Separated Twins

Separated Twins

Clue 1

The combination is a six digit number.

Clue 2

There are two ones separated by one other digit.

Clue 3

There are two twos separated by two other digits.

Clue 4

There are two threes separated by three other digits.

A Mathematics Lesson Starter Of The Day


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That was easy! Here's the real challenge!

The combination of the Transum safe is a 14 digit number.

The two 7s are separated by seven other digits;
The two 6s are separated by six other digits;
The two 5s are separated by five other digits;
The two 4s are separated by four other digits;
The two 3s are separated by three other digits;
The two 2s are separated by two other digits;
The two 1s are separated by one other digit.

Separated Twins Interactive
Click here for an interactive version.

Topics: Starter | Logic | Puzzles

  • 9k1, Kettlethorpe High School
  • other answers, 46357432652171, 23726351417654, 72632453764151 and 72452634753161.
  • Transum,
  • Well done 9k1, Kettlethorpe High School. I wonder if that is all possible answers? Note that answers in the comments are hidden for all but Transum subscribers.
  • Mrs. Peacock, Downe House School and Kennet School
  • My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions.
  • Sohana, Gateway Academy
  • Students found 47364352762151.
  • Lana, Lindsworth North, Birmingham, UK
  • We found another solution: 17126425374635 (Which is also my phone number!)
  • Mr Smith, Durrington High School, Worthing
  • Starter of the day 18th September. Other possible answers which class 11Y1 found are: 73625324765141 and 17126425374635.
  • Chloe Beames, Broadoak W-s-M
  • I found 45671415362732.
  • Sam Yr 8, Broadoak Weston-Super-Mare
  • I found this one 26721514637543 and 34573641512762
  • Mr Hamshaw-Hart, Beverley Grammar School
  • Year 11 top set also found 57263254376141 and 71416354732652
  • Miss K Smith, Wildern School
  • My Year 11m1 class found one solution 52462754316137. They thought it was silly but actually all had a go.
  • Wednesfield High School, JSS
  • Top set year 9 got 2 solutions: 73625324765141 and 71316435724625.
  • 8H1, Helenswood School
  • 15173465324726
  • Wednesfield High, JSS
  • Our Year 8 students discovered this solution to separated twins
  • Ross West & Friends, Sleaford
  • We got 76543121726435, from Y11 at St.George's, Sleaford.
  • Curtis, 7
  • Other Solutions: 61517346532472, 41617435263275 and 41716425327635.
  • Sevgi, London
  • Another solution:
  • Harrytown High School, 9A2
  • 46357432652171 Adrien Parry
    35743625427161 Ross Scrivener and Charlotte Bailey
    73625324765141 Antoine Parry
    these all work backwards too!
  • Mr Ian Rowe, United Kingdom
  • Year 11 class at Royal Alexandra and Albert School, UK, with the help of James got 34673245261715.
  • 8X3, MSJ
  • Twintastic. This really got the group thinking and Billy really enjoyed it. Jamie was the first to solve the problem.
  • Year 6, Stamford Green Primary School
  • 4 children came up with the same solution of
    It was a fab experience!
  • Mr Hudson, King Richard School
  • Year 9 set 1 72462354736151.
  • Ross Roberton, International School Of Luxembourg
  • Tamas H was the fastest to solve this and won an amazing sweet!
  • Mr Aveyard, Garforth Community College
  • We found this activity a challenge but interesting at the same time.
  • Mrs Barnett And 8x1 & 8y1, Bredon Hill Middle School
  • My Year 8 group have managed to find:
    26325734615147 (found by Archie)
    56171354632742 (found by Jamie)
    and of course they both work in reverse!
  • Confused, .com
  • Is there any logic to it? My pupils were asking me - and I just assumed it was trial and error at the time, but now I'm thinking there might be a logical method?

  • Mr N Parrett, Staffs
  • The class also found the second solution to the original problem 231213 is also correct.
  • Andrew Evers, Y6EV - St Giles
  • My class of 10 year olds found 2 possibilities to the 6 digit combination. The answer you gave 312132 and one you didn't mention 231213.
  • Hannah, Bolton
  • I also got the answer of 231213 which is the reverse of 312132.
  • Maths Is Fun,
  • Find a 10 digit number where the first digit is how many zeros in the number, the second digit is how many ones in the number, the third digit is how many twos are in the number etc.
  • Transum,
  • The combination locks on safes should really be called permutation locks because it does matter which order the digits are entered.

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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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... #ad

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... #ad

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... #ad

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... #ad

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

"The ideas come from two sources. First, from the wonderful guests on his Tips for Teachers podcast - education heavyweights such as Dylan Wiliam, Daisy Christodoulou and Tom Sherrington, as well as talented teachers who are not household names but have so much wisdom to share. Then there's what he has learned from working with amazing teachers and students in hundreds of schools around the world.

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.

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

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... #ad

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

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... #ad

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

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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:

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 student version of this activity.

Student Activity



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