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3x3 numerical puzzle

  1. Dec 9, 2014 #1
    1. In a 3 x 3 square, place the numbers 2,2,2,3,3,3,4,4,4 in it so that when any line of three numbers is added up in any direction (including diagonally) the total is always 9.

    2. I have tried for hours, can anyone tell me if this problem is actually possible?

    The best I get is when I do

    234
    342
    423

    And only get one diagonal of 4s which you can also do with only 3s or 2s. Any help would be truly welcomed. Thank you!
     
  2. jcsd
  3. Dec 9, 2014 #2

    jedishrfu

    Staff: Mentor

    Start with the center square and think what number can be placed there so that the two diagonals and middle row and middle column can sum to 9 with the same number?
     
  4. Dec 9, 2014 #3
    Is there only one solution to this problem. Is the centre square 2?
     
  5. Dec 9, 2014 #4
    I just can't do this... There are no numbers that can go in the middle and satisfy this problem
     
  6. Dec 9, 2014 #5

    Mark44

    Staff: Mentor

    It took me about 4 tries, but I came up with two solutions, and there are probably four or maybe more. I don't have 2 in the center.

    Yes there are.
     
  7. Dec 9, 2014 #6
    Got the answer

    342
    234
    423

    Thanks!
     
  8. Dec 9, 2014 #7
    In my head only 4, 3 and 2 made 9... Ahhh basic! Forgot the 3, 3, 3.

    Has anyone got any other combinations by pure interest?
     
  9. Dec 9, 2014 #8
    Excluding rotations, I think there's only one. With rotations, four, and allowing reflections makes no difference.

    There must be at least one 3 in every line (9 is odd), which forces the diagonal of 3s, and the rest is determined by your next number placement.
     
  10. Dec 9, 2014 #9
    Gosh how do you guys work all this out! Brainy!!
     
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