Problems

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

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

Cut the "biscuit" into 16 congruent pieces. The sections are not necessarily rectilinear.

Abigail’s little brother Carson found a big rectangular cake in the fridge and cut a small rectangular piece out of it.

Now Abigail needs to find a way to cut the remaining cake into two pieces of equal area with only one straight cut. How could she do that? The removed piece can be of any size or orientation.

Cut an arbitrary triangle into parts that can be used to build a triangle that is symmetrical to the original triangle with respect to some straight line (the pieces cannot be inverted, they can only be rotated on the plane).

The diagram shows a \(3 \times 3\) square with one corner removed. Cut it into three pieces, not necessarily identical, which can be reassembled to make a square:

Cut a \(7\times 7\) square into \(9\) rectangles, out of which you can construct any rectangle whose sidelengths are less than \(7\). Show how to construct the rectangles.