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On the Road

Four vehicles travelled on a road. What can you deduce from the times that they met?

A Scale for the Solar System

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Swimmers

Swimmers in opposite directions cross at 20m and at 30m from each end of a swimming pool. How long is the pool ?

Pentagonal

Age 14 to 16
Challenge Level

If you have decided that the result holds for a regular hexagon, what is it exactly about the hexagon that lets it work?
What does a regular hexagon also have that isn't needed for this result?

For the regular pentagon, put a point somewhere inside, perhaps not at the centre.
Join that point to each of the vertices of the pentagon and think about the five triangles.

Finally, what does a regular pentagon also have that isn't needed for this result?