Question

На окружности расставлено 27 точек. За один ход разрешается соединить любые две из них отрезком, не пересекающим ранее проведённые отрезки. Проигрывает тот, кто не может сделать ход. Кто выигрывает при правильной игре?

Answer 1

26 ходов возможно.
27 будет проигрышным.
значит, тот, кто 1 ходит, тот и проиграет.
если правильная игра это самая долгая игра

Answer 2

Game of Connecting Points on a Circle

In this game, 27 points are placed on a circle, and players take turns connecting any two unconnected points with a line segment. The goal is to avoid being unable to make a move. Let's determine who wins this game when played correctly.

Mathematical Analysis: The game of connecting points on a circle is a well-known problem in combinatorial game theory. The player who is unable to make a move loses the game. This problem can be approached using graph theory and combinatorics to determine the winning strategy.

Winning Strategy: The winning strategy for this game is to ensure that each move creates a new region enclosed by the line segments. By following this strategy, a player can always make a move and avoid being unable to continue the game, ultimately forcing the opponent into a losing position.

Conclusion: Therefore, the player who plays correctly and follows the winning strategy will emerge victorious in this game of connecting points on a circle.