# 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)` and `(3, 3)`.

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

Not all ranges of factors can produce a Palindrome, and ranges must have their max at least as large
as their min. This exercise uses the OCaml `Result.t` type to specify errors.

## Example 1

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

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

## Example 2

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

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


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## Source

Problem 4 at Project Euler

Wikipedia [http://projecteuler.net/problem=4](http://projecteuler.net/problem=4)

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