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Part of 2018 Greece JBMO TST

Problems(1)

largest possible value of sum of third powers in a tennis tournament

Source: Greece JBMO TST 2018 p3

4/29/2019
1212 friends play a tennis tournament, where each plays only one game with any of the other eleven. Winner gets one points. Loser getos zero points, and there is no draw. Final points of the participants are B1,B2,...,B12B_1, B_2, ..., B_{12}. Find the largest possible value of the sum Σ3=B13+B23+...+B123\Sigma_3=B_1^3+B_2^3+ ... + B_{12}^3 .
algebracombinatoricsmaximumSumSum of powers