almost-locked-sets (ALS) for beginners

Advanced methods and approaches for solving Sudoku puzzles

Postby tarek » Thu Mar 09, 2006 1:26 pm

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:

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... so I need to return to tweak the solver a bit more.........

Tarek
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Postby ronk » Thu Mar 09, 2006 5:34 pm

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
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Postby tarek » Thu Mar 09, 2006 8:08 pm

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.

The elimination should be easy to add as it would already adentify the sets....................
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Postby aeb » Thu Mar 09, 2006 9:40 pm

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.
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Postby tarek » Fri Mar 10, 2006 1:46 pm

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

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Postby tarek » Fri Mar 10, 2006 1:49 pm

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.

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Postby ronk » Fri Mar 10, 2006 1:58 pm

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.

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