# Squares, Floors and Fractions? Pfft!

**Number Theory**Level 5

\(x_1 , x_2 , x_3 , x_4\) and \(x_5\) are positive integers such that

\[\left \lfloor \dfrac {x_1 + x_2}{3} \right \rfloor^2 + \left \lfloor \dfrac {x_2 + x_3}{3} \right \rfloor^2 + \left \lfloor \dfrac {x_3 + x_4}{3} \right \rfloor^2 + \left \lfloor \dfrac {x_4 + x_5}{3} \right \rfloor^2 = 38\]

and \(x_1 > x_2 > x_3 > x_4 > x_5\). Find the sum of all the numbers \(x_1, x_2, x_3, x_4, x_5\) in all solutions.