The New Sudoku Players' Forum

[David P Bird]

The acceptability of unidirectional Sudoku methods is rather similar to the acceptability of gay marriages in different states. Who knows, perhaps recognising polygamous gay marriages is a possible future step that might be considered equivalent to accepting forcing nets.

As for me, I've no longer so phobic about Forcing Chains, but don't expect me to turn up in a FC club!

[eleven]

David, if you are addressing me, please note, that i took an effort to write it as (bidirectional) AIC too.
I am happy to see that the general tolerance for other points of view is growing. But i will not come out with my kind of marriage now

[DonM]

In my eyes the als, Sue de Coq, base/cover and ring interpretations are more of theoretical interest.
All you have to spot is a simple forcing chain:
r1c8=7->r9c7=7
r1c8=8->r9c7=8
The rest falls into place.
7r9c7=7r123c7-(7=8)r1c8-8r13c7=8r9c7 => r9c7<>169, and if you want r3c8<>8

IMO, the above premise falls under the same category as 'Sue-de-Coq is subsumed by doubly-linked ALSs'. In both cases, things become very simple/obvious when any SDC is reversed engineered: The 'simple forcing chain' and the doubly-linked ALSs suddenly become very apparent.

The fact is that It is very rare to see the same exclusions provided by the more useful SDCs (as opposed to simpler SDCs that provide few exclusions) presented, originally, in a solution using manually-derived alternative methods (forcing chains, doubly-linked ALSs or otherwise).

(Edited for clarity)

[aran]

Plenty to disagree with there !

[David P Bird]

In my eyes the als, Sue de Coq, base/cover and ring interpretations are more of theoretical interest.
All you have to spot is a simple forcing chain:
r1c8=7->r9c7=7
r1c8=8->r9c7=8
The rest falls into place.
7r9c7=7r123c7-(7=8)r1c8-8r13c7=8r9c7 => r9c7<>169, and if you want r3c8<>8

As I've said before, using two forcing chains away from strongly linked candidates (78c1c8) is equivalent to tracking an AIC. However by calling your process a forcing chain method, you appear to advocate FCs in all the other less disciplined ways they can be used. I'm not sure if that is the message you really want to send. As we've discovered, there are terminology differences between different sources too.

Before I rose to your bait my original intention was to point out that overlapping AHSs can also produce locked set patterns as in this PM grid:

Code: Select all

 *--------------------*--------------------*-------------------*
 | 346   356    9     | 8      7     1     | 36    245   245   |
 | 37    8      2     | 6      3459  3459  | 1     79    345   |
 | 1     367    45    | 459    3459  2     | 79    8     3456  |
 *--------------------*--------------------*-------------------*
 | 239   239    167   | 12459  23459 34569 | 679   12479 8     |
 | 5     4      16    | 129    8     7     | 369   1239  1236  |
 | 8     239    167   | 1249   2349  3469  | 5     12479 1246  |
 *--------------------*--------------------*-------------------*
 | 279-4 1279-5 45    | 27-459 6     459   | 8     135   135   |
 | 69-24 169-25 8     | 3      2459  459   | 24    15    7     |
 | 247   257    3     | 2457   1     8     | 24    6     9     |
 *--------------------*--------------------*-------------------*

MSHS: (27)r7,(169)b7: 5 candidates/available cells => r7c1 <> 4, r7c2 <> 5, r7c4 <> 459, r8c1 <> 24, r8c2 <> 25

I'd be interested in your route to these eliminations.

TAGdpbMSHS

[Edit 14/12/17 TAG added]

[daj95376]

While we're waiting on eleven's response ...

A loop embedded in a longer chain?

Code: Select all

 +-----------------------------------------------------------------------+
 |  346    356    9      |  8      7      1      |  36     245    245    |
 |  37     8      2      |  6      3459   3459   |  1      79     345    |
 |  1      367    45     |  459    3459   2      |  79     8      3456   |
 |-----------------------+-----------------------+-----------------------|
 |  239    239    167    |  12459  23459  34569  |  679    12479  8      |
 |  5      4      16     |  129    8      7      |  369    1239   1236   |
 |  8      239    167    |  1249   2349   3469   |  5      12479  1246   |
 |-----------------------+-----------------------+-----------------------|
 |  2479   12579  45     |  24579  6      459    |  8      135    135    |
 |  2469   12569  8      |  3      2459   459    |  24     15     7      |
 |  247    257    3      |  2457   1      8      |  24     6      9      |
 +-----------------------------------------------------------------------+
 # 126 eliminations remain

                  (2)r7c12 = (2-7)r7c4 = r7c12 - (7=245)r7c3,r9c12 - loop  =>  r7c4<>459, r8c12<>2
 (457=2)r7c3,r9c12 - r7c12 = (2-7)r7c4 = r7c12 - (7=245)r7c3,r9c12         =>  r78c1<>4, r78c2<>5


If I were to use forcing chains, then I'd choose the grouped strong inference on <7> in [r7].

Code: Select all

 (7  )r7c12 - ...
 (7-2)r7c4  = ...


[eleven]

However by calling your process a forcing chain method, you appear to advocate FCs in all the other less disciplined ways they can be used. I'm not sure if that is the message you really want to send.

Well, i take it as it comes. If i don't have a better idea, i also will try to see, how far i can come following one candidate.
In this case i just wanted to point out, that also people with some practice, but no knowledge of advanced techniques and terminologies could find the eliminations.

Code: Select all

 *--------------------*--------------------*-------------------*
 | 346   356    9     | 8      7     1     | 36    245   245   |
 | 37    8      2     | 6      3459  3459  | 1     79    345   |
 | 1     367    45    | 459    3459  2     | 79    8     3456  |
 *--------------------*--------------------*-------------------*
 | 239   239    167   | 12459  23459 34569 | 679   12479 8     |
 | 5     4      16    | 129    8     7     | 369   1239  1236  |
 | 8     239    167   | 1249   2349  3469  | 5     12479 1246  |
 *--------------------*--------------------*-------------------*
 | 279-4 1279-5 45    | 27-459 6     459   | 8     135   135   |
 | 69-24 169-25 8     | 3      2459  459   | 24    15    7     |
 | 247   257    3     | 2457   1     8     | 24    6     9     |
 *--------------------*--------------------*-------------------*

MSHS: (27)r7,(169)b7: 5 candidates/available cells => r7c1 <> 4, r7c2 <> 5, r7c4 <> 459, r8c1 <> 24, r8c2 <> 25

I'd be interested in your route to these eliminations.

Nice move.

Probably i would not have found that pattern at all. So i only can try to explain, what could had happened.

Suppose i checked the almost 27. Normally i would try to find 2 cells for them, where i can continue in both directions (if they are the pair or not).

I could notice here, that 27 in r7c12 directly leads to a contradiction in box 7, because it leaves 45 only in 3 cells. So r7c4 has to be 27.
Now we either have a triple 245 or 745 in box 7, so 45 can be eliminated in the rest of the box.
I dont think, that i would spot the overlapping almost triple 169 (leading to r8c12=169).
But i will try to find that in future.

[Edit:] Following David's link i came here 3 years later.

Code: Select all

*---------------------*--------------------*-------------------*
 | 346   356     9     | 8      7     1     | 36    245   245   |
 | 37    8       2     | 6      3459  3459  | 1     79    345   |
 | 1     367     45    | 459    3459  2     | 79    8     3456  |
 *---------------------*--------------------*-------------------*
 | 239   239     167   | 12459  23459 34569 | 679   12479 8     |
 | 5     4       16    | 129    8     7     | 369   1239  1236  |
 | 8     239     167   | 1249   2349  3469  | 5     12479 1246  |
 *---------------------*--------------------*-------------------*
 | 279-4 1279-5 #45    | 27-459 6     459   | 8     135   135   |
 | 69-24 169-25  8     | 3      2459  459   | 24    15    7     |
 |#247  #257     3     | 2457   1     8     | 24    6     9     |
 *---------------------*--------------------*-------------------*

Now i would look at the obvious ALS 2457 in r7cr9c12:
1) 2 in ALS -> 2r7c4, 7 in ALS -> 7r7c4 => r7c4=27 and 45 must be in ALS, not in the rest of the box
2) One of 2 and 7 must be both in r7c12 and in the ALS => 27 not in the rest of the box

[aran]

Using this excellent example it will be interesting to see which approach portrays the eliminations most simply.
The base cover approach, as mentioned by David P Bird, has much to merit attention.
One of the most interesting aspects of base/cover is that no knowledge of AICs is required and that the logic once grasped is simple (enough) and very elegant (I shall personally never forget Allen Barker's illuminating presentation of the famous SK loop as a base cover exercise)

Just to set out the logic for this example :

base of 5 truths : 169b7 27r7 (5 and only 5 truths : there can only be one 7 in row 7, only one 9 in box 7, and so on, and none of those can overlap)
cover of 5 truths : cells r7c1 r7c2 r7c4 r8c1 r8c2 (5 and only 5 truths : each cell has exactly one truth)
all of the truths in the base are contained in the cover : so the cover must contain at least those five truths, but it contains only 5 truths, so it must contain those 5 truths alone.

Conclusion : therefore anything extraneous in the cover must be false => <4>r7c1 <5>r7c2 <459>r7c4 <24>r8c1 <25>r8c2

[eleven]

The problem is not the logic for the eliminations, but to find the sets.
Here the almost 27 pair is hard to spot. The 169 are obvious, but who looks for them ? In most cases almost hidden triples are not fruitful.
So if you have a hint, how to find these sets other than by practice (or using xsudo), please let us know.

[eleven]

[quote="eleven"]The problem is not the logic for the eliminations, but to find the sets.
Here the almost 27 pair is hard to spot. The 169 are obvious, but who looks for them ? In most cases almost hidden triples are not fruitful.
So if you have a hint, how to find these sets other than by practice (or using xsudo), please let us know.

PS: After looking at Danny's loop now, i should have seen from my observation "we either have a triple 245 or 745 in box 7", that the triple 745 implies 7r7c4 and 2r7c12, i.e. r8c12<>2.

[aran]

The problem is not the logic for the eliminations, but to find the sets.
Here the almost 27 pair is hard to spot. The 169 are obvious, but who looks for them ? In most cases almost hidden triples are not fruitful.
So if you have a hint, how to find these sets other than by practice (or using xsudo), please let us know.

btw I don't use xsudo.

For a start I might have looked for DL-ALS.
Why ? Because I like DL-ALS...
In that quest, I might have considered {13459}r7c3689 interesting because of the split of 1 and 9 (confined to r7b9, and r7b8 respectively).
Now in mind as potential RCs.
Interest now in {12459}r8c5678.
1 and 9 are indeed RCs. Present as :
{34519}{91245} ie with the RCs facing each other in a symmetrical way.
The eliminations can then be written out almost without thought (a somwewhat distinguishing feature from loops with multi-valued nodes where some thought is at least required)
1 : nil
9 : <9>r7c4
3 : nil
4 : <4>r7c14
5 : <5>r7c24
2 : <2>r8c12
4 : <4>r8c1
5 : <5>r8c2

[ronk]

Code: Select all

 *---------------------*--------------------*-------------------*
 | 346   356     9     | 8      7     1     | 36    245   245   |
 | 37    8       2     | 6      3459  3459  | 1     79    345   |
 | 1     367     45    | 459    3459  2     | 79    8     3456  |
 *---------------------*--------------------*-------------------*
 | 239   239     167   | 12459  23459 34569 | 679   12479 8     |
 | 5     4       16    | 129    8     7     | 369   1239  1236  |
 | 8     239     167   | 1249   2349  3469  | 5     12479 1246  |
 *---------------------*--------------------*-------------------*
 | 279-4 1279-5 a45    | 27-459 6    a459   | 8    b135  b135   |
 | 69-24 169-25  8     | 3     c2459 c459   |c24   b15    7     |
 | 247   257     3     | 2457   1     8     | 24    6     9     |
 *---------------------*--------------------*-------------------*

a,b,&c labels added by ronk

MSHS: (27)r7,(169)b7: 5 candidates/available cells => r7c1 <> 4, r7c2 <> 5, r7c4 <> 459, r8c1 <> 24, r8c2 <> 25

I'd be interested in your route to these eliminations.

Extended doubly-linked als-xz:

(94=45)als:r7c36 - (5)grp:r7c89 = (5)r8c8 - (524=249)als:r8c567 - loop ==> r7c1<>4, r7c2<>5, r7c4<>459, r8c1<>24, r8c2<>25

[eleven]

I guess, (9=45) is good enough.

Thanks aran,
so it reduces to find such a DL-ALS. It is basically the same, what Ron does with his loop, but gives a better idea, how to find it.

btw, when reading your post, i had a deja vu, that you already explained me a similar thing before years. But i could not find it, maybe it was in the lost forum crash posts.

[daj95376]

I guess, (9=45) is good enough.

I don't believe that using (9=45) would account for r7c1<>4 in the eliminations.

Like using a candidate twice in an ERI expression within a loop, the <4> must be expressed twice in this loop. Consider the loop based on a forcing chain using two streams on <5> in r8c8:

Code: Select all

 (5)r8c8 = r7c89 - (5=49)r7c36 - (9=245)r8c567 - loop
 *--------------------------------------------------------------------*
 | 346    356    9      | 8      7      1      | 36     245    245    |
 | 37     8      2      | 6      3459   345    | 1      79     345    |
 | 1      367    5      | 459    3459   2      | 79     8      3456   |
 |----------------------+----------------------+----------------------|
 | 239    239    167    | 12459  23459  3456   | 679    12479  8      |
 | 5      4      16     | 129    8      7      | 369    1239   1236   |
 | 8      239    167    | 1249   2349   346    | 5      12479  1246   |
 |----------------------+----------------------+----------------------|
 | 27     127    4      | 27     6      9      | 8      135    135    |
 | 69     169    8      | 3      245    45     | 24     1      7      |
 | 27     257    3      | 2457   1      8      | 24     6      9      |
 *--------------------------------------------------------------------*


Code: Select all

 (5)r8c8 - (5=249)r8c567 - (9=45)r7c36 - (5)r7c89 = loop
 *--------------------------------------------------------------------*
 | 346    356    9      | 8      7      1      | 36     24     245    |
 | 37     8      2      | 6      3459   3459   | 1      79     345    |
 | 1      367    45     | 459    3459   2      | 79     8      3456   |
 |----------------------+----------------------+----------------------|
 | 239    239    167    | 12459  23459  34569  | 679    12479  8      |
 | 5      4      16     | 129    8      7      | 369    1239   1236   |
 | 8      239    167    | 1249   2349   3469   | 5      12479  1246   |
 |----------------------+----------------------+----------------------|
 | 279    1279   45     | 27     6      45     | 8      13     13     |
 | 6      16     8      | 3      249    49     | 24     5      7      |
 | 247    257    3      | 2457   1      8      | 24     6      9      |
 *--------------------------------------------------------------------*


Thus, (94=45)r7c36 and (524=249)r8c567.

[DonM]

Since Xsudo was mentioned above in a discussion of constructs that are difficult to find manually eg. doubly-lined ALSs and David's MSHS, it occurs to me that while it and 'human-style' computer solvers are ingenious creations, they have also put a dent, apparently, in what is perceived as manual solving.

IMO, there should be full disclosure -as one frequent poster does do- when one of these or a personally-created solver are/is used to present a solution or part of a solution even if it is a single chain/construct.

Fwiw: Manual solutions have some distinguishing characteristics: They have a consistent originality. They often use constructs that were not addressed in the 'human-style' computer solvers and they occasionally have both logic and carelessness based mistakes (something that has certainly dogged me over my solving years). And it goes without saying that manual solutions can take a lot of time- the more difficult the puzzle, the longer the time.