MathDB

In a tennis tournament of

10

players, everyone played against everyone once. In this tournament, if player

i

won the match against player

j

, then the total number of matches

i

lost plus the total number of matches

j

won is greater than or equal to

8

. We will say that three players

i

j

k

form an atypical trio if

i

beat

j

j

beat

k

and

k

beat

i

. Prove that in the tournament there were exactly

40

atypical trios.

6