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!