MathDB

In a chess tournament, each player played at most one game against each other, and the number of games played by each player is not less than the set natural number

n

. Prove that it is possible to divide players into two groups

A

and

B

in such a way that the number of games played by each player of group

A

with players of group

B

is not less than

n/2

and at the same time the number of games played by each player of the

B

group with players of the

A

group was not less than

n/2

Problem Statement