This train line has two tracks which cross at different points.
Can you find all the routes that end at Cheston? 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? Moira is late for school. What is the shortest route she can take from the school gates to the entrance? 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? On which of these shapes can you trace a path along all of its edges, without going over any edge twice? 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. 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. 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. 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?
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? 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?
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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? 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? A little mouse called Delia lives in a hole in the bottom of a tree The PM download can Enter a time for the course of mining community compositions.
Combinatorics of Train Tracks. (AM-125), Volume 125
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combinatorics - Permutation At A Railway Track - Mathematics Stack Exchange
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