3-5. Five people play several games of dominoes (two on two) so that each player has each other as a partner once and as an opponent twice. Find the number of games played and all possible ways of distributing the players.
Solution 5. Answer: 5 games; the distribution of players is unique (up to their numbering). First, let's see who the 1st player played with. We can assume that the 1st and 2nd played against the 3rd and 4th, and the 1st and 5th played against the 2nd and 3rd (this can be achieved by swapping the 3rd and 4th). The 3rd player has already been an opponent of the 1st twice, so the 2nd and 5th play against the 1st and 4th. After this, the 2nd cannot play against the 1st, so the 4th and 5th play against the 1st and 3rd. The last game remains: the 2nd and 4th play against the 3rd and 5th.

\section*{10th Grade}