11.3. For what smallest $n$ is the following condition satisfied: if $n$ crosses are placed in some cells of a $6 \times 6$ table in any order (no more than one per cell), then there will definitely be three cells forming a strip of length 3, either vertical or horizontal, each containing a cross?
Answer. $n=25$.

Solution. If there are no fewer than 25 crosses, then one of the rows of the table contains no fewer than 5 crosses, and no more than one empty cell. Then either the three left cells of this row, or the three right cells of it, all contain crosses and form the desired strip.

If there are fewer than 25 crosses, they can be arranged so that there are no three crosses forming a strip. For this, all cells of one main diagonal, and the cells of two parallel diagonals of length 3, should be left empty.

Grading criteria. Estimation (if more than 24, then a strip will always be found): 3 points. Example of arranging 24 or fewer crosses without three crosses in a row: 4 points.