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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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Redblue

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

A pentagon has five diagonals (lines drawn between the corners). You can trace over all of the diagonals without lifting your pencil and without going over any more than once. Try it.


Can the same thing be done with a hexagon (6 sides) or with a heptagon (7 sides)?

(Take care to find ALL the diagonals. Drawing a large shape will help.)