Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days. Every match has a winner and a loser. Show that it is possible to select a winning player each day without selecting the same player twice. / / / / / textit{Hint: Remember Hall's Theorem}

Question

Mathematics

Perry

18 September, 08:57

Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days. Every match has a winner and a loser. Show that it is possible to select a winning player each day without selecting the same player twice. / / / / / textit{Hint: Remember Hall's Theorem}

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Arthur · Answer 1

Step-by-step explanation:

given that Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days.

this is going to be proved by contradiction

Let there be a winning player each day where same players wins twice, let n = 3 there are 6 tennis players and match occurs for 5days from hall's theorem, let set n days where less than n players wining a day let on player be loser which loses every single day in n days so, players loose to n different players in n days if he looses to n players then, n players are winner but, we stated less than n players are winners in n days which is contradiction. so, we can choose a winning players each day without selecting the same players twice.