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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?

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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?

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Boxed In

Age 11 to 14 Challenge Level:

Catherine of Mount School, York and Joel of ACS Barker, Singapore realised that it is not necessary to calculate the lengths of the edges of the cuboid and they sent very similar solutions. This is Catherine's solution:


If the sides of the cuboid are x, y, and z and the areas of the rectangular faces are p, q and r then:
p = xy, q = yz and r = zx
It follows that pqr = (xy)(yz)(zx) = x 2 . y 2 . z 2 = (xyz) 2
So the volume = xyz = sqrt (pqr) = sqrt (3 x 12 x 25) = sqrt 900 = 30

Students from West Flegg Middle School, Norfolk and Madras College, St Andrew's and Russell Lower School, Ampthill also found the correct answer.