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Euler's Thirty-six officers problem?

  1. Apr 14, 2010 #1
    I randomly came accross this problem:

    http://en.wikipedia.org/wiki/Thirty-six_officers_problem

    however, the problem is described as NOT being solvable.
    But just goofing around, I found TWO solutions:
    1 6 5 4 3 2
    2 1 6 5 4 3
    3 2 1 6 5 4
    4 3 2 1 6 5
    5 4 3 2 1 6
    6 5 4 3 2 1

    1 2 3 4 5 6
    2 3 5 6 1 4
    3 1 6 5 4 2
    5 6 4 3 2 1
    6 4 1 2 3 5
    4 5 2 1 6 3


    Clearly, I am not smarter that every mathmetician since 1782. I must not actually unstand what the problem is.

    Could someone explain it to me?

    thanks :)
     
  2. jcsd
  3. Apr 14, 2010 #2
    Afraid you've only done half the job.

    Let's assume the numbers 1-6 are the ranks of the officers, you still have to put on the regimental uniforms. E.g. 1a, 1b, ... 1f, 2a, 2b, ... 6f. Then you need to make sure you also don't have an a, b, c etc. twice in any row or column.


    E.g. if it were three ranks and regiments:

    1b 2c 3a
    2a 3b 1c
    3c 1a 2b
     
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