Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: HELP ON THE 36-officersproblem

  1. Jul 25, 2004 #1
    Can anyone explain me the problem of the 36-officers and the relation to finite fields ???

    References to other explainatory website-links are also very usefull.
     
  2. jcsd
  3. Jul 26, 2004 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Unfortunately, I (and, I suspect, others) have no idea what the "problem of the 36-officers" is! Could you give us more information?

    Okay, I just googles on "36-officers" and "finite fields" and got this:

    "Orthogonal latin squares have been considered by Euler probably for their entertaining value. He posed the problem of 36 officers: Is it possible to arrange 36 officers, each having one of six different ranks and belonging to one of six different regiments, in a square formation 6 by 6, so that each row and each file shall contain just one officer of each rank and just one from each regiment?"

    Hmmm, I am reminded of the fact that the "operation table" for a group must have each member exactly once in each row and column, in order that each member have an inverse.
     
    Last edited by a moderator: Jul 26, 2004
  4. Jul 26, 2004 #3

    You are correct, this is exactly what I mean. Sorry for the bad description of mine. Do you have some more info concerning this problem. Don't mind if the explanaition is pure algebraic, i will try to understand. Any link to some nice sites will also be more then wellcome.


    Thanks a lot
     
  5. Jul 26, 2004 #4

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    The answer to the question as Halls states is yes. What is your question?
     
  6. Jul 26, 2004 #5
  7. Jul 27, 2004 #6
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook