Chebotarev A.S.

A square napkin was folded in half, and the resulting rectangle was folded in half again (see figure). The resulting square was cut with scissors (in a straight line). Could the napkin have split a) into 2 pieces? b) into 3 pieces? c) into 4 pieces? d) into 5 pieces? If yes - draw such a cut, if no - write the word "impossible".

![](https://cdn.mathpix.com/cropped/2024_05_06_7ebe57248fabc5f818b0g-16.jpg?height=265&width=1164&top_left_y=-1&top_left_x=1)
If the cut is "moved" within the same side, the number of pieces will not change. When the cut passes through a corner or moves to an adjacent side, the number of pieces may change.

## Solution

Notice that if the cut is "moved" within the same side, the number of pieces will not change. When the cut passes through a corner or moves to an adjacent side, the number of pieces may change.

Here are all possible ways to cut the napkin:
a)


b)



$\square$
TE
NN:
) $\square \square:$
c)

## Answer

In all cases, it is possible. See examples in the "Solution" section.