In case people don't know the Collatz Conjecture, It's based on a simple rule: take any natural number n. If it is even, divide it by 2. If it is odd, multiply by 3 and add 1. The conjecture states that no matter what number you start with, you will eventually reach the number 1.

It would seem simple, but many simple iterative calculations get us to Turing machine territory regarding computability.