You may also like

problem icon

Walk and Ride

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

problem icon

Rolling Around

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?

problem icon


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.

N Is a Number

Age 11 to 14 Challenge Level:

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.

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 ?