modulo 3 is about finding the remainder when some big number is divided by 3. there is trick: the remainder for the original number is the same as the remainder for the sum of each digit of the original number when it is divided by 3. For example, 123 mod 3 = 6 mod 3 where 1+2+3 = 6. first trick number is the sum of each digit of the original number and second trick number is the sum of each digit of the first trick number.