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On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

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Pentagonal

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

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A Scale for the Solar System

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

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