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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

Square with a random point selected inside


Can you prove that the sum of the distances of any point inside a square from its sides is always equal?

Can you prove it to be true for a rectangle or a regular hexagon?
Does the hexagon need to be regular?

Can you show the same is the case for a regular pentagon?
Does the pentagon need to be regular?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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NRICH is part of the family of activities in the Millennium Mathematics Project.