The discussion revolves around the problem of the 36 officers and its connection to finite fields, specifically focusing on the arrangement of officers in a square formation while adhering to certain constraints related to ranks and regiments.
There is an ongoing exploration of the problem, with participants sharing links and expressing a desire for more information. Some have provided initial insights, while others are still seeking understanding.
Participants have noted a lack of familiarity with the problem and have requested algebraic explanations and additional resources. There is an acknowledgment of the complexity of the topic, with references to external links for further exploration.
HallsofIvy said: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.
marlon said: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.
Eman said:I found this link by searching euler 36 officers in google.
http://www.math.sunysb.edu/~tony/whatsnew/column/latin-squaresII-0901/latinII1.html