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?
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4
respectively so that opposite faces add to 7? If you make standard
dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there
are 2 and only 2 different standard dice. Can you prove this ?
We received only one correct solution to this
There are only 49 winning lines, which no
doubt many of you will find hard to believe. Duplication of lines
obviously helped muddy the approaches that were used with this
Laura of West Flegg GM Middle School used an
approach which classified the type of winning line possible with
accompanying sketches :