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Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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?

Circles Ad Infinitum

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Instant Insanity

Age 11 to 18 Challenge Level:

These are the nets of 4 cubes. Build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Cube Net 1    Cube Net 2    Cube Net 3    Cube Net 4

Printable NRICH Roadshow resources.