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
The 36-officers problem is a mathematical puzzle that involves arranging 36 officers into six groups of six officers each, with each group consisting of one captain, one lieutenant, and four sergeants. The goal is to create groups where no two officers with the same rank are in the same row, column, or diagonal.
The 36-officers problem is significant because it can help develop critical thinking and problem-solving skills. It also has real-world applications, such as in scheduling and resource allocation.
There are several strategies that can be used to solve the 36-officers problem, including trial and error, visualization, and breaking the problem into smaller parts. Other methods include using mathematical principles such as symmetry and combinatorics.
Yes, there is a guaranteed solution to the 36-officers problem. However, due to the complexity of the problem, it may not be easily found. It may require multiple attempts and different strategies before finding the solution.
There are many other similar problems that involve arranging objects or people in a specific way, such as the eight queens puzzle, Sudoku, and the knight's tour problem. These problems also require critical thinking and problem-solving skills.