$\underline{\text { Folklore }}$

Among the actors of Karabas Barabas theater, a chess tournament was held. Each participant played exactly one game with each of the others. One solido was given for a win, half a solido for a draw, and nothing for a loss. It turned out that among any three participants, there would be a chess player who earned exactly 1.5 solido in games with the other two. What is the maximum number of actors that could have participated in such a tournament?
Example. Let's denote the participants with letters A, B, V, G, D. Suppose A won against B, B won against V, V won against G, G won against D, D won against A, and all other matches ended in a draw. The condition of the problem is satisfied.

Evaluation. From the condition, it follows that for this tournament, two statements must be true:

1) there are no three players, all matches between whom ended in a draw;
2) there are no players whose matches did not end in a draw.

Assume that there were at least six players in the tournament. Let's leave only them and draw a complete graph with six vertices (corresponding to these six players), where blue edges correspond to decisive matches, and red edges correspond to draws. According to problem $\underline{30815}$, there are three vertices in it, all edges between which are of the same color. But this contradicts the statements just formulated.

## Answer

5 players.