# Luhn

Medium

## Instructions

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.

### Validating a Number

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.

#### Example 1: valid credit card number

``````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!

#### Example 2: invalid credit card number

``````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.

### Source

The Luhn Algorithm on Wikipedia
Edit via GitHub

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