Re: Why do multiples of 3 also add to multiples of 3?

Any number, say "abcd", where a, b, c, d are figures chosen in 
{0,1,2,3,4,5,6,7,8,9} has a value equal to d+10*c+100*b+1000*a (* is put 
instead of "times" or x).

Each number 10000…0 (power of 10) is equal to 3333…3*3 +1, that is = 
multiple of 3 + 1. Thus, a number like 1000*a = multiple of 3 +a and 
so, "abcd" = multiple of 3 +a+b+c+d, exactly 9*c+99*b+999*a + a+b+c+d.

If "abcd" is already a multiple of 3, then it must be the same for 
a+b+c+d, because a+b+c+d appears to be the difference of two multiples of 
3 !

You may do the same for 9 instead of 3, using the same figures and 
replacing 3333…3*3 by 1111…1*9

Have a nice day