Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?