Topics: Starter | Number Patterns

• Cmurtaugh, Park High School
• Friday, November 03, 2006
• "This did not work can not have an even and odd number"
• Peter Mayne, Crieff High School
• Friday, November 10, 2006
• "This puzzle is impossible! There are not 4 multiples of 5 from 1 to 16."
• Year 5 , Ardingly College
• Thursday, November 16, 2006
• "We have also found this impossible to do!!"
• A Dixon, NDTC Doncaster
• Friday, November 17, 2006
• "If you continue to read down the page it does say that it is impossible but asks for pupils to prove why!"
• Daniel, Honk Kong
• Sunday, October 07, 2007
• "No wonder everyone thinks its impossible! It said to rearrange everything! Not just the numbers."

 

• 8x2, Portchester Community School
• Monday, November 05, 2007
• "This is impossible as the headings do not make sense."
• Scott, Birmingham
• Tuesday, November 13, 2007
• "Surely you also need another multiple of 5?"
• Year 8, Wyedean
• Wednesday, November 14, 2007
• "This is too hard for my year 8 class, is it possible?"
• Mrs Humphreys' maths group, Nevill Road, Bramhall, Stockport
• Thursday, November 15, 2007
• "The children were frustrated that it didn't work but it generated some good discussion."
• C Southward, Carlisle
• Friday, November 16, 2007
• "My Year sevens were amazed at some of the earlier comments, obviously these people had not even understood the question."
• J.Barclay-Devine, Ashton, Bedfordshire
• Monday, November 19, 2007
• "Once my year 6 class decided that some properties would not go together we tried to fill in the grid using different numbers. The problem generates a lot of discussion. Presumably this is what the comment meant when saying people hadn't understood."
• Kerry Meaden-Kendrick, Bangkok Patana
• Tuesday, November 20, 2007
• "My Year 5 maths class found this VERY frustrating-we were missing the fourth multiple of five!!!
  
  This cannot be done without it, surely???!!!
  
  We did well but no biscuit...:("
• Year 8, set 1, Okehampton College, Devon
• Tuesday, November 20, 2007
• "We don't think there is any way to arrange the column and row headings, even if you allow, say, 6 headings across the top and 2 headings down the side. This is because odd and even have to go in the same area (either row or column), because otherwise they will contradict each other. Also multiples of 4 have to go with these two, as multiples of 4 cannnot be odd, then prime numbers have to go with these, as primes cannot be multiples of 4. Then we saw that square numbers cannot be prime, so that's 5 headings together already. There are similar contradictions for all the headings except multiples of 3!
  There are not enough multiples of 3 to fit with all the other headings.
  
  Even then, there are not enough numbers which are multiples of 5!"
• Mrs A Morris, VCC Rutland
• Wednesday, November 21, 2007
• "We found similar problems but it did cause a huge debate and uproar!"
• Ms. Toofail, Willowfield school Walthamstow
• Wednesday, November 21, 2007
• "A student from my class got 11 of the numbers into the grid. Try and see if anyone can beat that, if so leave a comment."
• Class 8a5, The Whitby High School, Ellesmere Port
• Wednesday, November 21, 2007
• "Impossible! There are no numbers there that are both prime and square, odd and even and prime and multiple of 4."
• Mr Barnett, Glenwood High School, Fife, Scotland
• Wednesday, November 21, 2007
• "When the pupils rearranged the grid into a 5 x 3 grid, narrowing the options to 15, one of our pupils managed to fit in 12 numbers having managed the 11 numbers with the 4 x 4 grid.
  A great activity that we've spent a lot of time discussing"
• Mr Barnett, Glenwood High School (Again)
• Thursday, November 22, 2007
• "One of my 1st year girls has just brought a homework in with the 4 x 4 grid. We have all checked very carefully and she managed to fit 12 numbers into the grid.........we'll keep trying."
• Mrs. Schultz, Hylands School, Chelmsford, Essex.
• Thursday, November 22, 2007
• "My year 8 class took 5 minutes to work this out by looking at the multiples of 5."
• Emma Cox, Sir James Smiths School Camelford
• Friday, November 30, 2007
• "My year 7 group worked really well on this. 4 students got 12 numbers in their grids and one took it home for a parent to get 13! Ive not seen this solution. They cut out numbers and headings to make manipulation easier."
• Mr Jan, Haydock Sports College
• Monday, November 10, 2008
• "Closest we got was 4 numbers left over! anyone beat that?"
• Hamish,
• Sunday, November 16, 2008
• "It clearly says at the bottom that its supposed to be impossible so why are so many people complaining that it is! don't use it then."
• Yr 5/6 Class, Holy Eucharist , East Malvern. Melbourne.VIC. Australia
• Tuesday, November 18, 2008
• "The problem was really hard and it created alot of discussion in our class.We couldn't solve it even when we concluded that "1" is a multiple of 5.It was frustrating when we could solve 3 numbers in either a row or column but we couldn't solve the other number.Some people didn't realise that you could move the titles as well."
• Mrs Taylor's P7 Set, Carolside Primary
• Tuesday, November 18, 2008
• "Although we found this a bit frustrating, we did investigate triangular numbers."
• Yr 8, Sana Maria College
• Friday, November 21, 2008
• "We found we could put all numbers except the number 14 onto the grid once we arranged the headings. Thanks to Emily."

 

• Year 5, O, N, J, L, St Nicholas
• Friday, November 21, 2008
• "We managed 12! Can anyone beat that?"
• Daniel, Maidenhead
• Wednesday, November 18, 2009
• "My daughter asked me for help with this exercise and as it appeared to be impossible I believe that my (and most other people's) initial understanding of the problem was incorrect. Keeping this in mind I took a different approach and took a careful look at the row and column headings. Take one heading as an example 'Multiple of four', it is singular and not plural. Therefore I believe that the headings are not related to the cells but to the sum of the cells in each row and column. Taking this approach it is possible to complete the exercise. Have fun trying this out."
• Year Six, Tickhill St. Mary's
• Wednesday, November 18, 2009
• "Our Year Six class managed a maximum of 13 numbers placed. No-one thought to rearrange the grid to try to make it easier! Some thinking skills need developing..."
• Mr Bennett, St Stephen's C.E. Junior School
• Wednesday, November 18, 2009
• "My clever Year 6 class found that this doesn't work. As a suggestion, they said: " make sure you can do it yourself before putting it on line!"
  " Keep the column and row titles but change the numbers?"."
• Miss Farmer + 8LM4, Landau Forte College, Derby
• Wednesday, November 18, 2009
• "My year 8 group found this quite annoying! We tried for ages to rearrange things only to find there were not enough multiples of 5! good discussion though!"
• 8 Larch, St Anne's
• Wednesday, November 18, 2009
• "St Anne's year eight did not like having a task that could not be done."
• Mrs. Fischl, Grade 11 College Class
• Wednesday, November 18, 2009
• "My class would like to see more of this, however, we would like a puzzle that can actually be solved. It would have been nice to have the instruction read, why is this puzzle impossible?"
• Miss James, Shiplake
• Wednesday, November 18, 2009
• "This is impossible and my calss found it really Fustrating!"
• A Year 8 Student, Wilmslow High School, Wilmslow, Cheshire
• Wednesday, November 18, 2009
• "It says at the bottom of the page that is impossible."
• Emma Cox, Sir James Smiths School Camelford
• Wednesday, February 03, 2010
• "Sam and Jared from my year 7 Maths group, managed to fit 13 numbers onto the grid by cutting the heading and numbers out to rearrange them. They quickly realised there were only 3 multiples of 5. Results were then put on a poster."
• Hanxiao, Jinchengxiaoqu
• Thursday, November 18, 2010
• "Impossible!
  Because the multiples of 5 is not enough."
• Chelsay Sharlotte, TVA
• Thursday, November 18, 2010
• "My teacher should have checked that it worked before he gave it to us."
• 8X1, Hadleigh High
• Thursday, November 18, 2010
• "We also managed to only find 12 to fit in."
• Mr Winning's Class, OLHS
• Friday, November 19, 2010
• "This puzzle would be better if it was not impossible."
• Mrs Price, York
• Tuesday, November 08, 2011
• "My class would like to think they could get all the numbers in the grid however it is an impossible problem."
• Niole Jordan, Charing
• Tuesday, November 15, 2011
• "This is easy. Did you know that you could move the headings? I am 9 and I even know that."
• J Cousins, Oakfield School Academy
• Friday, November 18, 2011
• "This would be an excellent starter, if it worked!!"
• 7a2 - Harton Technology College, South Shields
• Friday, November 18, 2011
• "We managed to enter 13 numbers and remove one heading."
• Tia, Weston
• Friday, November 18, 2011
• "Disappointed in this one."
• GMU 5-7, Pairc School, Isle Of Lewis
• Tuesday, November 06, 2012
• "It's impossible. You can't get an odd and even number."
• Ashley Black, Sgoil Ainart
• Wednesday, November 07, 2012
• "You can not have an even and odd."
• Mrs Cooper, Cornelius Vermuyden School, Canvey Island
• Monday, November 19, 2012
• "What a wonderful thinking starter... I was disappointed that the student version that I was told did work did not. It was different to the solution given, having got several of the headings different than in the question. If this were corrected it would be fantastic!
  Thank you Transum Starter of the Day!
  
  TRANSUM: 'Mrs Cooper, the student version has a button for changing the headings. The student version is indeed possible!'"
• Our Lady Of Lourdes, Year 6 &7
• Tuesday, November 20, 2012
• "This is impossible my class were very disappointed they couldn't figure the answers."
• Mrs S, Wilmslow
• Tuesday, November 20, 2012
• "Disappointing for a morning starter.
  I hoped my children could learn about numbers while I did register.
  Could have spent a lesson on it after I realised it was impossible!!
  No more!"
• Class 201, Cork, Ireland
• Thursday, November 22, 2012
• "We found this fun but tricky. It took a long time and we eventually found out that it wasn't possible. We created our own table which worked- this one doesn't."

 

• Heather, The Priory Academy LSST, England
• Tuesday, November 27, 2012
• "The reason it's impossible with those numbers is the number 14, which only fits into one category, even numbers, when every number has to fit 2 categories."

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.
Click here to enter your comments.

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:

This starter has scored a mean of 2.4 out of 5 based on 96 votes.

Previous Day | This starter is for 18 November | Next Day