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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

This proved quite a challenge! It was Helen (Maidstone Girls' Grammar) and Joel (of ACS in Singapore) who correctly found that only 3 weighings are needed.

Here is one way to solve the problem. We've labelled the coins ABCDEFGHIJKL.

Solution with three weighings

At West Flegg Middle School Polly and Rebecca found a method for 4 weighings, as did Michael (Cranmore Primary School, in Perth, West Australia).