How Do the 36 Officers Problem and Finite Fields Relate?

[marlon]

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.

 

[HallsofIvy]

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]

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.

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

 

[NateTG]

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.

The answer to the question as Halls states is yes. What is your question?

 

[Eman]

I found this link by searching euler 36 officers in google.
http://www.math.sunysb.edu/~tony/whatsnew/column/latin-squaresII-0901/latinII1.html

 

[marlon]

I found this link by searching euler 36 officers in google.
http://www.math.sunysb.edu/~tony/whatsnew/column/latin-squaresII-0901/latinII1.html

thank you all, for helping me out here. I think I will browse some more sites



Thanks again for replying