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I must be missing something, because it seems this question about Euler's 1779 Conjecture from Quanta Magazine is trivial: "Six army regiments each have six officers of six different ranks. Can the 36 officers be arranged in a 6-by-6 square so that no row or column repeats a rank or regiment?"

Assuming regiments are numeric 1-6 and ranks are alpha A-F, isn't this a solution?

1a 6b 5c 4d 3e 2f 
2b 1c 6d 5e 4f 3a 
3c 2d 1e 6f 5a 4b 
4d 3e 2f 1a 6b 5c 
5e 4f 3a 2b 1c 6d 
6f 5a 4b 3c 2d 1e

This was created just by offsetting each row sideways 1 letter and each column down 1 number.

What aspect of this problem am I misunderstanding? I'm not positing this as an answer. I'm trying to find out why the conjecture is more complicated than my guess.

Here's the original link: https://www.quantamagazine.org/eulers-243-year-old-impossible-puzzle-gets-a-quantum-solution-20220110/

Thanks!

Jim
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    You appear to have duplicate individuals, if I have understood your notation. $1a$, for instance, appears twice and we haven't got a $1d$. – lulu Jan 14 '22 at 15:55
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    This has been proven to be impossible for size $6$. For $10$ and $14$ however, solutions were found and they were called "Euler spoilers". – Peter Jan 14 '22 at 16:16
  • @lulu I knew it was something simple. I was reading this before my coffee. Thanks for the insight! – Jim Jan 14 '22 at 16:31
  • No worries. It is a fascinating old problem. – lulu Jan 14 '22 at 16:39
  • It is not magic squares, it is orthogonal latin squares https://en.wikipedia.org/wiki/Mutually_orthogonal_Latin_squares – Jean Marie Jan 14 '22 at 21:46

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