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 )
Savionf
573
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
Jbarth
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
- 928 views
- $10.00
Related Questions
- IRS Game Theory Question
- Bayesian Nash Equilibrium
- Rubinstein Bargaining Variation Problem in Game Theory
- If both $n$ and $\sqrt{n^2+204n}$ are positive integers, find the maximum value of $𝑛$.
- Prove that one of $(n+1)$ numbers chosen from $\{1,2, \dots, 2n\}$ is divisible by another.
- Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that $f(2n)+2f(2m)=f(f(n+m))$, $\forall m,n\in \mathbb{Z}$
- Is it possible to transform $f(x)=x^2+4x+3$ into $g(x)=x^2+10x+9$ by the given sequence of transformations?
- A car running out of gas on a circular track
