# Palindrome Products

Detect palindrome products in a given range.

A palindromic number is a number that remains the same when its digits are
reversed. For example, `121` is a palindromic number but `112` is not.

Given the definition of a palindromic number, we define a palindrome _product_
to be the product `c`, such that `a * b = c`, where `c` is a palindromic number and
 `a` and `b` are integers (possibly, but _not_ necessarily palindromic numbers).

For example, the palindromic number 9009 can be written as the palindrome
product: `91 * 99 = 9009`.

It's possible (and indeed common) for a palindrome product to be the product
of multiple combinations of numbers. For example, the palindrome product `9` has
the factors `(1, 9)`, `(3, 3)`, and `(9, 1)`.

Write a program that given a range of integers, returns the smallest and largest
palindromic product within that range, along with all of it's factors.

## Example 1

Given the range `[1, 9]` (both inclusive)...

The smallest product is `1`. It's factors are `(1, 1)`.
The largest product is `9`. It's factors are `(1, 9)`, `(3, 3)`, and `(9, 1)`.

## Example 2

Given the range `[10, 99]` (both inclusive)...

The smallest palindrome product is `121`. It's factors are `(11, 11)`.
The largest palindrome product is `9009`. It's factors are `(91, 99)` and `(99, 91)`.

## Getting Started

Make sure you have read the
[C page](http://exercism.io/languages/c) on the Exercism site. This covers
the basic information on setting up the development environment expected
by the exercises.


## Passing the Tests

Get the first test compiling, linking and passing by following the [three
rules of test-driven development][3-tdd-rules].

The included makefile can be used to create and run the tests using the `test`
task.

    make test

Create just the functions you need to satisfy any compiler errors and get the
test to fail. Then write just enough code to get the test to pass. Once you've
done that, move onto the next test.

[3-tdd-rules]: http://butunclebob.com/ArticleS.UncleBob.TheThreeRulesOfTdd

As you progress through the tests, take the time to refactor your
implementation for readability and expressiveness and then go on to the next
test.

Try to use standard C99 facilities in preference to writing your own
low-level algorithms or facilities by hand.

## Source

Problem 4 at Project Euler [http://projecteuler.net/problem=4](http://projecteuler.net/problem=4)

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