Start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. Otherwise, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value positive integer n, the sequence will always reach 1.

Very easy to

*understand*this problem, but not even the world's best mathematicians have managed to come even close to proving it. I should also warn you that this problem is worth more than $500, maybe about $10 million!