The hardest sudokus (new thread)

Everything about Sudoku that doesn't fit in one of the other sections

Re:

Postby jemsnixon » Tue Jan 10, 2023 4:45 pm

Please include one additional detail in the second post. The command line that was used to create the output, if appropriate (understanding the options available on the gsf command line can be challenging). You specify converting to the row-normal Minlex line format and providing questions 1 and 2, but you don't specify how to construct them.
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Re: The hardest sudokus (new thread)

Postby StrmCkr » Thu Jan 12, 2023 6:30 pm

I believe it is the case that all MSLS has a corresponding SET partition


msls use a balance of naked{which includes givens} and hidden sets in a sector for 9 digits in 9 cells exactly as set does...
how is that not a given they are equivalent, exactly the same concepts just using different words

phistomefel-s-theorem-t38410.html?hilit=phistomefel#p297553

might be the same as Naked SK-loop but can it find the Hidden SK loop that co-sides with it?
as there is 2 types of Sk loops. Naked set & Hidden set

hidden SK loop
Code: Select all
+-------------------------+--------------------------+-------------------------+
| 5       17(3)     1467  | 23468   234678    378    | 12     46(8)     9      |
| 46(3)   2         46(9) | 1       -46(389)  (3589) | 46(5)  7         46(8)  |
| 1467    17(9)     8     | 24569   24679     579    | 3      46(5)     12     |
+-------------------------+--------------------------+-------------------------+
| 13678   4         15679 | 389     1389      2      | 5679   -6(3589)  3678   |
| 123678  -17(389)  12679 | 3489    5         1389   | 24679  -46(389)  234678 |
| 238     (3589)    259   | 7       3489      6      | 2459   1         2348   |
+-------------------------+--------------------------+-------------------------+
| 24      17(5)     3     | 2569    12679     1579   | 8      46(9)     1467   |
| 17(8)   6         17(5) | (3589)  -17(389)  4      | 17(9)  2         17(3)  |
| 9       17(8)     24    | 2368    123678    1378   | 1467   46(3)     5      |
+-------------------------+--------------------------+-------------------------+


normal naked sk loop
Code: Select all
+-----------------------+---------------------+-----------------------+
| 5       (137)   1467  | 23468  234678  378  | 12     (468)   9      |
| (346)   2       (469) | 1      389-46  3589 | (456)  7       (468)  |
| 1467    (179)   8     | 24569  24679   579  | 3      (456)   12     |
+-----------------------+---------------------+-----------------------+
| 13678   4       15679 | 389    1389    2    | 5679   3589-6  3678   |
| 123678  389-17  12679 | 3489   5       1389 | 24679  389-46  234678 |
| 238     3589    259   | 7      3489    6    | 2459   1       2348   |
+-----------------------+---------------------+-----------------------+
| 24      (157)   3     | 2569   12679   1579 | 8      (469)   1467   |
| (178)   6       (157) | 3589   389-17  4    | (179)  2       (137)  |
| 9       (178)   24    | 2368   123678  1378 | 1467   (346)   5      |
+-----------------------+---------------------+-----------------------+

it is pretty easy to issomorphically change the naked sk-loop into a phistomefel-ring directly showing that they are similar constructs

these two sets types should given you enough to formalize a proof on how msls is a balance of 9 digits in 9 cells per sector IE set
{as msls uses both of these in constructs}

my 2 cents
Some do, some teach, the rest look it up.
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