# Luhn

Welcome to Luhn on Exercism's C++ Track.
If you need help running the tests or submitting your code, check out `HELP.md`.

## Instructions

Given a number determine whether or not it is valid per the Luhn formula.

The [Luhn algorithm](https://en.wikipedia.org/wiki/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

```text
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

```text
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:

```text
8569 6195 0383 3437
```

Then sum all of the digits:

```text
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

```text
8273 1232 7352 0569
```

Double the second digits, starting from the right

```text
7253 2262 5312 0539
```

Sum the digits

```text
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

### Created by

- @junming403

### Contributed to by

- @elyashiv
- @KevinWMatthews
- @patricksjackson
- @siebenschlaefer

### Based on

The Luhn Algorithm on Wikipedia - http://en.wikipedia.org/wiki/Luhn_algorithm