This is a simple visualization of http://en.wikipedia.org/wiki/Collatz_conjecture - and from the Wikipedia article :

Paul Erdős said, allegedly, about the Collatz conjecture: "Mathematics is not yet ripe for such problems." and also offered $500 for its solution.

Which is a very strong indication that this will be a tough nut to crack... Even if many people are given it as year 7 homework.