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?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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?

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?

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?

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?

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.

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

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.

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?

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?

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

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 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?

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?

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?

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

How many pieces of string have been used in these patterns? Can you describe how you know?

Can you imagine where I could have walked for my path to look like this?

How many loops of string have been used to make these patterns?