Problems

Sometimes life can make us do the craziest of things. In this problem you just need to find out how one can cut an \(8\times8\) chessboard into 20 pieces each having the same perimeter and consisting of a whole number of cells.

Divide a square into several triangles in such a way that every triangle shares a boundary with exactly three other triangles.

Jennifer draws a hexagon, and a line passing through two of its vertices. It turns out one of the figures in which the original hexagon is divided is a heptagon. Show an example of a hexagon and a line for which it is true.

Can Jennifer draw an octagon and a line passing through two of its vertices in such a way that this line cuts a 10-gon from it?

Cut the following shape into two equal parts.

Cut the following shape into four equal figures.

Daniel has drawn on a sheet of paper a circle and a dot inside it. Show that he can cut a circle into two parts which can be used to make a circle in which the marked point would be the center.

Does there exist a quadrilateral which can be cut into six parts with two straight lines?

Is it possible to cut such a hole in \(10\times 10 \,\,cm^2\) piece of paper, though which you can step?

Cut a square into \(3\) parts which you can use to construct a triangle with angles less than \(90^{\circ}\) and three different sides.