>>9451455>>9451518>Sum every number 3 times and you get 3 6 9, no idea why tough.That's because you are multiplying by 3. Summing the same number 3 times is multiplication by 3. Since 3 is the lowest common denominator between 3, 6 and 9, you will always end up with one of those numbers.
The real question is about adding the digits. I vaguely recall some memetic mental math tricks where 3, 6 and 9 had their own special rules. If I could remember, that may be the explanation for it. It might go something like "for any number that is a multiple of 3, its digits will add up to 3, 6 or 9".
What I wrote above trivializes the question.
Whatever is the real answer, it would have to be geometric in nature.
