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Decision Mathematics and Combinatorics > Route inspection problems

##### Age 7 to 11 Challenge Level:

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?

##### Age 7 to 11 Challenge Level:

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?

##### Age 5 to 11 Challenge Level:

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

##### Age 7 to 11 Challenge Level:

I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?

##### Age 7 to 11 Challenge Level:

In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?

##### Age 7 to 11 Challenge Level:

Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?

##### Age 7 to 11 Short Challenge Level:

A garden has square flower beds surrounded by paths. Can you find a
way to walk all around the paths without walking on the same part
twice?

##### Age 7 to 11 Challenge Level:

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:

Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.

##### Age 7 to 11 Challenge Level:

Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
took.

##### Age 7 to 11 Challenge Level:

On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?

##### Age 7 to 14 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

##### Age 5 to 11 Challenge Level:

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

##### Age 7 to 11 Challenge Level:

Can you go through this maze so that the numbers you pass add to exactly 100?

##### Age 7 to 11 Challenge Level:

Freddie Frog visits as many of the leaves as he can on the way to
see Sammy Snail but only visits each lily leaf once. Which is the
best way for him to go?

##### Age 7 to 11 Challenge Level:

A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?