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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?

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Set Square

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

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Wrapping Gifts

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

Instant Insanity

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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