Euler's Thirty-six officers problem?

  • Thread starter tora
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In summary, the Thirty-six officers problem is a mathematical problem that involves arranging 36 officers in a regimental fashion without repeating any rank or regimental uniform. Although the problem is believed to be unsolvable, a few solutions have been found through experimentation.
  • #1
tora
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I randomly came across this problem:

http://en.wikipedia.org/wiki/Thirty-six_officers_problem

however, the problem is described as NOT being solvable.
But just goofing around, I found TWO solutions:
1 6 5 4 3 2
2 1 6 5 4 3
3 2 1 6 5 4
4 3 2 1 6 5
5 4 3 2 1 6
6 5 4 3 2 1

1 2 3 4 5 6
2 3 5 6 1 4
3 1 6 5 4 2
5 6 4 3 2 1
6 4 1 2 3 5
4 5 2 1 6 3


Clearly, I am not smarter that every mathmetician since 1782. I must not actually unstand what the problem is.

Could someone explain it to me?

thanks :)
 
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  • #2
Afraid you've only done half the job.

Let's assume the numbers 1-6 are the ranks of the officers, you still have to put on the regimental uniforms. E.g. 1a, 1b, ... 1f, 2a, 2b, ... 6f. Then you need to make sure you also don't have an a, b, c etc. twice in any row or column.


E.g. if it were three ranks and regiments:

1b 2c 3a
2a 3b 1c
3c 1a 2b
 

1. What is Euler's Thirty-six officers problem?

Euler's Thirty-six officers problem is a mathematical problem that involves arranging 36 officers of six different ranks in a square formation so that no row or column contains officers of the same rank.

2. Who is responsible for creating this problem?

The problem was created by the famous Swiss mathematician Leonhard Euler in the 18th century.

3. What is the significance of this problem?

Euler's Thirty-six officers problem is significant because it is one of the earliest examples of a combinatorial design problem and has applications in areas such as coding theory and experimental design.

4. Has this problem been solved?

Yes, Euler's Thirty-six officers problem has been solved. The solution involves using a specific mathematical algorithm to systematically arrange the officers in the desired formation.

5. Are there variations of this problem?

Yes, there are variations of Euler's Thirty-six officers problem, such as increasing the number of ranks or changing the dimensions of the square formation. These variations can make the problem more challenging and have different solutions.

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