Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
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?
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?
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
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 $n \times n \times n$
This problem is taken from "Sums for Smart Kids" by Laurie
Buxton, published by BEAM Education. To obtain a copy call the BEAM
orderline on 020 7684 3330 quoting product code SMAR. (Price:
£13.50 plus handling and delivery.)