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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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.

Go Genius Maths

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How Not To Be Wrong

How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

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Graphic Display Calculator

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Calculator

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

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

Craig Barton's Tips for Teachers

Teaching is complex. But there are simple ideas we can enact to help our teaching be more effective. This book contains over 400 such ideas." more... #ad

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Another Craig Barton Book

The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

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Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

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A Compendium Of 	Mathematical Methods

A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more... #ad

Math with Bad Drawings

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Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone. more... #ad

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

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

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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