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

Ответ:

22 кузнечика можно поставить.

Объяснение:

В условиях не было сказано о том, что нельзя делать так, что у них был бы всего 1 ход, поэтому рассчитав всё, вышла вот такая картинка:

Б-это белая клетка

Ч-это чёрная

К-это кузнечик

 1 2 345678

1.ЧКЧБКБЧК

2.КЧБКБЧКЧ

3.ЧБКБЧКЧБ

4.БКБЧКЧБК

5.КБЧКЧБКБ

6.БЧКЧБКБЧ

7.ЧКЧБКБЧК

8.КЧБКБЧКЧ

Answer 2

Introduction

The new chess piece, called the "Slonovy Kuznechik" (Elephant Grasshopper), can move by jumping diagonally in any direction through one square. The task is to determine the maximum number of Slonovy Kuznechiks that can be placed on an 8x8 chessboard without any of them attacking each other. Additionally, we need to provide an example of a suitable arrangement with the maximum number of Slonovy Kuznechiks and prove that a greater number cannot be achieved while satisfying all the conditions of the problem.

Maximum Number of Slonovy Kuznechiks

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

Each Slonovy Kuznechik can only occupy squares of the same color on the chessboard (either black or white). Since there are 32 squares of each color on an 8x8 chessboard, the maximum number of Slonovy Kuznechiks that can be placed is 32.

Example of Suitable Arrangement

Here is an example of a suitable arrangement with the maximum number of Slonovy Kuznechiks (32) on an 8x8 chessboard:

B . B . B . B .
. B . B . B . B
B . B . B . B .
. B . B . B . B
. . . . . . . .
W . W . W . W .
. W . W . W . W
W . W . W . W .

In this arrangement, the Slonovy Kuznechiks are represented by "B" and "W" for black and white squares, respectively. Each Slonovy Kuznechik is placed on a square of the same color, and no two Slonovy Kuznechiks are attacking each other.

Proof of Maximum Number

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

Since each Slonovy Kuznechik can only move diagonally through one square, it can only occupy squares of the same color. On an 8x8 chessboard, there are 32 squares of each color. Therefore, the maximum number of Slonovy Kuznechiks that can be placed is 32, as shown in the example above.

If we try to place more than 32 Slonovy Kuznechiks, there will not be enough squares of the same color to accommodate them without violating the condition that no two Slonovy Kuznechiks can attack each other. Thus, it is not possible to place a greater number of Slonovy Kuznechiks while satisfying all the conditions of the problem.

Therefore, the maximum number of Slonovy Kuznechiks that can be placed on an 8x8 chessboard without any of them attacking each other is 32, and it is not possible to place a greater number while satisfying all the conditions of the problem.

I hope this explanation helps! Let me know if you have any further questions.