Back in 1937, a mathematician by the name of Lothar Collatz came up with a problem or a conjecture depending on your view. However, since his discovery, it has become one of the most famous unsolved problems in mathematics. In essence, it appears to be a simple procedure. Honestly, follow me on this one. But, the problem is proving why this should happen.
So, how does it all work?
Take any positive number. If it is even, then halve it. If it is odd, multiply by 3 and add 1. An example which has been used before is starting off with the number 11. It is an odd number and so we will multiply it by 3 and add 1.
11 x 3 = 33 + 1 = 34
That’s nice and simple. Now, repeat the process. To save you the time, it is as follows:
11 – 34 – 17 – 52 – 26 – 13 – 40 – 20 – 10 – 5 – 16 – 8 – 4 – 2 – 1
So, what’s so strange about this you might ask?
Well, take the final three numbers in the sequence. They are 4 – 2 – 1.
If you repeat the process with any positive odd or even number you will end up with 4 – 2 – 1.
Let us take the last three numbers: 4 – 2 – 1.
4 is even, so halve it = 2
2 is even = 1
1 is odd = 4
4 is even = 2 and on and on.
Try it with some other numbers and the sequence will eventually arrive at 4 – 2 – 1 recurring.
Now, work out why!
John Pullen 