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# N Is a Number

A group of N people holidaying in the seaside town**A** decided to visit
their friends staying town **B** which is
**N** km (kilometres) along the coast.

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Age 11 to 14

Challenge Level

A group of N people holidaying in the seaside town

Some of the group walk along the cliff path at a steady
**N** km an hour. The rest, one less in number than
the walkers, go by car which (not counting stops) averages $10$
times the speed of the walkers.

The road is much longer than the cliff path.

Those in the car stop for **N** minutes for fuel,
then **N** times as long as that for coffee, and are
further delayed for **N** minutes by a flock of sheep.
They finally reach town **B** one minute before the
walkers.

How long is the road between towns **A** and
**B** ?

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.