kamilmatematik100504
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25 tennis players played a tournament in one round (each played with each exactly 1 time). Among any five players, there is a player who won from all the other four, and a player who lost to all the other four.
Prove that if tennis player A won from tennis player B, and tennis player B won from tennis player C, then tennis player A won from tennis player C

Respuesta :

francocanacari

Since 25 tennis players played a tournament in one round (each played with each exactly 1 time), and among any five players, there is a player who won from all the other four, and a player who lost to all the other four, To prove that if tennis player A won from tennis player B, and tennis player B won from tennis player C, then tennis player A won from tennis player C, the following mathematical logical reasoning must be performed:

Given that in every group of 5 players, there will be one who won 4 matches and another who lost 4 matches, and as there is no tie in tennis, the following results may occur:

  • -Player victories A = B, C, D and E
  • -Victures of Player B = C, D and E
  • -Player wins C = D and E
  • -Player wins D = E
  • -Player victories E = None

Thus, the given relationship is demonstrated, with which the proposal is correct.

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