Question

Вадим располагает на клетчатой доске n×n плитки в виде прямоугольников 1×4 так, чтобы оне не имели общих точек (плитки не могут даже касаться друг друга). При каком наименьшем n Вадиму удастся расположить таким образом 2021 плитку?

Answer 1

Ответ:а я ток вышел с олимпиады и хз как оно решается

Пошаговое объяснение:

Answer 2

Minimum value of n to arrange 2021 tiles without common points

To determine the minimum value of n for Vadim to arrange 2021 tiles in the form of non-overlapping 1x4 rectangles on an n x n checkerboard, we need to find a configuration that satisfies the given conditions.

Since the tiles cannot have any common points, they cannot even touch each other. This means that each tile must have at least one empty row or column between them. Let's consider a possible arrangement:

- Each tile occupies 4 cells horizontally. - To ensure that the tiles do not touch each other, we need to leave at least one empty cell between each tile horizontally. - Therefore, the total number of cells occupied by the tiles and the empty cells between them is 5 cells horizontally.

Based on this configuration, we can calculate the minimum value of n as follows:

- The total number of cells occupied by the tiles and the empty cells between them is 2021 * 5 = 10105 cells. - Since the checkerboard is square (n x n), the total number of cells is n^2. - Therefore, we need to find the smallest square number (n^2) that is greater than or equal to 10105.

Using this approach, we can calculate the minimum value of n as follows:

- n^2 >= 10105 - n >= sqrt(10105) - n >= 100.52 (rounded up to the nearest integer)

Therefore, the minimum value of n for Vadim to arrange 2021 tiles without common points is 101.

Please note that this calculation assumes that the tiles can be arranged in a single row. If the tiles need to be arranged in multiple rows, the minimum value of n may be different.