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


3 1 2 1 3 2

Easy ?

Here's a 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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