Collatz Conjecture: The Unsolvable Problem

Recently I discovered a series of videos called Numberphile. I only watched two, both about a very interesting problem: the Collatz Conjecture.

Imagine you take a number. If it is even, divide it by two, if it is odd, multiply it by three and add one. Take the next number and repeat. Simple, right?

Let’s try it with the number 7.

3 * 7 + 1 = 22

22 / 2 = 11

3 * 11 + 1 = 34

34 / 2 = 17

3 * 17 + 1 = 52

52 / 2 = 13

3 * 13 + 1 = 40

40 / 2 = 20

20 / 2 = 10

10 / 2 = 5

3 * 5 + 1 = 16

16 / 2 = 8

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1

Let’s continue from 1, then.

3 * 1 + 1 = 4

4 / 2 = 2

2 / 2 = 1

The idea of the Collatz Conjecture is that it will always reach 1, and that once it reaches one, it will keep on looping 1,4,2,1,4,2 forever. Nobody knows why this phenomenon happens.

Another interesting problem comes from counting how many steps it takes to get from a certain number to 1 with the Collatz Conjecture. I wrote a program for it which you can see right here:

The problem is finding the pattern between the number and Collatz Conjecture operations. So far, no one has been able to, and some mathematicians think no one will.

Thanks for reading!

For a program which calculates the steps to get from a number to 1 using the Collatz Conjecture, click here.