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v^2_1 +v^2_2 +...+v^2_n = p^2_1 +p^2_2 +...+p^2_n, in basketball tournament

Source: ITAMO 1988 p2

February 2, 2020
gamecombinatorics

Problem Statement

In a basketball tournament any two of the nn teams S1,S2,...,SnS_1,S_2,...,S_n play one match (no draws). Denote by viv_i and pip_i the number of victories and defeats of team SiS_i (i=1,2,...,ni = 1,2,...,n), respectively. Prove that v12+v22+...+vn2=p12+p22+...+pn2v^2_1 +v^2_2 +...+v^2_n = p^2_1 +p^2_2 +...+p^2_n
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