Collatz Conjecture

How it works:

1. Start with any positive integer, n.
2. If n is even, the next number is n / 2.
3. If n is odd, the next number is 3n + 1.
4. Repeat the process with the new number. The conjecture is that you will always eventually reach 1.

Why is it unsolved? While computers have tested quintillions of numbers and found they all reach 1, this isn't a mathematical proof. A proof must show it's true for every positive integer. No one has found a pattern that guarantees the sequence doesn't either grow to infinity or get stuck in another loop for some incredibly large number.