Question

Новая шахматная фигура Слоновый кузнечик умеет за ход прыгать по диагонали в любую сторону через одну клетку. Какое наибольшее число слоновых кузнечиков можно расставить на доске 8×8 так чтобы никакие двое не били друг друга? Кузнечик бьёт те клетки на которые может попасть за один ход. Ставить 2 кузнечиков в одну клетку нельзя. 1.Приведи пример подходящие расстановки наибольшего количества слоновых кузнечиков. 2.Докажи что большее количество слоновых кузнечиков с соблюдение всех условий задачи расставить нельзя

Answer 1

Хз))) хз))) хз)))хз)))

Answer 2

Introduction

The new chess piece called the "Slonovy Kuznechik" (Elephant Grasshopper) can move by jumping diagonally in any direction, but only one square at a time. The task is to determine the maximum number of Slonovy Kuznechiks that can be placed on an 8x8 chessboard without any of them being able to capture each other.

Maximum Number of Slonovy Kuznechiks on an 8x8 Chessboard

To find the maximum number of Slonovy Kuznechiks that can be placed on an 8x8 chessboard without any of them being able to capture each other, we can use a mathematical approach.

Each Slonovy Kuznechik can occupy a square of either black or white color on the chessboard. Since the chessboard has an equal number of black and white squares, the maximum number of Slonovy Kuznechiks that can be placed on the chessboard is equal to the number of squares on the chessboard divided by 2.

The number of squares on an 8x8 chessboard is 64, so the maximum number of Slonovy Kuznechiks that can be placed on the chessboard is 64/2 = 32.

Example Placement of the Maximum Number of Slonovy Kuznechiks

Here is an example of a placement of the maximum number of Slonovy Kuznechiks on an 8x8 chessboard:

W B W B W B W B
B W B W B W B W
W B W B W B W B
B W B W B W B W
W B W B W B W B
B W B W B W B W
W B W B W B W B
B W B W B W B W

In this arrangement, the Slonovy Kuznechiks are placed alternately on black and white squares, ensuring that no two of them can capture each other.

Proving that a Greater Number of Slonovy Kuznechiks Cannot Be Placed

To prove that a greater number of Slonovy Kuznechiks cannot be placed on an 8x8 chessboard while adhering to the given conditions, we can use a mathematical argument.

Since each Slonovy Kuznechik can move by jumping diagonally in any direction, but only one square at a time, it can only move to squares of the opposite color. This means that a Slonovy Kuznechik placed on a black square can only move to white squares, and vice versa.

Since the chessboard has an equal number of black and white squares, and each Slonovy Kuznechik can only move to squares of the opposite color, it is not possible to place more Slonovy Kuznechiks on the chessboard without violating the condition that no two of them can capture each other.

Therefore, the maximum number of Slonovy Kuznechiks that can be placed on an 8x8 chessboard without any of them being able to capture each other is 32, as shown in the example placement above.

Note: The proof provided here is a logical argument based on the properties of the Slonovy Kuznechik and the chessboard. No external sources are required for this proof.