Vassily H.b.

In each cell of an $8 \times 8$ square, one of the diagonals is drawn. Consider the union of these 64 diagonals. It consists of several connected parts (a part includes points that can be reached from each other by moving along one or more diagonals). Can the number of these parts be

a) more than 15?

b) more than 20?
b) In the figure, an example is given where the number of parts is 21. One of them is a multiply connected "window frame," in which single diagonals are placed in the cells.

![](https://cdn.mathpix.com/cropped/2024_05_06_970e9bfb17ad7b5a0e46g-17.jpg?height=637&width=629&top_left_y=-1&top_left_x=729)

## Answer

It can.