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

Russian Cubes

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

Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Find the Fake

Age 14 to 16
Challenge Level

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).