2005 Austrian Mathematical Olympiad Final Round-Part 1/Problem 5

5. Find all real solutions (a,b,c,d,e,f) of the system 4a = (b+c+d+e)^4, 4b = (c+d+e+f)^4, ········· 4 f = (a+b+c+d)^4.

Try it! Hint: Use the concept of "without loss of generality" to create a order relation between a,b,c,d,e,f.