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Great Squares

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

Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Rope Mat

How many centimetres of rope will I need to make another mat just like the one I have here?

Walk and Ride

Age 7 to 14 Challenge Level:

Work out all the fixed points - the times when you know the exact whereabouts of everybody, then think about each section separately.

You may want to alter the problem to use easier numbers, eg $30$ miles, $30$mph and $5$mph in order to find suitable methods to use on the main problem.