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Star Gazing

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

Slippage

Age 14 to 16 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base.
Between the wall and the base of a ladder is a garden storage box 1m tall and 1m wide.
What is the maximum distance up the wall that the ladder can reach?