# HELP ON THE 36-officersproblem

1. Jul 25, 2004

### 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.

2. Jul 26, 2004

### HallsofIvy

Staff Emeritus
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: Jul 26, 2004
3. Jul 26, 2004

### marlon

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

4. Jul 26, 2004

### NateTG

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

5. Jul 26, 2004

### Eman

6. Jul 27, 2004