Zaytsev C.A.

A checkerboard paper square $8 \times 8$ was folded several times along the cell 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?
Let the cut be vertical. Draw vertical segments in all $1 \times 1$ squares, connecting the midpoints of opposite sides. When folding along the lines of the cells, these segments overlap with each other. Therefore, when cutting, only these segments are cut. As a result, 9 parts are obtained.

![](https://cdn.mathpix.com/cropped/2024_05_06_7c6a12be356bd13b62cag-31.jpg?height=792&width=749&top_left_y=10&top_left_x=660)

## Answer

Into 9 parts.

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