3. Vitya has a white board consisting of 16 cells in the form of a $4 \times 4$ square, from which he wants to cut out 4 white three-cell corners. Petya, on the other hand, wants to prevent him by coloring some cells red. What is the minimum number of cells he will have to color? (A corner is a figure shown in the picture, possibly rotated.)

![](https://cdn.mathpix.com/cropped/2024_05_06_f9eb37aa5326e8abce5ag-1.jpg?height=144&width=133&top_left_y=1370&top_left_x=1820)
Solution. If you cut out one cell (any) from the board, the remaining part can be divided into five corners. If you cut out another one, four of these five corners will remain. Therefore, one or two cut-out cells are not enough to prevent Vitya. The placement of three cells (for example, in a row along one of the main diagonals) is sufficient.