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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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Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

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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.

Intersecting Circles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?