All in the Mind

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Tic Tac Toe

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?

Changing Areas, Changing Volumes

Age 11 to 14 Challenge Level:
Try working on Changing Areas, Changing Perimeters first, as it is a two-dimensional version of this three-dimensional problem.

If I know two rectangles have the same area, how can I decide, just by looking at their dimensions, which has the greater perimeter?
If I know two cuboids have the same volume, how can I decide, just by looking at their dimensions, which has the greater surface area?