A Mathematics Lesson Starter Of The Day

Arrange the numbers 1 to 5






Arrange the numbers 1 to 5 on the yellow circles so that consecutive numbers are not connected by blue lines.

How many different ways can this be done?


Topics: Starter | Logic | Puzzles

  • Mr. Walsh & Class 2, Blackboys Primary School
  • Michael Reeder thought it was quite challenging! Everyone really enjoyed it and rose to the challenge!
  • 8PF, Varndean School, Brighton
  • A good starter. quite easy, but it made us think !!!
  • 7C/Ma4, Canterbury High
  • Great - a little too easy, but interesting for all!
    Need some more like this!
  • D.Wanasingha, PGCE (UOH)
  • The answer 14 is if we arrange them as a line. Otherwise it reduces to 10 when we consider it as a circle. If it is a line it would be a quite tricky puzzle even for secondary students.
  • Pearl Oberon,
  • Why are there only 2 solutions?
  • Nancy, NY
  • I found only 2 solutions. How is it 10? only 1, 3, and 5 can go on the outside of the circle. And only 1 and 5 could be placed in the outsides of the 4 linked numbers, that leaves us with 1, 4, 2, 5 and 3 or 5, 2, 4, 1 and 3. How is that it has 10 combinations?
  • Mr Cansdale, Wintringham Grimsby
  • 10Y3 think this is the most amazing thing they have ever attempted!
  • Steve Eastop, Kent, UK
  • Please note there is another solution: (reading down the page and left to right):
    1 - 4 - 5
  • Matt, Burton On Trent
  • I only found 2 also, cannot see how you can get anymore.
  • M Trainor, Edinburgh
  • My class absolutlely loved this!!!! They said it was too easy for them.
  • Jimbobaloola, NKS6
  • S.E, Can you please check your answers before entering incorrect info. There are Year 6 pupils here in Fulham who have proved that there are only 2 answers. Many thanks.
  • Mr Cansdale, Oasis Wintringham Academy
  • 7A4, the majority think that there are more than 2 ways of doing this!
  • 9C1, Titus Salt School
  • Emily said it's obvious. 1 3 and 5 have to go on the outside. So there can only be 2 solutions.
  • Miss Clarke, Holton - Le - Clay Juniors
  • We thought this activity was fun because it was challenging.
    Chloe said she learnt a new word doing this activity - 'consecutive'.
    Some of us found it a little confusing when arranging the numbers but we found the right answers in the end!
    Shaun wants us to try and make our own up now.
  • Kartik, India
  • Hey Kids,
    There are 12 ways in total.
    In outer ring 1,3 and 5 can be arrange in 3! ways that is 6 different ways and 2 and 4 can be arrange in 2 ways there for 6 * 2 = 12 different ways.
  • Kartik, India
  • Its 2 ways sorry about previous answers as I forgot abt consecutive thing.
  • Mr Pierce, 10R1 - Liverpool
  • Absolutely AMAZING!!!!!!!!!!!! Found all 8 solutions.
  • Mike M, Swansea
  • Really great. Two solutions possible: Either (from top round clockwise) 1 , 3, 5, 2, 4 or 5, 3, 1, 4, 2. Class loved it.
  • Gabby, Gabby
  • Hey Kids,
    There are ? ? ways in total.
    I really enjoyed this starter even if it was too easy,
    but it made me and my younger, elder siblings thinking a lot !

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This starter has scored a mean of 3.5 out of 5 based on 397 votes.

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