Solve the system of equations where are four different real numbers.
%V0
Solve the system of equations $$|a_1-a_2|x_2+|a_1-a_3|x_3+|a_1-a_4|x_4=1$$ $$|a_2-a_1|x_1+|a_2-a_3|x_3+|a_2-a_4|x_4=1$$ $$|a_3-a_1|x_1+|a_3-a_2|x_2+|a_3-a_4|x_4=1$$ $$|a_4-a_1|x_1+|a_4-a_2|x_2+|a_4-a_3|x_3=1$$ where $a_1, a_2, a_3, a_4$ are four different real numbers.
Izvor: Međunarodna matematička olimpijada, shortlist 1966
Školjka 
where 
are four different real numbers.