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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

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Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

Find the Fake

Stage: 4 Challenge Level: Challenge Level:1
There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. Using only a simple balance, what is the minimum number of weighings needed to locate the fake coin and how is this done?