MathDB

n

players (

n \ge 4

) took part in the tournament. Each player played exactly one match with every other player, there were no draws. There was no four players

(A, B, C, D)

, such that

A

won with

B

B

won with

C

C

won with

D

and

D

won with

A

. Determine, depending on

n

, maximum number of trios of players

(A, B, C)

, such that

A

won with

B

B

won with

C

and

C

won with

A

. (Attention: Trios

(A, B, C)

(B, C, A)

and

(C, A, B)

are the same trio.)

Problem Statement