2. In a $10 \times 10$ grid, the centers of all unit squares are marked (a total of 100 points). What is the minimum number of lines, not parallel to the sides of the square, needed to cross out all the marked points?
2. Let's draw all lines parallel to one of the diagonals of the square and containing more than one of the marked points - there are 17 such lines. The un-

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Fig. 77 erased will be the two corner points. They can be erased by drawing one more line - the other diagonal (Fig. 77).

We will prove that it is impossible to manage with a smaller number of lines. Indeed, consider the centers of the unit squares located along the perimeter of the large square. It is clear that a line not parallel to the side of the square can erase no more than two such points, but there are 36 such points in total (see also fact 1).