Kalinin D.,.

What is the minimum number of $1 \times 1$ squares that need to be drawn to create an image of a $25 \times 25$ square divided into 625 $1 \times 1$ squares?
To draw the border of a square, it will be necessary to draw all 96 border squares. Let's divide the inner square $23 \times 23$ into 264 dominoes $1 \times 2$ and one square $1 \times 1$. One of the squares of each domino needs to be drawn (otherwise, the segment of the grid inside the domino will not be shown). In total, it will be necessary to draw no fewer than $96+264=360$ squares.

On the other hand, 360 squares are sufficient. Consider a chessboard coloring of the square, where the corner squares are black. Each segment of the grid serves as a side of a border or white square. Therefore, it is sufficient to draw all the border squares (96 of them) and all the inner white squares (264 of them).

## Answer

360 squares.