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?
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?
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.
A little grey mouse called Delia lives in a hole in the bottom
of a tree in a small square garden (A).
The garden is paved with 6 large square paving stones in each
direction and has a circular pond right in the middle that has a
diameter of 3 of the paving stones. Delia's tree is at the left
hand corner at the bottom of the garden. At the top right hand
corner of the paved area there is a bird table (B).
How many days will it be before Delia has to take the same route