Results 1 to 11 of 11

Math Help - Challenging Number placement puzzle

  1. #1
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1

    Challenging Number placement puzzle

    Imagine you have a 5 x 5 grid. You have to place the numbers 1-25 on the grid so that each row, column and diagonal add up the the same number, can it be done?

    For example, here's what I mean with a 3x3 version.

    4 9 2
    3 5 7
    8 1 6

    All columns, rows and diagonals all add up to 15.

    I would love someone to work this out, been annoying me for ages.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by craig View Post
    Imagine you have a 5 x 5 grid. You have to place the numbers 1-25 on the grid so that each row, column and diagonal add up the the same number, can it be done?

    For example, here's what I mean with a 3x3 version.

    4 9 2
    3 5 7
    8 1 6

    All columns, rows and diagonals all add up to 15.

    I would love someone to work this out, been annoying me for ages.
    If you have Matlab, just type:
    Code:
    magic(5)
    I think that's what you're looking for.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Quote Originally Posted by janvdl View Post
    If you have Matlab, just type:
    Code:
    magic(5)
    I think that's what you're looking for.
    Do you have the corresponding Maple command by any chance ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by craig View Post
    Do you have the corresponding Maple command by any chance ?
    I'm afraid not (I've only done a Matlab course), but just give me a moment, I'm installing Matlab now, then I'll just post the matrix here for you.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Quote Originally Posted by janvdl View Post
    I'm afraid not (I've only done a Matlab course), but just give me a moment, I'm installing Matlab now, then I'll just post the matrix here for you.
    Thankyou! Someone gave me this problem & I've been stumped ever since
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    I'm sorry, the bloody thing refuses to activate my LEGAL copy... I'll get back to you on this one in the next hour.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Quote Originally Posted by janvdl View Post
    I'm sorry, the bloody thing refuses to activate my LEGAL copy... I'll get back to you on this one in the next hour.
    Just found some on the internet.

    19 8 22 11 5
    12 1 20 9 23
    12 24 13 2 16
    3 17 6 25 14
    21 15 4 18 7

    Thanks for the help anyway
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by craig View Post
    Just found some on the internet.

    19 8 22 11 5
    12 1 20 9 23
    12 24 13 2 16
    3 17 6 25 14
    21 15 4 18 7

    Thanks for the help anyway
    Sorry I couldn't help you earlier.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,660
    Thanks
    600
    There are hundreds of 5-by-5 Magic Squares
    and there are formulas for generating them.


    Here's one of them:

    . . \begin{array}{ccccc}17 & 24 & 1 & 8 & 15 \\ 23 & 5 & 7 & 14 & 16 \\ 4 & 6 & 13 & 20 & 22 \\ 10 & 12 & 19 & 21 & 3 \\ 11 & 18 & 25 & 2 & 9 \end{array}

    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Quote Originally Posted by janvdl View Post
    Sorry I couldn't help you earlier.
    No worries, I didn't actually know what they were called until you said so thank for that
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Banned
    Joined
    Oct 2009
    Posts
    769

    Response

    My first step is to write out the numbers from 1 to 25 from left to right.

    The second step is to flip the diagonals around the center number (which is 13).

    The third step is to switch numbers to balance out the rows and columns in the 5 x 5 magic square (where all the rows, columns and diagonals sum to 65 in a normal 5 x 5 magic square).

    Here's why it's so hard to work out. There are 275,305,224 distinct normal 5 x 5 magic squares. If it takes just a second to make one of them, how long would it take someone to make all of them? (for that matter, how many methods would one need to make all of them?)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. New more challenging and interesting calculus puzzle
    Posted in the Math Puzzles Forum
    Replies: 6
    Last Post: February 1st 2011, 12:23 PM
  2. A number puzzle for u
    Posted in the Math Challenge Problems Forum
    Replies: 7
    Last Post: October 12th 2009, 09:37 PM
  3. Number puzzle...
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: April 9th 2009, 09:24 PM
  4. Replies: 3
    Last Post: June 16th 2008, 08:48 AM
  5. number puzzle
    Posted in the Algebra Forum
    Replies: 10
    Last Post: September 12th 2006, 05:37 PM

Search Tags


/mathhelpforum @mathhelpforum