Question

Consider a tournament with n players where each player plays against every other player. Suppose each player wins
at least once. Show that at least 2 of the players have the same number of wins.

Answer 1

Given :  Consider a tournament with n players where each player plays against every other player.  

each player wins at least once.

To Find : Show that at least 2 of the players have the same number of wins.

Solution:

n players  

Each player plays n-1  matches

each player plays against every other player.  

Hence total matches    n(n - 1) /2    

each player wins at least once.  

Assume no one one wins same number of wins

Then wins can be

1  , 2 , 3 ,  _______________  ,  n  

But Maximum matches  a player  play is n - 1

Hence its not possible that some one wins n matches

Hence that 1 match will be added to some one else win Hence

at least 2 of the players have the same number of wins.  

Learn More

A badminton coach invites players for a practice tournament.

brainly.in/question/38408701

A badminton coach invites players for a practice tournament.

https://brainly.in/question/38406337