Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Which of these infinitely deep vessels will eventually full up?
How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?