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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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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.

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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?

There and Back Again

Age 11 to 14
Challenge Level

Bilbo decides to leave his hobbit-hole and go on an adventure. He walks 100 miles South, then 100 miles East, then finally 100 miles North, at which point he is surprised to find that he has arrived back home!

Many people would think that because of this Bilbo must live at the North Pole.
However, Bilbo doesn't live at the North Pole!

Can you describe where you think his home might be?
Have you found all the possible locations?