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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Wed Feb 27, 2008 10:36 pm Post subject: What should be easy, seems very difficult |
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I have been staring at this one, off and on, for a week now.
http://www.menneske.no/sudoku/eng/showpuzzle.html?number=1955784
| Code: | Puzzle: M1955784vh(0)
+-------+-------+-------+
| . . 3 | 2 . . | 4 . . |
| 2 9 4 | . 8 . | 1 6 3 |
| . . . | . . 1 | . . . |
+-------+-------+-------+
| . 7 . | . . . | 6 . . |
| . 4 . | 6 . 5 | . 8 . |
| . . 6 | . . . | . 7 . |
+-------+-------+-------+
| . . . | . . 6 | . . . |
| 8 5 7 | . 9 . | 3 4 6 |
| . . 1 | 3 . . | 7 . . |
+-------+-------+-------+ |
I thought that a Menneske rating of 0 (zero) means that it can be solved by the list of techniques he describes. Clearly, I am wrong!
The basics get me to here:
| Code: | +----------------+----------------+----------------+
| 17 18 3 | 2 6 9 | 4 5 78 |
| 2 9 4 | 5 8 7 | 1 6 3 |
| 567 68 58 | 4 3 1 | 289 29 2789 |
+----------------+----------------+----------------+
| 159 7 58 | 89 12 4 | 6 3 259 |
| 3 4 29 | 6 7 5 | 29 8 1 |
| 159 128 6 | 89 12 3 | 259 7 4 |
+----------------+----------------+----------------+
| 49 3 29 | 7 45 6 | 2589 1 2589 |
| 8 5 7 | 1 9 2 | 3 4 6 |
| 469 26 1 | 3 45 8 | 7 29 259 |
+----------------+----------------+----------------+ |
The only thing I can see is multicoloring (an extended skyscraper with the ground floors in R9) that takes out <2> in R3C7. Then, I am stuck.
I know there are a couple of chains, but am I missing some kind of named pattern?
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Feb 28, 2008 10:46 am Post subject: |
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Cant find something easy either. I solved it with this M-wing variation.
| Code: | *----------------------------------------------*
| 17 18 3 | 2 6 9 | 4 5 78 |
| 2 9 4 | 5 8 7 | 1 6 3 |
| 567 6-8 58 | 4 3 1 |#89 29 2789 |
|---------------+------------+-----------------|
| 159 7 58 |*89 12 4 | 6 3 *259 |
| 3 4 29 | 6 7 5 |*29 8 1 |
| 159 @128 6 |#89 12 3 |*259 7 4 |
|---------------+------------+-----------------|
| 49 3 29 | 7 45 6 | 2589 1 2589 |
| 8 5 7 | 1 9 2 | 3 4 6 |
| 469 26 1 | 3 45 8 | 7 29 259 |
*----------------------------------------------*
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After the coloring elimination of 2 the 89's in r3c7 and r6c4 can be connected by
r3c7=9 => r56c7<>9 => r4c9=9 => r4c4<>9 => r6c6=9
(there is also a coloring for 8 r3c7=8 => r6c4=8, but not needed here)
So with the strong link for 8 in r6c2 we have r3c7=8 or r6c2=8 |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Feb 28, 2008 11:45 am Post subject: |
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I can't find any named techniques, either. But, after that color wing removal of the <2>, the {29} UR allows removal of <9> from r9c9. This creates a "useless" XYZ Wing with one cell transported to remove <2> from r7c9, exposing an X-Wing.
After that, if we recall the <9> removed from r9c9 due to the UR, there is a 6-cell DP in b789 that requires r9c8=9 (through some roundabout implications).
I suspect that none of this is what you were looking for and the puzzle still isn't solved. To accomplish that, I resorted to Medusa multi-coloring (two clusters, no extensions) followed by a Medusa wrap (no extensions).
[Edit: Missed ravel's post while working on this. Wouldn't you know it!] |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Feb 28, 2008 11:59 am Post subject: |
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| Ravel's post made me revisit the Medusa. After that initial <2> removal, a simple Medusa multi-coloring (bridging <9>s in r35c7) removes <8> from r3c3. Then, a bit more basic Medusa removes <9> from r3c7 and solves the puzzle. Nothing else is required. |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Thu Feb 28, 2008 4:33 pm Post subject: simple |
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An xy-chain makes R3C7 an 8 and solves the puzzle.
Are such chains "dishonorable?"
Earl |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Feb 28, 2008 8:33 pm Post subject: Re: simple |
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| Earl wrote: | An xy-chain makes R3C7 an 8 and solves the puzzle.
Are such chains "dishonorable?"
Earl |
wouldn't call it dishonorable... I'd say your eyes and deductive reasoning are working strongly.
some find fish hard to look for, some find xy-chains hard to look for. regardless of the difficulty of the technique, its still a technique... 
consider this... a xy-wing is a xy-chain. if you allow yourself to look for xy-wings, you are essentially looking for a 3 cell xy-chain.
therefore, xy-chains (A.K.A. xy-wings) are arguably one of the most, if not the most sought after PATTERNS. I didn't say chains on purpose...
Asellus can say more, but he was good at pointing out that a xy-chain is just one pattern within a broader class of chains. his description of an xy-wing in eureka notation is an example. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Feb 28, 2008 8:37 pm Post subject: Re: simple |
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| Earl wrote: | | Are such chains "dishonorable?" |
Not at all for me.
I just dont like to search for them say from top left to right bottom. So i start to look for chains from a few UR patterns, remote pairs, "useless" xy-wings and similar.
I also dont find an xy-chain to eliminate 9 from r3c7, i just have one for r67c7<>9 or a "strong link chain" to eliminate 9 from r3c8 - either r3c8=2 or r9c8=2 => r3c7=9. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Feb 28, 2008 10:09 pm Post subject: |
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| ravel wrote: | Cant find something easy either. I solved it with this M-wing variation.
| Code: | *----------------------------------------------*
| 17 18 3 | 2 6 9 | 4 5 78 |
| 2 9 4 | 5 8 7 | 1 6 3 |
| 567 6-8 58 | 4 3 1 |#89 29 2789 |
|---------------+------------+-----------------|
| 159 7 58 |*89 12 4 | 6 3 *259 |
| 3 4 29 | 6 7 5 |*29 8 1 |
| 159 @128 6 |#89 12 3 |*259 7 4 |
|---------------+------------+-----------------|
| 49 3 29 | 7 45 6 | 2589 1 2589 |
| 8 5 7 | 1 9 2 | 3 4 6 |
| 469 26 1 | 3 45 8 | 7 29 259 |
*----------------------------------------------*
|
After the coloring elimination of 2 the 89's in r3c7 and r6c4 can be connected by
r3c7=9 => r56c7<9> r4c9=9 => r4c4<9> r6c6=9
(there is also a coloring for 8 r3c7=8 => r6c4=8, but not needed here)
So with the strong link for 8 in r6c2 we have r3c7=8 or r6c2=8 |
I'm missing something here (duh, what else is new?). I was under the impression that the essence of the M-Wing was connecting the pairs via two (or four) strong links. I count one from r4c4 to r6c4 and a second from r4c9 to r4c4. That's two, what about getting from r3c7 to r4c9? 
| Quote: | | Are such chains "dishonorable?" |
Like beauty, in the eye of the beholder? |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Feb 28, 2008 11:02 pm Post subject: |
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As to finding XY Chains, I recommend focussing first on locating potential pincers: two bivalue cells that share a digit and both "see" cells containing that digit. Next, look to see if they can be joined by a chain of bivalues. Often, it is immediately obvious that they cannot (e.g., the shared digit in one of the "pincer" bivalues cannot see another bivalue with that digit) and so that potential pincer can be abandoned. Also, this search for a connecting chain sometimes reveals another effective pincer even if it wasn't the one you set out to find a connection with.
Working in this way, one can do a top-left to bottom-right scan similar to that described in the Techniques forum by nataraj. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Feb 29, 2008 12:06 am Post subject: |
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1. Asellus, what is a "bivalue"? I imagine it is a cell with two candidates, but it seems it may also be a strong link?
2. "Honorable", I don't know. But I do have a mathematician's view of "elegant". What ravel does to find chains is elegant. See a pattern to exploit, add a twist, and you have something very clever. I can see how to get there, in time.
What my software does to find chains is not at all elegant. Maybe the algorithm is very clever, but the chains look, to me, like trial and error.
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Feb 29, 2008 9:15 am Post subject: |
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| keith wrote: | | Asellus, what is a "bivalue"? I imagine it is a cell with two candidates, but it seems it may also be a strong link? |
I was responding to the question of how easy, or not, it is to scan for XY Chains, so was only addressing the question of bivalue cells (cells that contain only two candidates).
The larger question of looking for AICs generally is more difficult to address. I don't believe that there any one way to go about it. I have found various things that work. To the extent that you focus on conjugates (bivalues and conjugate strong links in houses), then coloring seems the preferred approach... with some multicoloring thrown in here and there. That will ferret out those AICs pretty readily.
Another approach is that of transporting otherwise useless things, such as wing pincers or candidates that have a strong inference induced by a DP.
Also, one can focus on ALSs to see if they can form part of a useful chain.
At some point, however, the more one keeps at such things, the more it starts to resemble trial and error. One can focus on the technique and say, "Well, if I stick to strict coloring to find a chain, then that's okay," or "If I'm just transporting parts of a named technique, and not getting too fancy and involved in my transporting, then that's okay" or some such. But, bottom line, it's what works for you.
As for "elegance," I'd say that that arises when something involves a simple, clever, and insightful "twist" and produces significant results, as you note with ravel's M-Wing variant. I was annoyed, frankly, that I didn't find that implication with my Medusa multi-coloring. When I went back and looked again, it was evident that I would have had to have been quite lucky to have happened upon that particular chain by Medusa (excluding an exhaustive "all possiblities" approach, which is just about the antithesis of elegant, as I believe I demonstrated elsewhere).
Most often, the one thing one can be sure of is that if enough eyes look at a problem, someone else is likely to come up with a solution that is more elegant than yours. But now and then, they don't! |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Fri Feb 29, 2008 10:38 am Post subject: |
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| Marty R. wrote: | | I'm missing something here (duh, what else is new?). I was under the impression that the essence of the M-Wing was connecting the pairs via two (or four) strong links. I count one from r4c4 to r6c4 and a second from r4c9 to r4c4. That's two, what about getting from r3c7 to r4c9? :?: :?: |
Yes, the classical M-wing is connected by 2 strong links for one candidate. This makes sure, that both cells, say A and C, always must have the same value, say x or y. Then, if there is a strong link for x (or y) from C (or A) to a cell D, one of A (or C) and D must be x (or y).
Now one variant is, that you connect A and C with 4, 6 or 8 strong links.
Another is, you have 2 chains. A=x => C=x and A=y => C=y (no strong links necessary here, it can be any chain, coloring, bivalue, bilocation etc.).
Both also make sure that A and C must have the same value.
A 3rd variant is, you only have one chain A=x => C=x. This one you can only use, if there is a strong link for y from C to a cell D. Then either A=y or A=x => C=x => D=y, i.e. one of A and D must be y.
This is, what i used here (A is r3c7, C is r6c4, D is r6c2, x=9, y=8).
Because in this case there is also a chain
r3c7=8 => r3c3=5 => r4c3=8 => r4c4=9 => r6c4=8
we know that (like in classical M-wing) r3c7 and r6c2 must have the same value. But there is no other strong link for 8 or 9 from r3c7 or r6c4, that could be used for an elimination.
btw with the strong link for 8 in c3 r3c7 and r4c4 is a w-wing for 9.
With
r3c7=9 => r56c7<>9 => r4c9=9 => r4c4=8
we a w-wing variation for 8 (one of r3c7 and r4c4 must be 8) by means of the grouped strong link r56c7=9 or r4c9=9 in box 6.
But also no eliminations possible. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 29, 2008 4:44 pm Post subject: |
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| Thanks for the explanation, Ravel. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Mar 01, 2008 12:57 am Post subject: |
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xy-chains...
1. dishonorable?? probably not
2. elegant?? probably not
3. applying them?? Priceless!!  |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Mar 01, 2008 11:55 am Post subject: |
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| storm_norm wrote: | xy-chains...
1. dishonorable?? probably not
2. elegant?? probably not
3. applying them?? Priceless!! |
I'm with you there, Norm 
And I'd add
4. finding them?? not impossible
(and no worse than finding some of those ERs, snake hairs, fish and fowl ...) |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Mar 01, 2008 10:41 pm Post subject: |
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It's funny that I described my Medusa approach above as multi-coloring (which it is) when it is even easier to consider it as what I long ago described as a "special bivalue extension" in the Techniques forum (not that it is all that special, really). Here is the Medusa cluster derived from cell r5c7 (after that removal of <2> from r1c7 described by Keith):
| Code: |
+------------------+-----------+----------------+
| 17 18 3 | 2 6 9 | 4 5 78 |
| 2 9 4 | 5 8 7 | 1 6 3 |
| 56A7 #6a8A 58 | 4 3 1 |@89 29 2789 |
+------------------+-----------+----------------+
| 159 7 58 | 89 12 4 | 6 3 259 |
| 3 4 2a9A | 6 7 5 |#2A9a 8 1 |
| 159 12A8 6 | 89 12 3 | 259 7 4 |
+------------------+-----------+----------------+
| 49 3 2A9a | 7 45 6 | 2589 1 2589 |
| 8 5 7 | 1 9 2 | 3 4 6 |
| 46a9 2a6A 1 | 3 45 8 | 7 29 259 |
+------------------+-----------+----------------+
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Now, look at that {89} r1c7 bivalue. The <8> can "see" 8A in r3c2 and the <9> can see 9a in r5c7. So, polarity is induced and we can color the bivalue as 8a9A and perform the resulting trap eliminations:
| Code: |
+------------------+-----------+------------------+
| 17 18 3 | 2 6 9 | 4 5 78 |
| 2 9 4 | 5 8 7 | 1 6 3 |
| 56A7 6a8A #5-8 | 4 3 1 | 8a9A 29 #27-89 |
+------------------+-----------+------------------+
| 159 7 58 | 89 12 4 | 6 3 259 |
| 3 4 2a9A | 6 7 5 | 2A9a 8 1 |
| 159 12A8 6 | 89 12 3 |#25-9 7 4 |
+------------------+-----------+------------------+
| 49 3 2A9a | 7 45 6 |#258-9 1 2589 |
| 8 5 7 | 1 9 2 | 3 4 6 |
| 46a9 2a6A 1 | 3 45 8 | 7 29 259 |
+------------------+-----------+------------------+
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Nifty, no? However, it seems to occur rarely (which is why I forgot about it). |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Sun Mar 02, 2008 3:46 am Post subject: chains |
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Thanks for the comments on xy-chains. Very enlightening.
Earl |
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