# Luhn in Clojure

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

1 | ```
exercism fetch clojure luhn
``` |

# Luhn

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

1 |
```
4539 1488 0343 6467
``` |

The first step of the Luhn algorithm is to double every second digit, starting from the right. We will be doubling

1 |
```
4_3_ 1_8_ 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:

1 |
```
8569 2478 0383 3437
``` |

Then sum all of the digits:

1 |
```
8+5+6+9+2+4+7+8+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

1 |
```
8273 1232 7352 0569
``` |

Double the second digits, starting from the right

1 |
```
7253 2262 5312 0539
``` |

Sum the digits

1 |
```
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 http://en.wikipedia.org/wiki/Luhn_algorithm

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.