Someone asked me this question a few days ago, and I have a few ideas on how to do it, but it seems to be too much work for a problem of this nature.
We know that a number is divisible by 3 if the sum of all its digits are divisible by 3.
The question is either:
Prove that this is so
Prove why this is so
I don't remember, but I think they amount to pretty much the same thing