Problems

Fred and George had two square cakes. Each made two straight cuts on his cake from edge to edge. However, one ended up with three pieces, and the other with four. How could this be?

Remember that two shapes are congruent if they are the same in shape and size, even if one is flipped or turned around. For example, here are two congruent shapes:

Cut the following shape into four congruent figures:

A cube net is a 2D shape that can be folded into a cube. For example, in the following diagram we show a cube net and the steps that fold it into a cube:

Imagine that you want to cover an endless floor with this cube net, so there are no gaps or overlaps, how would you lay them out? This is called covering or tiling the plane.

Cut a square into three parts and use these pieces to form a triangle whose angles are all acute (i.e: less than \(90^\circ\))