There are lots of things one can say about Collatz which would seem to affect the problem but really don't. My favorite: All natural numbers belong to a Collatz

There are lots of things one can say about Collatz which would seem to affect the problem but really don't. My favorite: All natural numbers belong to a Collatz graph containing {4, 2, 1} if and only if all natural numbers not divisible by 2 or 3 belong to that Collatz graph.