Many Paths of the Collatz Conjecture

The Collatz Conjecture is one of mathematics' strange unsolved problems. The rule is deceptively simple: take any positive integer, and if it's even divide it by 2, if it's odd multiply by 3 and add 1. Repeat this process and the sequence seems to always eventually reach 1. Always. This is true for every number ever tested! Even still, no one has ever been able to prove it, though some attempts…