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

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• Transum,
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• 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, Trwitter
•

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If you can't see the images above it may be because you do not have a recent version of the Flash Player installed or that your device (such as the iPad) cannot show Flash diagrams.

• The orange loco and red carriage uncouple from the blue carriage and move into the siding;
• The orange and green train passes and links up with the blue carriage;
• The red loco and orange carriage return to the main line;
• The orange and green train shunts blue carriage into the siding;
• The orange and green train goes on it's way
• The orange loco and red carriage rejoin the blue carriage;

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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## 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.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

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

## Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

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.

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=January9

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

Transum.org/go/?to=shunting

## 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!

For Students:

For All: