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Delia's Routes

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

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Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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Rail Network

This drawing shows the train track joining the Train Yard to all the stations labelled from A to S. Find a way for a train to call at all the stations and return to the Train Yard.

Diagonal Trace

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

It might help to draw in all the diagonals first, then trace over them with a coloured pencil.
You could print off this sheet which has the shapes and the diagonals drawn for you.
Do you have some sort of system for trying to trace over the diagonals?