Euler's
36 officers problem has been in the news recently, following the passing of the last of 'Euler's Spoilers'.
It notoriously has no solution for the 6x6 square with 6 officers (colonel, lieutenant-colonel, major, captain, lieutenant, and sub-lieutenant) and 6 regiments.
One possible modification, while still keeping 6 regiments, would be to allow substitution of a junior officer (or officers) in one or more of the regiments by a new rank - say, Sensitivity Counsellor, or SC - more reflective of the needs and aspirations of a modern-day military.
What is the minimum number of SC's needed to make the problem solvable?
6/6 Whoops - TBC -
Status 15 July 2020
Here is my progress so far:
I did show that substituting 2 SC's of differing ranks and regiments
did allow a solution
I did prove that for _some_ starting pure (illegal) squares substituting-in one SC had no possible solutions.
So I took the suggestions of Steve and Brian in the comments below and systematically tried one substituted arrangement and by testing 5 possible variants of this starting arrangement (as suggested by B Smith) attempted to show _all_ possible arrangements would fail to give a solution. However cases 4 and 5 took too long of a run-time to finish so my conclusion was not yet supported. I tried several way of speeding up the tree search - but sadly this is still work in progress!
I have some ideas and think a better starting arrangement and code improvement will break the ~40 hour run-time barrier. But i would like more confidence that the scheme laid out by Brian does in fact suffice in its generality
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6/6
program running - 40 hours now - will complete before the 80 hour mark I think...
i am making progress understanding why my algorithm fails to complete for 2 out of the 5 needed test cases...
more soon
6/6 still at it.
Edited on June 6, 2020, 4:18 pm
Edited on July 15, 2020, 3:58 pm
solution
