Question 45
Twelve friends play a tennis tournament, where each player plays exactly one game with each of the eleven other players. The winner wins one point and the loser gets zero points, while there is no tie. If the number of points of the players are $B_1, B_2, ..., B_{12}$, find the maximum value of $\Sigma_3 = B_1^3 + B_2^3 + \dots + B_{12}^3$.