IKMC 2012 - Grades 11-12 - Paper 01 - Self-study Question 25

How many permutations $(x_1,x_2,x_3,x_4)$ of $\{1,2,3,4\}$ make $x_1x_2+x_2x_3+x_3x_4+x_4x_1$ divisible by 3?