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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?
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?