April 2003, Stage 4&5

Problems

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Squaring the Circle and Circling the Square

Age 14 to 16 Challenge Level:

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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The Root of the Problem

Age 14 to 18 Challenge Level:

Find the sum of this series of surds.

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Staircase

Age 16 to 18 Challenge Level:

Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?