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All in the Mind

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface of the water make around the cube?

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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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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.


Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
See all short problems arranged by curriculum topic in the short problems collection

Card with threaded string

A single piece of string is threaded through five holes on a piece of card. One side of the card is shown in the diagram above. Which of the diagrams below could represent the pattern of the string on the reverse of the card?
Five different cards showing threading

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.