Card Frame

 An interactive whiteboard resource to accompany a puzzle published in an old book by Henry Ernest Dudeney.  The puzzle is a useful one for teaching deeper mathematical thinking because while it can be solved by trial and error thinking about the maths behind it can make it much easier. 

The goal is to choose a number that all 4 sides of the frame can add up to and arrange the cards to do this.  Some numbers are possible some numbers are not.  This puzzle has been selected as it allows students of all abilities to have a go as the maths involved is not difficult.  The challenge should be to find a method of determining what numbers can be used as the common total amount and then how to make finding the layout much easier.  The resource provided here allows the puzzle to be demonstrated easily and can also allow whole class discussion of how to approach the problem.  Clicking on one card and then another causes them to swap places.  The resource totals the different lines automatically.  The original wording of the puzzle can be made to appear by clicking on the question mark button.

A printable sheet accompanies this resource which includes the original wording and diagram. It also includes the appropriate cards for cutting out to do the puzzle away from a computer.  If teachers would like the solution and maths behind it leave a comment with your email address in the box (it will not be published).  There will be at least a 5 day delay to ensure that students who have been set this as homework aren’t cheating by impersonating a teacher!

Go to interactive whiteboard resource.

Get printable resource.

37 comments for “Card Frame

  1. Mohammad Kalhoro
    June 21, 2009 at 3:24 pm

    Can I have the solution to this problem please? Many thanks.


  2. mars
    June 27, 2009 at 5:51 am

    could I have the ‘maths behind it’ info please. my group has been working with the problem and having lots of fun.

  3. A Allsopp
    July 28, 2009 at 3:16 pm

    I’d love to recieve the solution and maths behind this problem. I will use this in September.
    Many thanks.

  4. Roni
    August 3, 2009 at 2:46 pm

    Could I have the answer to card frame & the maths behind it please? Thanks

  5. Kjersti
    August 17, 2009 at 3:06 pm

    This seems like a great extra credit assignment could I get the solution? Thanks!

  6. A Allsopp
    August 27, 2009 at 2:08 pm

    I really would love your solution to this please, orignal request made in July. Thanks!

  7. admin
    August 27, 2009 at 2:55 pm

    Sorry you haven’t received it; it was sent on 3rd of August. I’ve sent it again today . Check it isn’t being put into to the junk folder.

    If you or anybody else still hasn’t received it let me know here.


  8. F McManus
    September 18, 2009 at 9:24 pm

    Love it. Please send the solution. Thanks

  9. K
    November 4, 2009 at 5:14 pm

    Hi, could you send me the solution please ? thanks

  10. Suzannah
    November 17, 2009 at 1:38 pm

    Could I please have the solution? Thanks

  11. January 30, 2010 at 3:54 pm

    Could I please have the solutions to the problems.Thanks

  12. SAM
    January 30, 2010 at 4:45 pm

    Please could i have the solution and maths behind it?! Thanks :)

  13. rajani
    February 1, 2010 at 7:42 pm

    give me the answer please to the card frame asap

  14. Linda Mckee
    March 22, 2010 at 1:36 pm

    Would love to receive the solution to this problem and the maths behind it.

  15. Mtro
    May 2, 2010 at 8:42 am

    Could you please send me the solution and the maths behind it

  16. Val
    May 9, 2010 at 5:11 pm

    Could you please send the answer and the maths behind it – thanks!

  17. Helen
    May 18, 2010 at 11:06 am

    Could you please send me the answer too – and how to do it! Thanks

  18. Flick
    May 26, 2010 at 11:54 pm

    Love the resources! Please may I have the solution to this problem. Thanks.

  19. Melissa
    August 11, 2010 at 11:15 pm

    Please send me the solution :-)

  20. Angela
    August 25, 2010 at 3:06 am

    AAH! The Year 7’s and I still can’t work it out. Help please!

  21. Spencer
    August 25, 2010 at 11:22 am

    Sorry for delays in sending the solutions – I’ve been away normal service now resumed.

  22. Anne-Marie Mills
    August 26, 2010 at 4:01 am

    Hi there,

    I will appreciate it if you could send me an sollution.

    Kind regards


  23. dan
    September 3, 2010 at 9:42 am

    solution to card frame problem please

  24. Lucy @Harrow BKK
    October 19, 2010 at 8:29 am

    Please can we have a solution!

  25. buzz
    November 4, 2010 at 12:13 am

    It was fun working on this problem with my children, will be thankful if you could send me its solution. Thanks.

  26. Sue G
    February 15, 2011 at 1:19 pm

    Could I have the solution please

  27. March 12, 2011 at 5:34 pm

    Would you please send me the solution? Thanks

  28. May 2, 2011 at 8:52 pm

    Great resource. Could I have the maths behind it and solution please. Thank you.

  29. Amanda
    June 28, 2011 at 8:30 pm

    Great activity. Can I have the maths and solution please.


  30. ....
    September 10, 2011 at 11:42 am

    please can i have the solution

  31. neil
    September 10, 2011 at 6:21 pm

    good puzzle my boy brought this home from school he spent ages on it lol took me 25 mins good one

  32. Spencer
    September 10, 2011 at 6:41 pm

    Good to hear that it proved an interesting challenge for him. 25 mins is pretty quick to solve it on your part too!

  33. Addy Godwin
    November 30, 2011 at 4:16 am

    can I please have the solution???? it is a gret problem and the kids are loving it but can’t figure it out!!

  34. August 19, 2012 at 11:33 am


  35. amanda
    September 18, 2012 at 5:11 am

    can I please have the solution and the maths behind it please?