5. In a white $10 \times 10$ square, on the first move, a $1 \times 1$ cell rectangle is painted, on the second move - a $1 \times 2$ cell rectangle, on the third - $1 \times 3$ and so on, as long as it is possible to do so. After what minimum number of moves could this process end? (Cells cannot be painted over again.)

#
# Answer: after 6 moves.

Solution. Evaluation. On the board, 16 rectangles of size $1 \times 6$ can be highlighted, of which a maximum of $1+2+3+4+5=15$ will contain colored cells, meaning that a sixth move is always possible. Example. The process is illustrated in the diagram, showing a scenario where a seventh move is no longer possible.

Criteria. If the solution is incorrect - 0 points.

If only a correct example is provided - 3 points.

If only the correct evaluation is provided - 3 points.

If the solution is correct (any correct example and justification of the evaluation) - 7 points.