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?

Defined Distances

Stage: 3 Short Challenge Level:

We plot $J$ and $K$ $13$ apart. There are a number of options for where to add $L$ and $M$, but working systematically we find that only one option is consistent with $MJ$ being $12$. The final layout looks like

The distance between the points furthest apart is $11+2+12=25$.

This problem is taken from the UKMT Mathematical Challenges.