Question

СРОЧНООООО!!!Дана клетчатая доска. Играют двое, ходят по очереди, за ход разрешается вычеркнуть любую горизонталь или любую вертикаль, если в ней к моменту хода есть хотя бы одна невычеркнутая клетка. Проигрывает тот, кто не может сделать ход. Кто может обеспечить себе победу — начинающий или его партнёр, если доска имеет размеры а) 5 × 5 клеток; б) 9 × 10 клеток.

Answer 1

Ответ:a), в) У второго; б) у первого.

Пошаговое объяснение:

а) Стратегия второго: всегда оставлять чётное число невычеркнутых строк и чётное число невычеркнутых столбцов. При этом у него всегда есть ход.

б) Стратегия первого: первым ходом оставить таблицу 8×10, а затем играть по стратегии п. а).

в) Стратегия второго: после любого хода первого игрока оставить 8×10, а затем играть по стратегии п. a)

Answer 2

Rules of the Game

In this game, two players take turns playing on a checkered board. Each player has the option to cross out any horizontal or vertical line on the board, as long as there is at least one unchecked cell in that line. The game continues until one player is unable to make a move. The player who cannot make a move loses the game.

Winning Strategy for a 5x5 Board

To determine who can guarantee a victory on a 5x5 board, we need to analyze the game. Let's consider the possible scenarios:

1. Starting Player: If the starting player makes a specific move, they can force a win regardless of their opponent's moves. The starting player can achieve this by crossing out the central cell on their first move. This forces the opponent into a losing position, and the starting player can always mirror their opponent's moves to secure a win.

2. Second Player: If the starting player does not make the winning move mentioned above, the second player can guarantee a win. The second player can achieve this by mirroring the starting player's moves. By doing so, they can always maintain symmetry and force the starting player into a losing position.

Therefore, the player who can guarantee a victory on a 5x5 board depends on the starting player's move. If the starting player crosses out the central cell, they will win. Otherwise, the second player will win.

Winning Strategy for a 9x10 Board

Analyzing the winning strategy for a 9x10 board is more complex due to its larger size. However, we can still determine the outcome based on the following observations:

1. Starting Player: If the starting player makes a specific move, they can force a win regardless of their opponent's moves. The starting player can achieve this by crossing out the central row or column on their first move. This forces the opponent into a losing position, and the starting player can always mirror their opponent's moves to secure a win.

2. Second Player: If the starting player does not make the winning move mentioned above, the second player can guarantee a win. The second player can achieve this by mirroring the starting player's moves. By doing so, they can always maintain symmetry and force the starting player into a losing position.

Therefore, the player who can guarantee a victory on a 9x10 board depends on the starting player's move. If the starting player crosses out the central row or column, they will win. Otherwise, the second player will win.

Conclusion

In summary, the player who can guarantee a victory in the game on a 5x5 board depends on the starting player's move. If the starting player crosses out the central cell, they will win. Otherwise, the second player will win. Similarly, on a 9x10 board, the player who can guarantee a victory depends on the starting player's move. If the starting player crosses out the central row or column, they will win. Otherwise, the second player will win.