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

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Walk and Ride

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

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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: Challenge Level:1

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.