Credit Check

Premise

The Luhn algorithm is a check-summing algorithm best known for checking the validity of credit card numbers.

You can checkout the full description on Wikipedia: http://en.wikipedia.org/wiki/Luhn_algorithm

Description

(adapted from Wikipedia)

The formula verifies a number against its included check digit, which is usually appended to a partial account number to generate the full account number. This full account number must pass the following test:

• from the rightmost digit, which is the check digit, moving left, double the value of every other digit
• if product of this doubling operation is greater than 9 (e.g., 7 * 2 = 14), then sum the digits of the products (e.g., 10: 1 + 0 = 1, 14: 1 + 4 = 5).
• take the sum of all the digits
• if and only if the total modulo 10 is equal to 0 then the number is valid

Example

Validating an Account Number

We can use the same process to validate an account number. Using 5541808923795240 as our sample input:

Account identifier:    5   5   4   1   8   0   8   9   2   3   7   9   5   2   4   0
2x every other digit:  10  5   8   1   16  0   16  9   4   3   14  9   10  2   8   0
Summed digits over 10: 1   5   8   1   7   0   7   9   4   3   5   9   1   2   8   0
Results summed:        1   5   8   1   7   0   7   9   4   3   5   9   1   2   8   0 = 70

Since the summed results modulo 10 is zero, the account number is valid according to the algorithm.

Exercise

Your objective, using the knowledge above, is to write a program that implements the Luhn algorithm to validate a credit card number