Take a number. Any number. Done?

Okay, now, we’re gonna do the following thing: if it’s even, we divide it by two. If it’s not, we multiply it by three and add one. Then, we repeat the process again and again.

10, 5, 16, 8, 4, 2, 1, 4, 2, 1…

11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1…

Notice something? They all end in 4, 2, 1! In a loop!

Cool, huh?

Maybe not “real world” cool, but it’s certainly math cool.

The thing is, we don’t know whether it happens for every number or only with the ones we’ve tried so far.

Here is a calculator for this conjecture (which, by the way, is called Collatz Conjecture, guess why)

We think it always finishes in the same loop of three numbers: 1, 2, 4, 1, 2, 4… One way to prove it, then, would be finding a new loop.

But, if there is another loop, it would have to be at least one million steps long. So good luck trying to find it.