Please, some help on the 36-officers problem

  • Thread starter marlon
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In summary, the 36-officers problem poses the question of whether it is possible to construct mutually orthogonal latin squares of order 6, and has been proven to be impossible through brute force by G. Tarry. The problem is often discussed in combinatorics classes and its relation to finite fields is still being studied.
  • #1
marlon
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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.
 
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  • #2
I believe you would get more responses if you actually described the problem. I'm sure most of us don't know what the 36-officers problem is.
 
  • #3
Euler's famous 36 officers problem basically asks the question "Is it possible to construct mutually orthogonal latin squares of order 6?" The answer is no there does not exist a pair. It was shown by brute force by G. Tarry. I remember learning about this problem in my combinatorics class. As for the relation to finite fields, I'm not sure, I'll email one of my professors.
 
  • #4

What is the 36-officers problem?

The 36-officers problem is a mathematical puzzle that involves arranging 36 officers into six groups of six officers each, with certain restrictions on which officers can be grouped together.

What are the restrictions on grouping the officers?

The restrictions are that no group can have more than one officer from the same rank (captain, lieutenant, sergeant, or corporal), and no group can have more than one officer from the same unit (Army, Navy, Air Force, or Marines).

What is the objective of the 36-officers problem?

The objective is to find a way to group the officers that satisfies all of the restrictions and results in six groups of six officers each.

Is there a specific strategy or method for solving the 36-officers problem?

Yes, there are various strategies and methods that can be used to solve the 36-officers problem, including trial and error, logic and deduction, and mathematical algorithms. However, there is no one definitive solution and different approaches may result in different groupings.

What real-world applications does the 36-officers problem have?

The 36-officers problem is a famous example of a combinatorial optimization problem and has applications in fields such as computer science, operations research, and logistics. It can also be used as a brain-teaser or puzzle for entertainment purposes.

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