ALS-W-Wing Example

Advanced methods and approaches for solving Sudoku puzzles

ALS-W-Wing Example

Postby Bud » Wed Dec 03, 2008 5:27 am

This is an example of a W-Wing that uses 2 ALS's which are not identical pairs in the pattern. This may not be a good example since it eliminates only 1 candidate and does not solve the puzzle, but it illustrates the technique. The conjugate pair cells X=2 are labled a and b in the grid. The 2 cell ALS 127 is labled c and the 3 cell ALS 1237 is labeled d. Note that X=2 must be common to both c and d. The W digit 7 appear only once in both c and d. Now a = 2 => r2c5 = 7 and b = 2 => r3c1 =7. In either case 7 cannot be in r3c5 and can be eliminated.

ALS-W-Wing Example
Code: Select all
 |-----------------+-----------------+-----------------|
 |  57    9   25   |   3   267   8   |   4    1   67   |
 |   6   48   48   |   9   127c 12c  |   3   27a   5   |
 |  37d  13d  12d  |   4   26-7  5   |   8  279b 679   |
 |-----------------+-----------------+-----------------|
 |   1  458 4589   |   7   289   3   |  29    6  489   |
 |  89    7    3   |   6  1289 124   | 129    5 1489   |
 |   2    6  489   |   5   189  14   | 179 4789    3   |
 |-----------------+-----------------+-----------------|
 |   4  358    7   |   1    35   6   |  59   89    2   |
 |  89  158 1589   |   2    45   7   |   6    3   48   |
 |  35    2    6   |   8   345   9   | 157   47  147   |
 |-----------------+-----------------+-----------------|


The puzzle is Sudoku9981 Book 43 #1. Only basic moves were used to reach this point in the puzzle.
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Postby ronk » Wed Dec 03, 2008 6:56 am

Bud, you are trying too hard to put a name on everything. Moreover, I don't think this Advanced solving techniques forum is the proper place for a new thread for your every discovery of a "new pattern."

Just imagine what this forum would look like if everyone did the same!
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ALS-W-Wing Example

Postby Bud » Wed Dec 03, 2008 7:27 am

Sorry Ron, it won't happen again.
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Postby ronk » Wed Dec 03, 2008 7:53 am

Bud, I apogize for not suggesting an alternative strategy.

You might consider starting a thread titled something like "Bud's pattern discoveries" in the General/puzzle forum here. You could then put several pattern discoveries in the single thread. Moreover, you could make the first post like a table of contents, editing it as necessary to add links to the newer items.

I didn't mean to discourage your enthusiasm, just channel it to a more appropriate forum.
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Postby udosuk » Wed Dec 03, 2008 8:06 am

Somehow I don't see a big problem for Bud posting this thread here. It's a genuine logical technique, and it's surely an advanced one for most beginner-to-medium level players.

Of course it's not as advanced as the complex analytical solve-all techniques/systems posted by the big guns boys but why must we allow only those expert level contents here? I think this forum surely has more freedom than that! (Also I don't see the issue of "everyone doing the same" because there is not much posting out here anyway.)

I happen to find this particular pattern useful. Here is another application, for the latest puzzle posted in this thread:

Code: Select all
+----------------------+----------------------+----------------------+
|-1457  -13457  9      | 8      6      2      |B37     1457   145    |
| 245    2345   6      | 1      7      9      |B23     245    8      |
| 8      127   A27     | 5      4      3      | 6     -1279   129    |
+----------------------+----------------------+----------------------+
| 24     24     8      | 3      5      1      | 9      6      7      |
| 6      57     57     | 9      2      4      | 1      8      3      |
| 3      9      1      | 7      8      6      | 5      24     24     |
+----------------------+----------------------+----------------------+
| 19     8     *257    | 4      3      57     |*27     19     6      |
| 579    6      3      | 2      1      8      | 4      579    59     |
| 1257   1257   4      | 6      9      57     | 8      3      125    |
+----------------------+----------------------+----------------------+

2 @ r7 locked at r7c37 (*)
=> At least one of the ALSs A (r3c3) and B (r12c7) must be without 2
=> At least one of them must have 7
=> r1c12+r3c8, seeing all 7s of A & B, can't have 7

You can probably yield the same eliminations via some sort of chains, but for me an ALS-related name probably sounds more elegant.:idea:

(Added later: I wrote this before reading Ron's reply minutes ago.)
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Postby DonM » Wed Dec 03, 2008 9:01 am

I think Ron's suggestion was a good one. First, because I think it was envisioned that the 'Advanced solving techniques' section would reserved for truly overall advanced techniques. More importantly is the fact that if someone puts several new names on techniques that are really variations of already tried-and-true ones and places them in the 'Advanced solving techniques' area, newer solvers may think that these must be really new techniques that should be learned.

Most of us have been around long enough that we can separate these things out, but I haven't soon forgot how long it took me to categorize in my head all the various acronyms and letter-entitled techniques. If anything, we should be trying to simplify some of the naming of the techniques we already have.

Still, ingenuity needs to be supported and if Bud comes up with something truly innovative, it will be noticed in the General Puzzle section.
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"bent naked subsets"?

Postby Bob Hanson » Tue Dec 23, 2008 2:16 am

I'm interested in whether people have recognized that many linked almost-locked sets (but not all) fall into a very easy to recognize pattern -- that of what I am calling a Bent Naked Subset. For example:

http://www.stolaf.edu/people/hansonr/sudoku/index.htm?SHHALSHINTMARKS=57,-9,25,-3,267,-8,-4,-1,67,-6,48,48,-9,127,12,-3,27,-5,37,13,12,-4,267,-5,-8,279,679,-1,458,4589,-7,289,-3,29,-6,489,89,-7,-3,-6,1289,124,129,-5,1489,-2,-6,489,-5,189,14,179,4789,-3,-4,358,-7,-1,35,-6,59,89,-2,89,158,1589,-2,45,-7,-6,-3,48,35,-2,-6,-8,345,-9,157,47,147

Code: Select all
   |---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9--
-----------------------------------------------------------------------------
r1 |    57 |     9 |    25 ||     3 |   267 |     8 ||     4 |     1 |    67
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r2 |     6 |    48 |    48 ||     9 |   127 |    12 ||     3 |    27 |     5
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r3 |    37 |    13 |    12 ||     4 |   267 |     5 ||     8 |   279 |   679
===========================||=======================||=======================
r4 |     1 |   458 |  4589 ||     7 |   289 |     3 ||    29 |     6 |   489
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r5 |    89 |     7 |     3 ||     6 |  1289 |   124 ||   129 |     5 |  1489
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r6 |     2 |     6 |   489 ||     5 |   189 |    14 ||    17 |  4789 |     3
===========================||=======================||=======================
r7 |     4 |   358 |     7 ||     1 |    35 |     6 ||    59 |    89 |     2
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r8 |    89 |   158 |  1589 ||     2 |    45 |     7 ||     6 |     3 |    48
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r9 |    35 |     2 |     6 ||     8 |   345 |     9 ||   157 |    47 |   147
.............................................................................


The almost-locked set analysis is:

r6c7 ISN'T 9: weakly linked to two almost-locked sets already weakly linked by 1: ALS 74 ALS-Y(r4c7(2,9) r5c7(1,2,9)) and ALS 117 ALS-Y(r4c9(4,8,9) r5c9(1,4,8,9) r8c9(4,8))

But what I find interesting is that together the two linked sets form a naked quintet -- {29 129 489 1489 48} involving 12489. If you consider just the cells outside the intersection of this block and column, you have a disjoint pair of sets-- {129} and {48}. As explained at http://www.stolaf.edu/people/hansonr/sudoku/explain.htm#bent this means that this set works as any naked subset -- all candidates k in cells that can see all candidates k within this subset may be eliminated. In this case it is r6c7#9 and r6c8#9.

Same for XY-Wings, XYZ-Wings, and WXYZ-Wings.

I think there is significant cross-over between linked ALS pairs and these bent-naked subsets. But I don't think one is a subset of the other. (I'm not certain of that.) As of yesterday Sudoku Assistant is finding all sorts of almost-locked sets. (See http://www.stolaf.edu/people/hansonr/sudoku/examples.htm) And many of them (but not all) are of this variety.
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Postby Bob Hanson » Tue Dec 23, 2008 2:17 am

sorry about the long line there.
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