### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Walk and Ride

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

### 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?

# N Is a Number

##### Stage: 3 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 ?