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no UR but remote pair?
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Tue Oct 30, 2007 3:03 pm    Post subject: no UR but remote pair? Reply with quote

Eager to apply my new half-knowledge about unique rectangles I tried the Thursday, Oct 25 nightmare (http://www.sudocue.net/olddaily.php?id=682&sol=0). It says on the daily nightmare master page to expect uniqueness methods on Thursdays. Well I came to this position and could not find any URs:
Code:

+--------------------------+--------------------------+--------------------------+
| 2       68      14       | 56      59      5689     | 7       14      3        |
| 458     3       457      | 1       26      78       | 9       26      458      |
| 158     9       67       | 267     3       4        | 58      26      158      |
+--------------------------+--------------------------+--------------------------+
| 148     68      46       | 37      14      37       | 2       5       9        |
| 459     145     3        | 245     8       259      | 6       14      7        |
| 7       2       459      | 456     1459    569      | 48      3       148      |
+--------------------------+--------------------------+--------------------------+
| 345     145     1245     | 9       7       26       | 345     8       456      |
| 3459    45      2459     | 8       26      1        | 345     7       456      |
| 6       7       8        | 345     45      35       | 1       9       2        |
+--------------------------+--------------------------+--------------------------+



BUT - there is a simple coloring chain in "1"s ending in cells r1c3 and r4c5:
r1c3=r1c7=r5c7=r6c9=r6c5=r4c5
Since both cells contain the same pair {1,4} they form a remote pair and allow the elimination of "4" from r4c3.

Questions:
a) is the diagnosis "remote pair" and the therapy: remove 4 from r4c3 correct?
b) which URs did I miss?
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Tue Oct 30, 2007 3:47 pm    Post subject: Re: no UR but remote pair? Reply with quote

nataraj wrote:

Questions:
a) is the diagnosis "remote pair" and the therapy: remove 4 from r4c3 correct?
b) which URs did I miss?


a) Yes, though this is a generalization of the usual notion of remote pair.
b) I don't see it either, at least at this point.
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Marty R.



Joined: 12 Feb 2006
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PostPosted: Tue Oct 30, 2007 4:53 pm    Post subject: Reply with quote

I'm learning new things all the time, but up to now, my understanding of Remote Pairs involved a chain of identical bivalue cells.

That 4 in r4c3 can also be eliminated by the W-Wing technique, since the 14 pairs are linked by the 1s in column 1.
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nataraj



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PostPosted: Tue Oct 30, 2007 6:40 pm    Post subject: Reply with quote

Marty, that's just why I'm trying to get some expert opinions here - I have a different notion that remote pairs are just like your good old naked pair (two cells X,Y with the same two candidates {a,b} and linked in such a way that if X is a then Y is B and vice versa) but not in the same house. The type of linkage (in my view) is of no relevance (could be xy chain, could be coloring, could be ALS chains, whatever). But then what I just described is called a w-wing here. hm. Confused I am sure that I am missing some crucial points.

Quote:
since the 14 pairs are linked by the 1s in column 1.
you are right. I took the long way ...


edit: I looked up remote pairs in sudopedia. your definition agrees completely with sudopedia. Good thing I asked. Thx!
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re'born



Joined: 28 Oct 2007
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PostPosted: Tue Oct 30, 2007 9:12 pm    Post subject: Reply with quote

Traditionally, remote naked pairs required a chain of cells each with the same two candidates. However, the theory of w-wings (a.k.a. semi-remote naked pairs) already suggests that it isn't important to have the middle cells be bivalued. I believe it was keith who first observed that if you have a w-wing were the link are all conjugates, then you can treat the endpoint cells as if they were a remote naked pair.

The reason for this is as follows. A traditional w-wing looks like:
{ab} -b- X =b= Y -b- {ab}
and the implication is that the first or last cell in the chain contains 'a'. However, if we can connect the b's with simple coloring (i.e., with conjugate links), then we also know that the first or last cell in the chain contains 'b', for we have the chain
{ab} =b= X -b- Y =b= {ab}.
This is exactly the information we have in the case of a remote naked pair.

So a more general definition of remote pair would be two different cells with the same candidates {a,b} such that there are strong links:
{ab} =a= {ab}
{ab} =b= {ab},
between them for both a and b.
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Asellus



Joined: 05 Jun 2007
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PostPosted: Tue Oct 30, 2007 10:38 pm    Post subject: Reply with quote

nataraj,

When Daily Nightmare puzzles refer to uniqueness solutions, it doesn't necessarily mean there's a UR. The Deadly Pattern is often more complex than a UR in these puzzles. In this case, I've looked but can't find one from which I can extract a solution. For instance, there is a potential 6-cell {34}, {45}, {56} DP in Boxes 7 and 9. But I couldn't figure out a way to exploit it.

That {14} pair solution is clearly a W-Wing, no matter how you "activate" it.

By the way, if you ignore the W-Wing, there is a long scenic route to the same place:

(1) The <4> in R6C3 is eliminated by an "ER Loop" in B136.
(2) The <4> in R5C4 is eliminated by Sue de Coq (B4 and R5C8).
(3) A Sashimi X-Wing in R15 eliminates that <4> in R4C3.
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keith



Joined: 19 Sep 2005
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PostPosted: Tue Oct 30, 2007 11:22 pm    Post subject: Reply with quote

Previously posted by yours truly in the Sudopedia discussion:

Definition is too restrictive

You do not need all the cells to have the same pair of candidates to make a remote pair elimination.

A remote pair is:

(a)XY==YX==XY==YX(A)

and any cell that "sees" both ends a and A cannot be X or Y. Necessarily, the chain is composed of strong links in both candidates. It must be comprised of an even number of cells connected by an odd number of links.

But, what if the strong links are only for one candidate?

(a)XY==WX==XZ==YX(A)

W and Z are anything - they do not have to represent a single candidate.

One of a and A must be X. AND, one must be Y! The eliminations for both chains are the same.

So, suppose you have two cells that have the same two candidates but are not a naked pair. If you can connect them by simple coloring on either of the candidates, and if the coloring chain has an uneven number of links (even number of cells), you can make the Remote Pair exclusions.

It seems to me this is a possibly useful rule when solving by hand. So far as programming is concerned, it is likely a special case of a number of chain types.

Keith
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Asellus



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PostPosted: Wed Oct 31, 2007 1:03 am    Post subject: Reply with quote

Keith,

Your example of the remote {XY} cells connected by a "color chain" on X is correct. It requires that the links between bivalue cells be conjugate ("strong") links.

But, in the case of the remote pairs with a chain of {XY} cells, the links between the {XY} cells can be (and usually are) weak.

In both cases, there must be an even number of "nodes".
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keith



Joined: 19 Sep 2005
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PostPosted: Wed Oct 31, 2007 1:47 am    Post subject: Reply with quote

Asellus wrote:
Keith,

Your example of the remote {XY} cells connected by a "color chain" on X is correct. It requires that the links between bivalue cells be conjugate ("strong") links.

But, in the case of the remote pairs with a chain of {XY} cells, the links between the {XY} cells can be (and usually are) weak.

In both cases, there must be an even number of "nodes".


Asellus,

I don't think so.

I presume you mean the classic remote pair chain: XY=YX=XY=YX

Each link XY=YX must be a pair, and is a strong link in both X and Y.

Can you quote an example?

Keith
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Asellus



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PostPosted: Wed Oct 31, 2007 2:49 am    Post subject: Reply with quote

Keith,

Forget what I wrote above: it was some sort of lapse! Embarassed

The chain is a consecutive set of Locked Pairs so, of course, they are inherently strongly linked.
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nataraj



Joined: 03 Aug 2007
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PostPosted: Wed Oct 31, 2007 8:40 am    Post subject: Reply with quote

once again, very instructive!

I was not aware of Keith's post in sudopedia but it expresses very elegantly what I was trying to say. From this am encouraged to continue using "remote pair" in the more general sense. Being a rather visual person I can see the "pair" quite clearly while I never had any success in seeing a "wing" in w-wings Wink
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re'born



Joined: 28 Oct 2007
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PostPosted: Wed Oct 31, 2007 12:25 pm    Post subject: Reply with quote

nataraj wrote:
once again, very instructive!

I was not aware of Keith's post in sudopedia but it expresses very elegantly what I was trying to say. From this am encouraged to continue using "remote pair" in the more general sense. Being a rather visual person I can see the "pair" quite clearly while I never had any success in seeing a "wing" in w-wings Wink

This is why I call w-wings "semi-remote naked pairs".
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nataraj



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PostPosted: Wed Oct 31, 2007 3:07 pm    Post subject: Reply with quote

re'born wrote:

This is why I call w-wings "semi-remote naked pairs".


While this may be a very diplomatic approach, I don't feel comfortable with the term "semi-remote". semi means "half", right? One half domestic, one half remote?

OK, OK what it is probably supposed to mean is semi-(remote pair). A remote pair but not quite (because the intermediate links are not the orthodox identical bi-value cells)

But the pair is remote, as remote as they ever will be, right? (in the sense of "not sharing a house"). So - let's face it: that naked pair may be longing for each other, may even have a weekend relationship, be on the phone all the time, may even (hopefully) exclude other candidates, but they are (fully, sadly, booohaha) Crying or Very sad Evil or Very Mad Rolling Eyes

-

remote.

ahem. hope you guys don't take this as a remotely serious contribution...
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keith



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PostPosted: Wed Oct 31, 2007 8:43 pm    Post subject: Reply with quote

nataraj wrote:
re'born wrote:

This is why I call w-wings "semi-remote naked pairs".


While this may be a very diplomatic approach, I don't feel comfortable with the term "semi-remote" ...


I think it depends on your point of view.

If you are a pattern-recognition person, you may prefer the term W-wing. If you are an inference person, you might see this all as different cases of alternating chains.

In the term "Semi Remote Pair" I think "semi" modifies "pair", not "remote". So, a remote semi-pair is perhaps a remote single? Which is exactly right. For any cell that sees both the pincer cells, the elimination is exactly the same as that of seeing a single.

And now, nataraj may have to update his soap opera! If you're one of a remote pair, seeing a single is definitely not a good idea!


Last edited by keith on Wed Oct 31, 2007 9:42 pm; edited 1 time in total
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Asellus



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PostPosted: Wed Oct 31, 2007 8:57 pm    Post subject: Reply with quote

nataraj wrote:
I never had any success in seeing a "wing" in w-wings

Why not? I see a "wing" as a structure with some sort of central "pivot" and two "wings" that sport "pincers." This is obvious in XY and XYZ Wings. In a Color Wing (Multi-Coloring), the "pivot" is the weak link "bridge" and the "wings" are the two color chains/clusters.

In a W-Wing, the "pivot" is the external strong link structure, of whatever sort and complexity. The "wings" are the two remote bivalue cells.

The only "wing" that gives me trouble is the X-Wing. But, I suppose the "pivot" can be the imagined centerpoint of two diagonal lines.
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Marty R.



Joined: 12 Feb 2006
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PostPosted: Wed Oct 31, 2007 9:18 pm    Post subject: Reply with quote

Quote:
I think it depends on your point of view.

If you are a pattern-recognition person, you may prefer the term W-wing. If you are an inference person, you might see this all as different cases of alternating chains.

In the term "Semi Remote Pair" I think "semi" modifies "pair", not "remote". So, a remote semi-pair is perhaps a remote single? Which is exactly right. For any cell that sees both the pincer cells, the elimination is exactly the same as that of seeing a single.


The right answer is "W-Wing" because that's what everyone else here calls it. Whatever the correct answer in the abstract is, we don't need any more terminology confusion. Laughing
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nataraj



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PostPosted: Wed Oct 31, 2007 9:51 pm    Post subject: Reply with quote

Asellus wrote:
I see a "wing" as a structure with some sort of central "pivot" and two "wings" that sport "pincers."


I can see it now. Great explanation.

I had always tried to imagine the "W" as sort of dragon with folded wings (or maybe like a bat - finally we have a Halloween theme Very Happy ). Instead it is really a huge body (pivot) with wee little pincer wings. Cute ...

As for the x-wing. The reference to Star Wars is quite obvious. Only the x-wings there have their lasers perpendicular to the plane of the x.

But - wait - that means ....

oh no!

they are shooting out at meeeeeeeeeeee.....
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nataraj



Joined: 03 Aug 2007
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PostPosted: Wed Oct 31, 2007 9:54 pm    Post subject: Reply with quote

Quote:
If you're one of a remote pair, seeing a single is definitely not a good idea!


might save the evening, though ....

edit: sorry, I meant to say "...might be part of the solution".

edit edit: soap season 2:

just imagine the implications of a single "see"ing both (members? partners? elements?) of a remote (!) pair at the same time - one of them in SF, one in NYC. If they are not (by some weird coincidence) in a teleconference - how can this happen?

talk about bilocation! (man, we are unravelling the secrets of the unverse, here!)


Last edited by nataraj on Wed Oct 31, 2007 10:38 pm; edited 1 time in total
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re'born



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PostPosted: Wed Oct 31, 2007 10:32 pm    Post subject: Reply with quote

keith wrote:
nataraj wrote:
re'born wrote:

This is why I call w-wings "semi-remote naked pairs".


While this may be a very diplomatic approach, I don't feel comfortable with the term "semi-remote" ...


I think it depends on your point of view.

If you are a pattern-recognition person, you may prefer the term W-wing. If you are an inference person, you might see this all as different cases of alternating chains.

In the term "Semi Remote Pair" I think "semi" modifies "pair", not "remote". So, a remote semi-pair is perhaps a remote single? Which is exactly right. For any cell that sees both the pincer cells, the elimination is exactly the same as that of seeing a single.

Here is my original explanation for the term:
re'born on the player's forum wrote:
I've lately been calling this type of deduction a semi-remote naked pair. I prefer this terminology as both techniques (this and the traditional remote naked pairs) start and end with bivalue cells containing the same candidates, and the "semi" is a reference to the semidirect product in group theory, where there is a "preferred" subgroup, namely the normal subgroup. In our case the preferred candidate is the one which links the endpoints while the other candidate is eliminated from the intersection of the endpoints.

Here are a couple of reasons I prefer it to w-wing.

First, xy-wings and xyz-wings are all have a specific number of cells in play. So, one would expect w-wings to also only use a specific number of cells. In practice, however, we can find w-wings with more than one set of weak and strong links to connect the endpoints. On the other hand, there is no bias against remote naked pair patterns having 4, 6, 8 or more cells.

Secondly, remote naked pairs was one of the first advanced techniques I learned and it is the same still with many people. Teaching sudoku classes, I've seen people mistakenly assume that any two bivalued cells with the same values can be treated as a remote naked pair. Many times, they've gotten lucky because there really were links making it so, or at least enough links to make it true for one of the candidates. When I've explained the logic, they tend to all gravitate towards something similar to "oh, so its like half a remote naked pair." So I think it is a better name as it generalizes a name and idea with which people are already familiar.

Of course...
Marty R. wrote:
The right answer is "W-Wing" because that's what everyone else here calls it.

It's hard to argue with that.
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storm_norm



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PostPosted: Thu Nov 01, 2007 6:42 pm    Post subject: Reply with quote

x-wings aren't named correctly anyways. x-wings are fish.

so I guess the fish are the "special" wings. are wings the more general rule??

I think wings come more naturally from a solvers stand point because the human eye is drawn to the cells with the least amount of candidates and therefore we see the relationships they present. Plus, one chain can solve a puzzle pretty fast. Fish, on the other hand, present the eye with a different challenge, not only finding the pattern for the type of fish it is, but the fish might be horizontal or vertical. And ! that fish you took 10 minutes to find probably eliminated the one candidate that took you one little step closer to finding the chain that solves it.
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