2. A square sheet of checkered paper $8 \times 8$ was folded several times along the grid lines so that a $1 \times 1$ square was obtained. It was then cut along a segment connecting the midpoints of two opposite sides of the square. Into how many pieces could the square have split as a result?
2. Let the cut be vertical (the case of a horizontal cut is analogous). Draw vertical segments in all $1 \times 1$ squares, connecting the midpoints of opposite sides. Notice that when folding along the grid lines, these

![](https://cdn.mathpix.com/cropped/2024_05_21_6455f48598646f41a890g-366.jpg?height=389&width=375&top_left_y=952&top_left_x=870)

Fig. 180 segments overlap each other. Therefore, when cutting, only these segments are cut. By counting the number of resulting parts, we see that the square has split into 9 parts.

Comment. It was important to solve the problem for any folding, not just a specific example. In particular, the problem does not specify that each fold was made in half.