IMAS 2014 — Middle Primary Grades 3–4 — Round 2 Question 14

One digit is chosen from each of the three groups \{1, 4, 7\}, \{2, 5, 8\} and \{3, 6, 9\}. The chosen digits are arranged in any order to form a three-digit number. How many such three-digit numbers are divisible by 6?