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?
A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't fight
each other but can reach every corner of the field?
How many different ways can I lay 10 paving slabs, each 2 foot by 1
foot, to make a path 2 foot wide and 10 foot long from my back door
into my garden, without cutting any of the paving slabs?
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?
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.)