The conjecture can be summarized as follows. Take any positive integer n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n+ 1. Repeat the process (which has been called “Half Or Triple Plus One”, or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1.
At the risk of embarrassing myself in front of God and everyone, I’m not a mathematician. Nevertheless, this “unsolved problem” is not only entirely solvable, it seems Lothar Collatz has simply pulled the proverbial hat over the entire mathematics community. How is this a “problem”?
Let’s look at the basics:
- All whole numbers starting with 1 follow a pattern of odd-even-odd-even to ∞
- All odd numbers multiplied by an odd number (in this case 3) always result in an odd number
- Adding 1 to an odd number will always create an even number
- Dividing even numbers by 2 will always (eventually) result in 1
While there maybe some ups and downs in the numbers (the “hailstone sequence”) it nevertheless is obvious that by observing the most basic rules of mathematics dictates that Collatz has no unsolvable “conjecture” but rather just an interesting pattern.
Yes, naturally, this conjecture will always result in 1.
Unless, of course, I’ve missed the point completely.