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Solution

A Triangular Problem

We have placed two counters in regions formed by joining the vertices of the hexagon ABCDEF. Note that each counter is inside more than one triangle whose vertices are vertices of the hexagon.

Which triangles whose vertices are vertices of the hexagon are the counters in?

What is the least number of counters needed to ensure that every triangle whose vertices are vertices of the hexagon has at least one counter inside it?

Where should the counters be placed for this to happen?

A Generalisation

Once you have tried the hexagonal version of this problem, what is the generalisation of the problem and result?