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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:
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?
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.
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?