Question

Можно ли в квадрате 5x5 покрасить 8 клеток . так чтобы у каждой покрашенной клетки было ровно 3 непокрашенных соседних клетки?клетки считаются соседними если у них есть общая сторона.

Answer 1

Можно в квадрате 5 на 5 покрасить 8 клеток так, кароче смотри на картинке :))

Answer 2

Can 8 cells in a 5x5 square be painted in such a way that each painted cell has exactly 3 unpainted neighboring cells?

To determine if it is possible to paint 8 cells in a 5x5 square such that each painted cell has exactly 3 unpainted neighboring cells, we can analyze the problem.

Let's assume that it is possible to paint 8 cells in the 5x5 square with the given conditions. In order for each painted cell to have exactly 3 unpainted neighboring cells, we need to consider the cells on the edges of the square separately from the cells in the middle.

Cells on the Edges: - Each corner cell has only 2 neighboring cells, so it cannot satisfy the condition of having exactly 3 unpainted neighboring cells. - Each cell on the edge (excluding the corners) has 3 neighboring cells, so it is possible for them to satisfy the condition.

Cells in the Middle: - Each cell in the middle of the square has 4 neighboring cells, so it cannot satisfy the condition of having exactly 3 unpainted neighboring cells.

Based on this analysis, it is not possible to paint 8 cells in a 5x5 square in such a way that each painted cell has exactly 3 unpainted neighboring cells. The conditions cannot be met due to the limitations of the corner cells and the cells in the middle of the square.

Please note that the search results did not provide specific information or solutions regarding this particular problem. The analysis above is based on the understanding of the problem and the properties of a 5x5 square.