Is it possible to cut out such a hole in a sheet of paper through which a person could climb through?
Try to fold the sheet in half and cut a narrow hole along the crease. You will get a narrow hole with wide edges. Try to increase the “length” of the edges by reducing their “width”.
It is enough to fold the sheet in half, cut a narrow hole along the crease, and then make a lot of rectilinear cuts as shown in the figure. The first cut makes a “hole”, and the others increase the length of the “edges” of this hole.
Yes.
Arrange in a row the numbers from 1 to 100 so that any two neighbouring ones differ by at least 50.
