MathDB

In a badminton tournament, each of

n

players play all the other

n-1

players. Each game results in either a win, or a loss. The players then write down the names of those whom they defeated, and also of those who they defeated. For example, if

A

beats

B

and

B

beats

C,

then

A

writes the names of both

B

and

C

. Show that there will be one person, who has written down the names of all the other

n-1

players. [hide="Clarification"] Consider a game between

A,B,C,D,E,F,G

where

A

defeats

B

and

C

and

B

defeats

E,F

C

defeats

E.

Then

A

's list will have

(B,C,E,F)

, and will not include

G.

Problem Statement