7. Find the reminder when 333666777888999 is divided by 3

Question

or 9 or 11 ?

Answer 1

Add up the digits - take mod 9. That's the remainder mod 9

Add up the digits - take mod 3. That's the remainder mod 3

Go from left to right, alternately subtracting and adding digits. The result is the remainder mod 11
(This is because 100 = 1 mod 11 but 10 = -1 mod 11)

Answer 2

3-0
9-0
11-5