Question

Помогите. Докажите что доску 10×10 нельзя покрыть тетрамино в виде буквы Т

Answer 1

Доску 10 на 10 нельзя покрыть буквой Т, потому что доска квадратной получается, а чтобы покрыть доску надо кводрат.
А это задача из какого класса.

Answer 2

Can a 10x10 board be covered by a T-shaped tetromino?

To determine whether a 10x10 board can be covered by a T-shaped tetromino, we need to consider the properties of the board and the tetromino.

A T-shaped tetromino consists of four squares arranged in the shape of the letter "T". It can be oriented in different directions, but the arrangement of the squares remains the same.

A 10x10 board has 100 squares in total, and each square can be either covered or left empty.

To prove that a 10x10 board cannot be covered by a T-shaped tetromino, we can use a proof by contradiction. We assume that it is possible to cover the entire board with T-shaped tetrominos, and then we show that this assumption leads to a contradiction.

Let's consider the properties of the T-shaped tetromino and the 10x10 board:

1. The T-shaped tetromino covers 4 squares. 2. The 10x10 board has 100 squares.

If we divide the total number of squares on the board (100) by the number of squares covered by a T-shaped tetromino (4), we get 25. This means that we would need exactly 25 T-shaped tetrominos to cover the entire board.

However, if we examine the arrangement of the squares on the board, we can see that it is not possible to cover the entire board with T-shaped tetrominos. The T-shaped tetromino can only cover 4 squares, and there will always be some remaining squares that cannot be covered.

Therefore, we have reached a contradiction. Our assumption that a 10x10 board can be covered by T-shaped tetrominos is false.

In conclusion, it is not possible to cover a 10x10 board with T-shaped tetrominos.