$\underline{\text { Khachaturyan A.V. }}$.

On a grid paper, a rectangle 200 cells wide and 100 cells high is drawn. It is filled cell by cell, starting from the top left and moving in a spiral (when reaching the edge or an already filled part, turn right, see fig.). Which cell will be filled last? (Specify the number of its row and column. For example, the bottom right cell is in the $100-$th row and $200-$th column.)

![](https://cdn.mathpix.com/cropped/2024_05_06_f36000480089c1ccffcbg-16.jpg?height=269&width=544&top_left_y=823&top_left_x=757)
First, the outer layer of cells will be filled in, after which a rectangle of $98 \times 198$ cells will remain. This rectangle will also be filled in spirally; after filling in its outer layer, a rectangle of $96 \times 196$ cells will remain, and so on. After filling in 49 layers, an uncolored rectangle of $2 \times 102$ will remain, located in rows 50-51 and columns 50-151. The last cell to be filled in will be the bottom-left cell of this rectangle.

## Otvet

The cell located in row 51 and column 50.