There is always a player such that every other player was either beaten by him or beaten by a player beaten by him
Every participant of a tournament plays with every other participant exactly once. No game is a draw. After the tournament, every player makes a list with the names of all the players, who either
(i) were beaten by him or (ii) were beaten by a player beaten by him.
Prove that there is a player whose list contains the names of all other players. (Hint: use the extremal principle )

574
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
160
-
Brilliant! Thank you.
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 1031 views
- $10.00
Related Questions
- Game Theory Question
- Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that $f(2n)+2f(2m)=f(f(n+m))$, $\forall m,n\in \mathbb{Z}$
- $2n$ ambassador seating around a round table so that no one seats next to an enemy
- Game theory questions
- Two players alternately remove nodes from a connected graph G
- Two persons with the same number of acquaintance in a party
- IRS Game Theory Question
- Rotational symmertries of octahedron, $R(O_3)$