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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?
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?
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.
Age 7 to 11
Challenge Level
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.)
NRICH is part of the family of activities in the Millennium Mathematics Project.