Arnošt cut out a $4 \times 4$ square from graph paper. Kristián cut out two holes in it, see the two black squares in the picture. Arnošt tried to cut this shape along the marked lines into two identical parts.

Find at least four different ways Arnošt could have done this. (Two cuttings are considered different if the parts created by one cutting are not congruent to the parts created by the other cutting.)

(A. Bohiniková)

![](https://cdn.mathpix.com/cropped/2024_04_17_e836f4ee23919875e85ag-1.jpg?height=254&width=257&top_left_y=1666&top_left_x=905)

Hint. Notice a certain symmetry.
One of the simplest possible divisions is indicated in the following figure:

![](https://cdn.mathpix.com/cropped/2024_04_17_e836f4ee23919875e85ag-1.jpg?height=260&width=260&top_left_y=2177&top_left_x=904)

The newly created parts are — like the original shape — symmetric with respect to the center of the bounding square. The previous division can be gradually modified so that the centrally symmetric squares belong to different parts. By adding or removing squares in the first column, we get the following possible divisions:
![](https://cdn.mathpix.com/cropped/2024_04_17_e836f4ee23919875e85ag-2.jpg?height=264&width=852&top_left_y=443&top_left_x=608)

Note. Any further modification leads either to a division identical to one of the previous ones, or to a division that consists of multiple disconnected parts. The four solutions mentioned thus represent all different ways of division.