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Putnam 1965 B2

Source:

September 28, 2020
Putnam

Problem Statement

In a round-robin tournament with nn players P1P_1, P2P_2, …\ldots, PnP_n (where n>1n > 1), each player plays one game with each of the other players and the rules are such that no ties can occur. Let wrw_r and lrl_r be the number of games won and lost, respectively, by PrP_r. Show that ∑r=1nwr2=∑r=1nlr2. \sum_{r=1}^nw_r^2 = \sum_{r=1}^nl_r^2.
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