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(531) 3

Part of 1997 Tournament Of Towns

Problems(1)

TOT 531 1997 Spring J A3 - 2n players in chess tournament,

Source:

9/11/2024
In a chess tournament, each of 2n2n players plays every other player once in each of two rounds. A win is worth 11 point, a draw is worth 12\frac12 point and a loss is worth nothing. Prove that if for every player, the total score in the first round differs from that in the second round by at least n points, then this difference is exactly n points for every player.
(B Frenkin)
combinatorics