# Squares, Floors and Fractions? Pfft!

$$x_1 , x_2 , x_3 , x_4$$ 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.

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