$\underline{\text { Folklore }}$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 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.