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Great Squares

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?

Sugary Diversion

Stage: 3 Short Challenge Level: Challenge Level:1

The ant climbs up the cube (adding $1 \; \text{cm}$), walks across the top of the cube on the same path as he would have done if the cube wasn't there, then climbs back down to the table (adding another $1 \; \text{cm}$), so the total extra distance is $2 \; \text{cm}$ .

This problem is taken from the UKMT Mathematical Challenges.