Prove that if no team loses all of its games, then at least two teams will finish the tournament with the same number of wins

995 Views Asked by At

Prove the following statement by induction.
Suppose that eight hockey teams are entered in a round-robin tournament, which means that each team plays every other team exactly once. Assume that no ties are allowed (e.g., all ties will go to a penalty shootout). Prove that if no team loses all of its games, then at least two teams will finish the tournament with the same number of wins.

1

There are 1 best solutions below

2
On

8 teams, each team can have 1 to 7 wins.
Pigeon hole the teams into the number of wins.