start with 34 or 37; most MasterCard numbers start with 51, 52, 53, 54, or 55 (they also have some other potential starting numbers which we won’t concern ourselves with for this problem); and all Visa numbers 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 (or humans who like math) to detect typos without having to query a database.

Luhn's Algorithm

So what’s the secret formula? Well, most cards use an algorithm invented by Hans Peter Luhn of IBM. According to Luhn’s algorithm, you can determine if a credit card number is (syntactically) valid as follows:

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! That’s kind of confusing, so let’s try an example with David’s Visa: 4003600000000014.

For the sake of discussion, let’s first underline every other digit, starting with the number’s second-to-last digit:

4003600000000014

Okay, let’s multiply each of the underlined digits by 2:

1•2 + 0•2 + 0•2 + 0•2 + 0•2 + 6•2 + 0•2 + 4•2

That gives us:

2 + 0 + 0 + 0 + 0 + 12 + 0 + 8

Now let’s add those products’ digits (i.e., not the products themselves) together:

2 + 0 + 0 + 0 + 0 + 1 + 2 + 0 + 8 = 13

Now let’s add that sum (13) to the sum of the digits that weren’t multiplied by 2 (starting from the end):

13 + 4 + 0 + 0 + 0 + 0 + 0 + 3 + 0 = 20

Yup, the last digit in that sum (20) is a 0, so David’s 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.

A test is written for you, but you can also use some fake valid card numbers from https://developer.paypal.com/docs/payflow/payflow-pro/payflow-pro-testing/