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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Mon Sep 15, 2008 4:29 pm Post subject: No Rating: Puzzle CA_2 |
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There may be URs present. If you skip them, then you may find it more interesting.
| Code: | +-----------------------+
| . 1 . | . 6 . | . . . |
| 2 6 . | . . 8 | . . . |
| . . 9 | . . 1 | 8 . 4 |
|-------+-------+-------|
| . . . | 1 2 9 | . . 8 |
| 1 . . | 8 . . | . . . |
| . 2 8 | 6 . 7 | . 4 . |
|-------+-------+-------|
| . . 2 | . . . | . . . |
| . . . | . . 6 | . 8 5 |
| . . 6 | 5 . . | . 9 1 |
+-----------------------+
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Hint: Empty Rectangle w/Naked Pair pincers |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Sep 15, 2008 9:06 pm Post subject: |
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I used four of the usual techniques and then was stuck. Medusa got me enough to finish it off with an XY-Wing with pincer coloring.
I'm not familiar with the technique in your hint. How about a brief explanation? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Sep 15, 2008 11:30 pm Post subject: |
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| Marty R. wrote: | | I'm not familiar with the technique in your hint. How about a brief explanation? |
Asellus caught me on a technicality when I called a pattern an M-Wing once before; so this time, I used the single-digit pattern present in the link (logically) joining the Naked Pair cells. Anyway, I believe that it has the look and feel of an M-Wing. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Sep 16, 2008 4:53 am Post subject: |
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A xy-wing with coloring (transporting the pincers) did the trick. Basics got me here:
| Code: |
*-----------------------------------------------------------*
| 8 1 347 | 347 6 5 | 379 237 2379 |
| 2 6 347 | 347 9 8 | 5 1 37 |
| 37 5 9 | 2 37 1 | 8 6 4 |
|-------------------+-------------------+-------------------|
| 6 4 357 | 1 2 9 | 37 357 8 |
| 1 79 57 | 8 34 34 | 679 257 2679 |
| 39 2 8 | 6 5 7 | 1 4 39 |
|-------------------+-------------------+-------------------|
| 5 8 2 | 9 1 34 | 3467 37 367 |
| 49 39 1 | 37 347 6 | 2 8 5 |
| 47 37 6 | 5 8 2 | 34 9 1 |
*-----------------------------------------------------------* |
Details:
| Quote: | pivot r8c2; pincers r5c2 & r8c4. Transport <7> in r8c4 to r9c1 via r8c5 to r3c5 to r3c1 to r9c1. Delete <7> r9c2.
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Sorry about using poor notation to describe the transport; just another thing for me to work on.
Ted  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Sep 16, 2008 4:54 pm Post subject: |
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Ted, impressive!
===== ===== ===== ===== ===== =====
I thought it best to explain my Hint.
| Code: | After Singles and Naked Pairs
+--------------------------------------------------------------+
| 8 1 347 | *347 6 5 | 379 237 2379 |
| 2 6 347 | *347 9 8 | 5 1 37 |
| *37 5 9 | 2 *37 1 | 8 6 4 |
|--------------------+--------------------+--------------------|
| 6 4 357 | 1 2 9 | 37 357 8 |
| 1 7-9 57 | 8 34 34 | 679 257 2679 |
| #39 2 8 | 6 5 7 | 1 4 39 |
|--------------------+--------------------+--------------------|
| 5 8 2 | 9 1 34 | 3467 37 367 |
| 4-9 #39 1 | *37 347 6 | 2 8 5 |
| 47 37 6 | 5 8 2 | 34 9 1 |
+--------------------------------------------------------------+
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Empty Rectangle (or grouped turbot fish) for 3 in [r3b2c4] -- (*). No eliminations, though.
Using pincers (I hope), the ER can be extended into cells [r6c1],[r8c2] -- (#).
This results in the puzzle cracking to Singles after the eliminations in 9.
To me, this is an M-Wing. To get Asellus to agree, I would probably need to apply ...
| Code: | finned Franken Swordfish r36b3\c19b2 => [r1c4]<>3
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... first.
Bottom Line: It's an AIC from [r6c1] to [r8c2] with all of the cell-to-cell links based on 3. |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Tue Sep 16, 2008 6:36 pm Post subject: |
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A W-wing offers a one-step solution:
| Code: | +-----------------------------------------------------------+
| 8 1 347 | 347 6 5 | 379 237 2379 |
| 2 6 347 | 347 9 8 | 5 1 37 |
| †37 5 9 | 2 †37 1 | 8 6 4 |
|-------------------+-------------------+-------------------|
| 6 4 357 | 1 2 9 | 37 357 8 |
| 1 79 57 | 8 34 34 | 679 257 2679 |
| 39 2 8 | 6 5 7 | 1 4 39 |
|-------------------+-------------------+-------------------|
| 5 8 2 | 9 1 34 | 3467 37 367 |
| 49 39 1 | *37 †347 6 | 2 8 5 |
| †47 *37 6 | 5 8 2 | 34 9 1 |
+-----------------------------------------------------------+ |
The (37)s in r8c4 and r9c2 are tempting. They are linked by the conjugates for 7 in columns 1 and 5 so 3 may be eliminated from r8c2.
Steve |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Sep 17, 2008 3:13 am Post subject: |
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| daj95376 wrote: | To me, this is an M-Wing. To get Asellus to agree, I would probably need to apply ...
| Code: |
finned Franken Swordfish r36b3\c19b2 => [r1c4]<>3
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... first. |
Wow! "Finned Franken Swordfish"! That's the first time I've encountered a reference to an actual one of those! I would see that as a r16 Skyscraper combined with the b3 ER.
But, I wouldn't agree about the M-Wing in any case because it's a W-Wing, not an M-Wing. (Perhaps you are confusing these two critters?) Also, the discussion I recall having was about Remote Naked Pairs, not M-Wings... but maybe I've forgotten.
Anyway, that is a 39 W-Wing activated by the 3 Kite/Turbot Fish. And, there is no problem with the <3> at r1c4 being present. Grouped pivot links are fine with me! The only requirement is that it be a weak inference grouped link, which means that r3c4 must not be <3>. ANY other cell in b2 can contain a <3> candidate and it's fine as a Kite/Turbot Fish with me, that's how radical I am! |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Sep 17, 2008 5:18 am Post subject: |
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Okay, I'll admit that I have the M-Wing confused with some other pattern whose name I don't have a clue.
However, there are more than four cells involved in my pattern, so it isn't a W-Wing, either.
| Code: | 9-[r6c1]-3-[r3c1]=3=[r3c5]-3-[r12c4]=3=[r8c4]-3-[r8c2]-9
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Is there a name for a pattern where identical XY cells are pincers in a (possibly grouped) chain of >4 cells linked by X such that either end must be true for Y 
[Addendum: Nice catch Steve R.]
Last edited by daj95376 on Wed Sep 17, 2008 6:40 am; edited 3 times in total |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Sep 17, 2008 6:04 am Post subject: |
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| daj95376 wrote: | | Is there a name for a pattern where identical XY cells are pincers in a (possibly grouped) chain of >4 cells linked by X such that either end must be true for Y |
Yes, it's called a W-Wing (either or both ends must be true for Y). It doesn't matter how the external strong link in X is created. It can be anything (and doesn't need to be >4 cells: two cells will suffice, but any number of cells are possible). If two (remote) XY cells can each see the opposite ends of a strong inference on X, no matter how that strong inference is created, then they act as pincers and eliminate Y from their mutual peers. That is a W-Wing (or "Semi-Remote Naked Pair").
A W-Wing has the form:
(Z=X) - X=X - (X=Z)
The remote bivalue XZ cells themselves contain the Z pincers. The intervening "X=X" can be anything... a Skyscraper, an XY wing, a Kite, a chain of some sort, it doesn't matter.
An M-Wing is quite different. It has the form:
(Z=X) - X = (X-Z) = Z
where XZ are the matching ("complementary") bivalues. HOWEVER, the "non-pincer" XZ cell does not really need to be a bivalue since the inference there is weak. Some don't like to call this an M-Wing since they insist that there be a remote pair of matching bivalues. But, logically, it makes no difference. It is semantics, depending upon whether the bivalue pattern or the link pattern is what predominates in your way of viewing the universe. Or at least that's how I see it.
By the way, in your "nice loop" notation, shouldn't the <9>s on the ends be strongly linked? I.e., "9=[r6c1]..." and "...[r8c2]=9"? Just wondering, since I always use Eureka. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Sep 17, 2008 6:27 am Post subject: |
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| Asellus wrote: | | Yes, it's called a W-Wing ... |
Not according to Sudopedia and keith's thread on Remote Pairs. Each specifically state that a W-Wing is comprised of four cells.
However, while reviewing keith's thread, I discovered that he calls my pattern a General Remote Pair. This is what I had confused with an M-Wing.
I believe that my NL notation is correct.
| Code: | 9-[r6c1]-3 <==> (9=3)r6c1
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Sep 18, 2008 12:39 am Post subject: |
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| daj95376 wrote: | | Not according to Sudopedia and keith's thread on Remote Pairs. Each specifically state that a W-Wing is comprised of four cells. |
Interesting that "W-Wing" has now appeared in Sudopedia. The term was coined on this board and named in honor of George Woods, who posted an elimination using a reasoning that no one knew a name for. (Some time later, re'born informed us that the technique had already been known elsewhere as "semi-remote naked pairs".)
There was immediately lots of discussion about exactly what this new "W-Wing" thing was and the general conclusion, and how it is most often used on this discussion board, is as a pair of matching (non-peer) bivalue cells each of which can "see" the opposite ends of an external strong link on one of their digits, and that external strong link can be formed in any way. There have been dozens of W-Wings posted on this board that involve more than 4 cells. So, if someone wants to stuff the W-Wing name back into a 4-cell bottle, good luck! I will continue to use it without regard to the number of cells.
I'm not going down the "general remote pair" road again because the only term I use is "remote naked pair," which is enough for me. I try to keep it simple, which means having expansive definitions of single terms based on a uniform logic rather than coining lots of different names for what are essentially the same things but with minor differences. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Sep 18, 2008 1:53 am Post subject: |
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Asellus:
| Quote: | | I'm not going down the "general remote pair" road again because the only term I use is "remote naked pair," which is enough for me. I try to keep it simple, which means having expansive definitions of single terms based on a uniform logic rather than coining lots of different names for what are essentially the same things but with minor differences. |
Is there any place that explains a "Remote Naked Pair" as anything other than XY=XY=XY=XY? Maybe you should write the Sudopedia article that eliminates the need for a definition of a "general remote pair"?
If you dig through Sudopedia, you may find my comments that their descriptions / definitions of "Remote Naked Pair" are too restrictive.
And, by the way, I think "Remote Pair" is an adequate descriptor. Unless someone has an example of a "Remote Hidden Pair".
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Sep 18, 2008 9:21 am Post subject: |
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The discussions about sudoku technique namings always were more exhausting than fruitful, so i want to keep out of them. Whenever i use a non 4-cell w-wing (semi-remote naked pair, y-wing or Y-wing), i will explain it explicitely, that should be sufficient.
Steve R's nice catch above probably would not be called a w-wing by others, but with his explanation it is very clear, how it works.
| keith wrote: | | And, by the way, I think "Remote Pair" is an adequate descriptor. Unless someone has an example of a "Remote Hidden Pair". |
We had a kind of remote hidden pairs here, where the combination of a skyscraper and a kite (in 2 numbers) force the cells to be pairs (but also allow other eliminations)
A hidden w-wing (or semi-remote hidden pair) could be something like this with strong link for 1 in column 1 and strong links for 2 in row 1 and box 2.
| Code: | 125 . . | 1234
. . . | .
. . . | .
--------------------
1279 . . | .
. . 124 | .
. . . | . |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Sep 18, 2008 11:14 am Post subject: |
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The problem I have with "remote pair" isn't that there may not be such a thing as a "remote hidden pair." It's that most matching bivalues in remote cells have no relationship between them whatsoever and someone could easily call these a "remote pair" since they are "remote" (not peers) and a "pair" (matching bivalue cells). Including "naked" in the name makes it clear that there is a special relationship between these two non-peer matching bivalue cells.
Since learning that some people consider "remote pair" to be synonymous with "remote naked pair" I have avoided use of the term "remote pair" altogether and, instead, write the longer "two non-peer matching bivalue cells" so that no one reads any more into it than that.
I still disagree with the claim that the name W-Wing only applies to a 4-cell construction. As I said, many W-Wings, called such by the posters and not contested by anyone, have been posted on this board that involve more than 4 cells. Frankly, this sudden concern with 4 cells strikes me as bizarre. I agree with ravel that the identity of the external strong link of a W-Wing should be mentioned when it is not immediately obvious.
For me, both Danny's use of the 39 pairs and Steve's use of the 37 pairs are W-Wings. (They are certainly NOT M-Wings. And while Steve's 37 thing meets the definition of "General Naked Pairs," Danny's 39 thing does not due to the weak link on <3> in r8. This term was misapplied once before in another thread much as it was misapplied above. I did not want to rehash the explanation of why.)
Leave it to ravel to produce the Remote Hidden Pair! I'm not convinced by the "Hidden W-Wing" though. A W-Wing requires the bivalue cells; they cannot be hidden. That's because the digits are each weakly linked to the external strong link and the pincer digits thus depend upon the strong links internal to the bivalues. Specifying the strong links in r1 and the box violates this weak link structure. I'd call your example just another nameless simple AIC. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Sep 18, 2008 5:02 pm Post subject: |
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This is not the only forum where this topic has been beat around. I was in a similar one in the Players' Forums. You might find ronk's suggestion there of use here.
http://www.sudoku.com/boards/viewtopic.php?p=57908#57908
| ronk wrote: | Many people are already familiar with the terms xy-wing and xy-chain. An xy-wing has three bivalues (strong inferences) and an xy-chain is a chain with more than three bivalues.
A w-wing also has three strong inferences. However, it is comprised of two identical bivalues and one (simple or grouped) conjugate link. With two or more conjugate links (in the chain between the two bivalues), using the term w-chain seems the most approprate to me.
| Code: | --- strong inferences ---
=3 >3
xy-wing xy-chain
w-wing w-chain
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I reserve the right to consider grouped strong inference as acceptable. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Sep 18, 2008 10:21 pm Post subject: |
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| Asellus wrote: | | I'd call your example just another nameless simple AIC. |
Apropos nameless.
This pattern, a special case of both kite and extended xy-wing, is probably rarer, but as easy to spot as a remote naked pair. Its a cross pair with a common box and the same number in both pairs.
| Code: | . . . | 13 . .
. . . | . . .
. 12 . | . . 12.
-----------------
. -1 . | 13 . . |
I found it today in a crazy newspaper puzzle ranked "tricky". It did not help much, i needed a chain to be able to place the 7th number (!).
It's a pity, that puzzle creators dont have such things in their program. I am sure, that there must be billions of puzzles out there, which nicely could be solved (also) with this trick - without having to do this rather boring job of looking for xy-wings or kites. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Sep 18, 2008 10:50 pm Post subject: |
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| I'm beginning to think that my Hint should have been the 5-cell XY-Chain from [r5c5] to [r8c1]. |
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