Given a number determine whether or not it is valid per the Luhn formula.
The Luhn algorithm is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers.
The task is to check if a given string is valid.
Strings of length 1 or less are not valid. Spaces are allowed in the input, but they should be stripped before checking. All other non-digit characters are disallowed.
4539 3195 0343 6467
The first step of the Luhn algorithm is to double every second digit, starting from the right. We will be doubling
4_3_ 3_9_ 0_4_ 6_6_
If doubling the number results in a number greater than 9 then subtract 9 from the product. The results of our doubling:
8569 6195 0383 3437
Then sum all of the digits:
8+5+6+9+6+1+9+5+0+3+8+3+3+4+3+7 = 80
If the sum is evenly divisible by 10, then the number is valid. This number is valid!
8273 1232 7352 0569
Double the second digits, starting from the right
7253 2262 5312 0539
Sum the digits
7+2+5+3+2+2+6+2+5+3+1+2+0+5+3+9 = 57
57 is not evenly divisible by 10, so this number is not valid.
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