Hannah, Samantha, Ava and Ashley have to walk through a long dark tunnel. They only have one torch between them so a maximum of two people can go through the tunnel at any one time. Each person takes a different amount of time to get through the tunnel and if two people walk together they must walk at the rate of the slowest.

 Hannah takes 2 minutes, Samantha takes 4 minutes, Ava takes 7 minutes, Ashley takes 9 minutes. What is the least amount of time for all four to walk through the tunnel? Notes: 1. All four begin at the same end of the tunnel. 2. The torch must be walked back through the tunnel by at least one person, it cannot be thrown. 3. The answer is less than 24 minutes!

Example:
If Ava and Ashley walk through the tunnel together it will take 9 minutes, If Ava then walks the torch back through the tunnel a total of 16 minutes will have passed. Continue till all four are at the other end of the tunnel.

Topics: Starter | Logic | Problem Solving | Puzzles

• Claudia Walters, St Mary's High
•
• These resources are excellent
Thank you
Can you recommend any practical resource sites for non-whiteboard resources?

[Transum: Have a look at the iPad Maths page.]
• Mounts Bay School, Top Set Year 7
•
• Hard but satisfying.
• Matt Wallace, Hopewell, Pa
•
• Wow! That was great!!! you definitely had to think outside of the box on that one!
• Michael Stainthorpe Gray, PRU, Oldham
•
• The first time we looked at the Transum Tunnel problem it had different number of minutes/names etc What has happened to them we need to check the answer!

[Transum: Sorry Michael, it is a feature of most of the Transum pages that each time the page is loaded a different version of the puzzle or problem is generated. This is so that if pupils are working from their own computers they are trying to answer different versions of the same question. This encourages discussions about method rather than the sharing of answers. This feature also allows you to revisit a Starter on another occasion and try to solve it again with different numbers involved.]
• Marry Singilton, Mount Cook School
•
• WOW Amazing a good use of 30min.
• Lauren And Year 9, Cramlington Learning Village
•
• This is a good question but we would like to know the answer because we are not quite sure.

• Class 1 Year 6, Brentwood Prep
•
• We calculated that it took 26 mins. Lucas and Juan start and take 13 mins. As soon as they finish Juan comes back shining the torch whilst Aaron starts from the other end at the same time, he takes 8 mins. When he is over the last 2 set off, Juan and Charles together taking 5 mins. 13+8+5=26 mins. It does not say that you cannot walk without a torch as long as there are only 2 people in the tunnel at one time.
• Transum,
•
• It's a great puzzle isn't it? Regarding the comments above, each time this page is loaded the names of the people change and the times change too so if you want to know the answer (subscribers only) make sure you scroll down the page before reloading it!

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.

Previous Day | This starter is for 8 February | Next Day

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter with different numbers and names.

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.

## Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

## 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.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

## Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

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...

## Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

## 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.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

## 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.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more...

## 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...

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. more...

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

## Maths T-Shirts

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

 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=February8 However it would be better to assign one of the student interactive activities below.

Here is the URL which will take them to Tran Tunnels, a mathematical adventure.

Transum.org/go/?to=tunnels

For Students:

For All: