Arrange the numbers on the yellow tiles so that the sum of the numbers in the vertical line is the same as the sum of the numbers in the horizontal line

1

2

3

4

5

6

How many different ways are there of doing this task?

A self-checking, interactive version of this activity with 30 different puzzles is here.

Share

Topics: Starter | Arithmetic | Number | Problem Solving

• K Hudson, Drigg
•
• Looks easy but proved quite tricky. Nice one!
• Helen McKenna, Elgin
•
• Hard to start, but then easy. We found 10 different solutions in 5 minutes.
• Class 2, Blackboys Primary School
•
• Ethan Peck found it a tough challenge, but soon got the hang of it. "It was really fun but tricky," says Poppy. "I enjoyed the challenge and found 1 solution," commented Kizzifer Budd. Top challenge.
• Mr M's Year 7s, CCS, Bali
•
• We noticed that you can only have an odd number in the middle (ie. 1,3 or 5). The total number is either 11,12 or 13 depending on what number you put in the middle. Great starter, thanks. :D.
•
• Enjoyed but kinda difficult!
• Paula, Coln House
•
• I teach in a SEBD secondary school, these starters help the classes to settle and they (the pupils) (mostly) enjoy the challenge. Sometimes we might spend longer on a problem if the pupils are very engaged.
If we vote on a starter I always ask for their input and comments.
For more practical starters we often cut up paper and model the problem, I find this helps , I also try to create a sense of controlled urgency as this helps the pupils concentrate and focus.
Sometimes the starters are too complex, or wordy, so I quickly search and find a more appropriate problem.
I think these starters are very useful as you can extract lots of mathematics from them to suit your particular level, style and type of class.
Thank you.
• Mrs Clay's Y5 Maths Set GMS, Bedfordshire
•
• We found three possible solutions, because we would not allow jiggling of the digits eg we think 4+1+6= 2+1+3+5 is the same as 6+1+4= 3+1+2+5 and the digit used twice must be odd. :)
4+1+6 = 2+1+3+5
5+3+4 = 6+3+2+1
6+5+2 = 4+5+1+3.
• Dan's Dad, Milton Keynes, UK
•
• There's a reason why the number in the middle must be odd:
First add up all the numbers: 1+2+3+4+5+6=21
If you put an odd number in the middle, for example 1, the numbers that are left now add up to 20.
And 20 can be split into two equal halves of 10
i.e. 6+4 and 2+3+5 both equal 10
6+1+4 = 2+1+3+5
Using any odd number in the middle will leave you with equal halves to share up and across
If you try it with a 2 in the middle, you are left with the numbers#
1+ 3+4+5+6=19
And 19 cannot be shared equally up and across.
• Mr Eagle, Eagletown
•
• My mixed year 5/6 thought it was an absolute doddle. They thoroughly enjoyed the compexities of this challenge and look forward to the next one!
• Mr. Townsend, Harmondsworth Primary Y3/4
•
• We found one solution as a starter activity. We used 4, 3, 5 in the vertical column and 1,3,2,6 in the horizontal. It was challenging!

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.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.4 out of 5 based on 275 votes.

Previous Day | This starter is for 3 February | Next Day

Here are all of the 36 possible solutions.

 2 1 5 3 4 6
 2 1 5 4 3 6
 2 3 5 1 4 6
 2 3 5 4 1 6
 2 4 5 1 3 6
 2 4 5 3 1 6
 4 1 3 2 6 5
 4 1 3 6 2 5
 4 2 1 3 5 6
 4 2 1 5 3 6
 4 2 3 1 6 5
 4 2 3 6 1 5
 4 3 1 2 5 6
 4 3 1 5 2 6
 4 5 1 2 3 6
 4 5 1 3 2 6
 4 6 3 1 2 5
 4 6 3 2 1 5
 5 1 3 2 6 4
 5 1 3 6 2 4
 5 2 3 1 6 4
 5 2 3 6 1 4
 5 6 3 1 2 4
 5 6 3 2 1 4
 6 1 5 3 4 2
 6 1 5 4 3 2
 6 2 1 3 5 4
 6 2 1 5 3 4
 6 3 1 2 5 4
 6 3 1 5 2 4
 6 3 5 1 4 2
 6 3 5 4 1 2
 6 4 5 1 3 2
 6 4 5 3 1 2
 6 5 1 2 3 4
 6 5 1 3 2 4

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 search box and some items chosen and recommended by Transum Mathematics to get you started.

## Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I'd taught Maths" is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

## Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

## Hello World

You are buying a (driverless) car. One vehicle is programmed to save as many lives as possible in a collision. Another promises to prioritize the lives of its passengers. Which do you choose?

Welcome to the age of the algorithm, the story of a not-too-distant future where machines rule supreme, making important decisions – in healthcare, transport, finance, security, what we watch, where we go even who we send to prison. So how much should we rely on them? What kind of future do we want?

Hannah Fry takes us on a tour of the good, the bad and the downright ugly of the algorithms that surround us. In Hello World she lifts the lid on their inner workings, demonstrates their power, exposes their limitations, and examines whether they really are an improvement on the humans they are replacing.

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

 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).

Transum.org/go/?Start=February3

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

Transum.org/go/?to=plane

For Students:

For All: