The New Sudoku Players' Forum

[eleven]

This is a puzzle by Big201 from an old chinese site here. ...

... Of course there are mutltiple ways.

This one is easy with SET, sk-loop-like.

Hidden Text: Show

Code: Select all

         v     v v v     v
     +-------+-------+-------+
 >   | * . 9 | . . . | 1 . * |
     | . # . | 4 # 5 | . # . |
 >   | 8 . * | . 3 . | * . 2 |
     +-------+-------+-------+
     | . 5 . | 1 . 7 | . 6 . |
     | . # 1 | . . . | 3 # . |
     | . 6 . | 5 . 3 | . 7 . |
     +-------+-------+-------+
 >   | 1 . * | . 5 . | * . 9 |
     | . # . | 7 # 4 | . # . |
 >   | * . 2 | . . . | 8 . * |
     +-------+-------+-------+


Box 5 can be ignored in the 5 colums (holds all digits 1-9, which must be more in the cols than in 4 rows).
(not sure, how the MSLS version does it - Leren?)

Then we have 8 givens and 8 empty cells in both sets.
=> # cells can only be 1289, * only 34567, leaving this grid:

Code: Select all

+-----------------------+----------------------+-----------------------+
| *34567  2347   9      |  268    2678   268   |  1      3458  *34567  |
|  2367  #12     367    |  4     #1289   5     |  679   #89     3678   |
|  8      147   *4567   |  69     3      169   | *4567   459    2      |
+-----------------------+----------------------+-----------------------+
|  2349   5      348    |  1      2489   7     |  249    6      48     |
|  2479  #289    1      |  2689   24689  2689  |  3     #289    458    |
|  249    6      48     |  5      2489   3     |  249    7      148    |
+-----------------------+----------------------+-----------------------+
|  1      3478  *3467   |  2368   5      268   | *467    234    9      |
|  3569  #89     3568   |  7     #1289   4     |  256   #12     1356   |
| *34567  3479   2      |  369    169    169   |  8      1345  *34567  |
+-----------------------+----------------------+-----------------------+

After 6 singles you get an x-wing for 5, 3 strong links for 3 (-3r1c19), xy-wing 496 and UR 28 to solve it.

[Edit: removed 7r2c2, thx to Leren]

[Leren]

Code: Select all

*-----------------------------------------------------*
| 34567 2347 9    | 268  2678  268  | 1    3458 34567 |
| 2367  12   367  | 4    1289  5    | 679  89   3678  |
| 8     147  4567 | 69   3     169  | 4567 459  2     |
|-----------------+-----------------+-----------------|
| 2349  5    348  | 1    2489  7    | 249  6    48    |
| 2479  289  1    | 2689 24689 2689 | 3    289  458   |
| 249   6    48   | 5    2489  3    | 249  7    1     |
|-----------------+-----------------+-----------------|
| 1     3478 3467 | 2368 5     268  | 467  234  9     |
| 3569  89   3568 | 7    1289  4    | 256  12   356   |
| 34567 3479 2    | 369  169   169  | 8    1345 34567 |
*-----------------------------------------------------*

MSLS : 18 Truths; r1379 c24568 : 18 Links; 28r1 19r3 28r7 19r9 ; 347c2 3c4 7c5 345c8 ; 6b2 6b8 ;

19 Eliminations get you to here. Looks the same except that 7 is missing from r2c2.

<edit>

FWIW I solved this in just four moves other than basics.

1. X Wing on 5 removes four 5's.

2. MSLS same as before but 1 less elimination (probably a 5).

3. Swordfish of 3's removes five 3's.

4. ALS XY Wing: (2=4) r235c8 - (4=3) r18c9 - (3=2) r2357c8 => - 2 r8c8.

btte

[eleven]

Ah thanks, i see.
Concerning the 7: I just missed to eliminate the 7r2c2 manually (there should only be those out of 1289 left - corrected it above).

[StrmCkr]

Those other grids are great for finding in naked fashion hidden subsets

RC space for naked subsets { Hitting set problem}: N cells = N digits { if you try to match N digits to a nCr [combination] instead of a direct count }
Rn,Cn,Bn space for Hidden subsets { a Hitting set Problem}: N digits = N positions { if you try to math N digits a nCR [combination instead of a direct count math }

the most you'd have to ever search for is size 4.

alternative is a Powers-Set combinations that does each RC sector for {Degrees of Freedom size 0 - 8 } then filter the list for 0 degrees of freedom for naked sets of size 1-9
same thing to Rn,Cn,Bn space

the bonus is you now have a list of ALS, AHS usable as a strong links.

my code has both versions of this operating { java if u want to see that }


the fun part is you can use NxN fish code directly on either Set to find them as a Hidden subset on Rows is a Fish on cols [ more intuition is that ALS xz,xy is also Nxn+k fish ]

RC space can be used to find hidden subsets but involves twiddling the N size naked set for M size "off" positions.
same thing to make naked subsets work as "fish" logic.

insights for finding MSLSs is using NxN+K math of twiddled naked sets then you can use Muti Digits as a Nxn+K setup to identify them

hidden subset sectors / naked subset sectors for a 1:1 assignment if not add more K naked sectors.
OR
naked subsets sectors / hidden subset sectors for a 1:1 assignment if not add more K naked sectors
or
hidden / hidden for a 1:1 assignment if not add more K naked sectors
or
naked / naked. for a 1:1 assignment if not add more K naked sectors

i would search spaces posts for insights as they where fond of converting msls to nxn+k formats.

my MSLS pascal code only gets basic types of SK loops as that was easy to code.