Shunting Problem

Shunting Problem

Two trains are travelling along the same stretch of single line track towards each other. Each train consists of a locomotive and two carriages. There is however a siding that can take one locomotive and one carriage. How is it possible for the two trains to pass each other by using this siding?

A Mathematics Lesson Starter Of The Day


Topics: Starter | Creativity | Fun | Logic | Multiple Intelligences | Problem Solving

  • Transum,
  •  
  • This make a change! Quite a different Starter Of The Day requiring logic, sequencing and lateral thinking (not necessarily in that order!). We envisage pupils working on this puzzle at their desks using items from their pencil cases to represent the locomotives and carriages. They will need to devise a system of recording their solution so that they don’t forget it and can explain it to others.

    If one objective of the Starter Of The Day is to engage pupils right from the very beginning of the lesson we hope this puzzle will fit the bill. It is one or many shunting problems that have proved popular with problem solvers for many years. These challenges are also known as railway shunting puzzles or railroad switching puzzles.

    Don’t forget to show the Flash animation of our solution further down the page.
  • Jason, Louisville
  •  
  • Where do I find the solution?

    [Transum: The answers are below but you need to be signed in to your Transum account to see them. You can sign up for an account here.]
  • Mrs Roberts, Sydney, Australia
  •  
  • This looks awesome.
  • Somerton Primary,
  •  
  • Thank you Transum - for taking our maths lesson in a completely different direction. What an amazing problem solving session. The buzz was fantastic in class.
  • Michael Bauers,
  •  
  • I found the rules unclear
    Can the locomotives push or pull cars both?
    I am assuming when the rule says one loco and one coach, that's the max number of locos and coaches. For example, two coaches not allowing on siding.
    Does the swap need to be perfect? Or could I, for example, end up with the coaches in a different order, or pushing one or both coaches, as opposed to pulling them.

    [Transum: Hello Michael. Yes locomotives can push and pull carriages from their front and back. The most efficient solution sees one locomotive and one carriage using the siding. It is not known if two carriages will fit in the siding so that shouldn't be part of the solution. Yes the swap should be perfect so that the trains continue on their journeys in the same configuration.]

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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Answers

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Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

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Apple iPad Pro

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Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

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Click the images above to see all the details of these gift ideas and to buy them online.

Maths T-Shirts

Maths T-shirts on Amazon
Maths T-Shirts on Amazon

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Educational Technology on Amazon

 

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

Transum.org/go/?Start=January9

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=shunting

Student Activity

 



Classic Shunting Puzzles

Classic Shunting Puzzles

If you have scrolled this far down the page you may well be interested in our collection of Classic Shunting Puzzles which are fascinating, enjoyable and adictive!


Toy Trains Shunting Problem

Teacher: If you have young children of your own borrow their toy trains and use these printable train tracks for a real hands-on experience (small plastic trees not included).

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