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?

Cubist Cuts

Age 11 to 14Challenge Level

A $3 \times 3 \times 3$ cube may be reduced to unit cubes ($1 \times1 \times1$ cubes) in six saw cuts if you go straight at it.

If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer? Answer the same question with a $4 \times 4 \times 4$ cube:

What about a cube of any size (an $n \times n \times n$ cube)?

This problem has been adapted from the book "Sums for Smart Kids" by Laurie Buxton, published by BEAM Education. This book is out of print but can still be found on Amazon.