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All in the Mind

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?

Chess

Age 11 to 14 Challenge Level:

Place a Knight from a chess set on the corner of a 3 by 3 square board:




It would need 4 usual Knight's moves to place it in the opposite corner. One possible set of moves is shown below:




  • What would be the smallest number of moves needed to move from one corner to the opposite corner of a 99 by 99 square board?

  • What would be the smallest number of moves needed to move from one corner to the opposite corner of an n by n square grid?