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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?


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?

Diagonal Trace

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

Hamilton's Puzzle

Age 7 to 11
Challenge Level

From Rio, where could you go next? Can you find a route using each of these second stops?

Starting at Australia, where can you go next? Can you choose one of these second countries and decide what the possibilities are now?

Might it help to record the routes?

How will you make sure you have found them all?