# Luhn

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

```
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

```
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:

```
8569 2478 0383 3437
```

Then sum all of the digits:

```
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

```
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.

## Running tests

In order to run the tests, issue the following command from the exercise
directory:

For running the tests provided, `rebar3` is used as it is the official build and
dependency management tool for erlang now. Please refer to [the tracks installation
instructions](http://exercism.io/languages/erlang/installation) on how to do that.

In order to run the tests, you can issue the following command from the exercise
directory.

```bash
$ rebar3 eunit
```

### Test versioning

Each problem defines a macro `TEST_VERSION` in the test file and
verifies that the solution defines and exports a function `test_version`
returning that same value.

To make tests pass, add the following to your solution:

```erlang
-export([test_version/0]).

test_version() ->
  1.
```

The benefit of this is that reviewers can see against which test version
an iteration was written if, for example, a previously posted solution
does not solve the current problem or passes current tests.

## Questions?

For detailed information about the Erlang track, please refer to the
[help page](http://exercism.io/languages/erlang) on the Exercism site.
This covers the basic information on setting up the development
environment expected by the exercises.

## Source

The Luhn Algorithm on Wikipedia [http://en.wikipedia.org/wiki/Luhn_algorithm](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.