Christmas Contest - Team Round - Problem 29

If a_1 + a_2 + ... + a_n = 64, Find the minimum value of:

\dfrac{{a_1}^4}{{a_1}^3 + {a_1}^2a_2 + a_1{a_2}^2 + {a_2}^3} + \dfrac{{a_2}^4}{{a_2}^3 + {a_2}^2a_3 + a_2{a_3}^2 + {a_3}^3} + ... + \dfrac{{a_n}^4}{{a_n}^3 + {a_n}^2a_1 + a_n{a_1}^2 + {a_1}^3}