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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?

Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?


Age 11 to 14
Challenge Level

It is possible to dissect any square drawn on a grid into smaller squares, by cutting along grid lines.

For example a 3 by 3 square can be dissected into either 9 smaller squares or 6 squares:

  • What is the minimum number of squares a 13 by 13 square can be dissected into?
  • What is the smallest size square which can be dissected into squares which are all different sizes?