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?
Here is a solution for 2 SC's introduced,
where I have numbered regiments and abbreviated ranks.
I have swapped out two unique ranks for two SCs
1_CO 5_CA 2_SC 4_LI 3_SL 6_MA
2_SL 1_LC 5_LI 3_MA 6_CA 4_CO
4_CA 6_SL 1_MA 2_LC 5_CO 3_LI
6_LI 3_CO 4_SL 1_CA 2_MA 5_LC
3_SC 4_MA 6_LC 5_SL 1_LI 2_CA
5_MA 2_LI 3_CA 6_CO 4_LC 1_SL
In case one prefers, I alternatively give the ranks as AA,BB,... with the two SCs now as GGs
1_AA 5_DD 2_GG 4_EE 3_FF 6_CC
2_FF 1_BB 5_EE 3_CC 6_DD 4_AA
4_DD 6_FF 1_CC 2_BB 5_AA 3_EE
6_EE 3_AA 4_FF 1_DD 2_CC 5_BB
3_GG 4_CC 6_BB 5_FF 1_EE 2_DD
5_CC 2_EE 3_DD 6_AA 4_BB 1_FF
(Still checking if one SC will work....)
More comments forthcoming...
Edited on May 25, 2020, 11:40 am
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