## almost-locked-sets (ALS) for beginners

Advanced methods and approaches for solving Sudoku puzzles
ronk wrote:"generalized" VWXYZ wing

Interesting puzzle, my solver did not catch that, I thought at first that the type 4 unique rectangle was the culprit but then I discovered that I tweaked my solver to search at the same time for an ALS xy rule which -I thought- was easier, it brought out this, which is a good example of the ALS xy rule also:

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`*-----------------------------------------------------------------*| 5      3      178   | 168    2      167   | 9      14678  146   || 678    2      4     | 1689   3      1679  | 67     5      16    || 678    168    9     | 1568   4      1567  | 23     1678   23    ||---------------------+---------------------+---------------------|| 69     69     35    | 35     1      4     | 8      2      7     || 2348   1458   1358  | 7      6      235   | 35     9      345   || 2347  *45     357   | 235    9      8     | 1     *46     3456  ||---------------------+---------------------+---------------------|| 49     49     358   | 123    78     123   | 2567  ^167    1256  || 38    %58     6     | 4     %78     123   |-257   ^17     9     || 1      7      2     | 69     5      69    | 4      3      8     |*-----------------------------------------------------------------*Eliminating 7 from r8c7(ALS-XY  A=456 in r6c2,r6c8   B=167 in r8c8,r7c8   C=578 in r8c5,r8c2   x=6 y=5 z=7)`

I don't think this is simpler, as we r talking about 3 goups of 6 cells compared to 2 groups & 5 cells... so I need to return to tweak the solver a bit more.........

Tarek

tarek

Posts: 2908
Joined: 05 January 2006

tarek wrote:
ronk wrote:"generalized" VWXYZ wing

Interesting puzzle, my solver did not catch that

Maybe it just looks that way. If your solver sees the "pattern" of the xz-rule but doesn't find an elimination -- in this case because it isn't programmed to recognize doubly-weakly-linked sets -- maybe it doesn't report it.

Ron
ronk
2012 Supporter

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Joined: 02 November 2005
Location: Southeastern USA

you're right, I didn't program it to pick the double link elimination, as it didn't have the ordinary single link elimination, it did not see it.

tarek

Posts: 2908
Joined: 05 January 2006

tarek wrote:
ronk wrote:"generalized" VWXYZ wing

Code: Select all
`*-----------------------------------------------------------------*| 5      3      178   | 168    2      167   | 9      14678  146   || 678    2      4     | 1689   3      1679  | 67     5      16    || 678    168    9     | 1568   4      1567  | 23     1678   23    ||---------------------+---------------------+---------------------|| 69     69     35    | 35     1      4     | 8      2      7     || 2348   1458   1358  | 7      6      235   | 35     9      345   || 2347  *45     357   | 235    9      8     | 1     *46     3456  ||---------------------+---------------------+---------------------|| 49     49     358   | 123    78     123   | 2567  ^167    1256  || 38    %58     6     | 4     %78     123   |-257   ^17     9     || 1      7      2     | 69     5      69    | 4      3      8     |*-----------------------------------------------------------------*Eliminating 7 from r8c7(ALS-XY  A=456 in r6c2,r6c8   B=167 in r8c8,r7c8   C=578 in r8c5,r8c2   x=6 y=5 z=7)`

I don't think this is simpler, as we r talking about 3 goups of 6 cells compared to 2 groups & 5 cells...
Tarek

I can't do anything about the number of cells, but as I have been showing recently the number of groups is always one. Try this case, a single group of size 6: r6c2,r6c8,r8c8,r7c8,r8c5,r8c2 with digits 145678 of max multiplicities 111121 for a total of 7, so this is an almost locked set, and every outside choice that eliminates two digits can be removed. But (8,7)7 would eliminate both sevens. Hence (8,7)!7.
aeb

Posts: 83
Joined: 29 January 2006

My attempt at illustrating a hypothetical double link with the xy rule:
Code: Select all
`                  *BA2        *CA2                  .   .       .   .                 .     .     .     .                   .       .   .       .               BA2.....BA2 CA2.....CA2               /         \ /         \*b.......b----B           A           C----c.......c*              |\         /.\         /|              | x.......x . y.......y |              | .       . . .       . |              |  .     .  .  .     .  |                 |   .   .   .   .   .   |              z    *x     *a   *y     z               .                     .                .                   .                 .........*z........`

BA2 & CA2 being the extra constraints

Tarek

tarek

Posts: 2908
Joined: 05 January 2006

aeb wrote:I have been showing recently the number of groups is always one. Try this case, a single group of size 6: r6c2,r6c8,r8c8,r7c8,r8c5,r8c2 with digits 145678 of max multiplicities 111121 for a total of 7, so this is an almost locked set, and every outside choice that eliminates two digits can be removed. But (8,7)7 would eliminate both sevens. Hence (8,7)!7.

This sounds intersting aeb, could you open a new thread to discuss this.....
If you have done so before, could you provide a link.

Tarek

tarek

Posts: 2908
Joined: 05 January 2006

tarek wrote:My attempt at illustrating a hypothetical double link with the xy rule:...

WOW, that's impressive looking! I haven't even attempted the ALS xy-rule yet. Me thinks we've gone beyond smoof's "beginner" outlook on this topic, but I helped cause that.

Ron
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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