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Iterative methods or the visual interpretation of graphical solutions are worth exploring. There is lots of room for different approaches, including practical ones, or partly practical and partly analytical.
Classic Cube
Age 16 to 18
Challenge Level 
Iterative methods or the visual interpretation of graphical solutions are worth exploring. There is lots of room for different approaches, including practical ones, or partly practical and partly analytical.
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Wrapping Gifts
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
Plane to See
P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
Four Points on a Cube
What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?