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Penta Colour

In how many different ways can I colour the five edges of a pentagon red, blue and green so that no two adjacent edges are the same colour?

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All the words in the Snowman language consist of exactly seven letters formed from the letters {s, no, wm, an). How many words are there in the Snowman language?

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Approximating Pi

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Major Trapezium

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A small circle is placed inside a square just touching the sides. The square is on top of a big circle with its vertices on the circle. Finally the big circle is on top of a trapezium which has its sides just touching the circle. Using the measurements and clue given, find the area of the trapezium.