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nataraj · Posted: Tue Oct 30, 2007 3:03 pm Post subject: no UR but remote pair?

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:

re'born · Joined: 28 Oct 2007 Posts: 80

Marty R. · Posted: Tue Oct 30, 2007 4:53 pm Post subject:

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.

nataraj · Posted: Tue Oct 30, 2007 6:40 pm Post subject:

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.

re'born · Joined: 28 Oct 2007 Posts: 80

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.

Asellus · Posted: Tue Oct 30, 2007 10:38 pm Post subject:

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.

keith · Posted: Tue Oct 30, 2007 11:22 pm Post subject:

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

Asellus · Posted: Wed Oct 31, 2007 1:03 am Post subject:

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".

keith · Posted: Wed Oct 31, 2007 1:47 am Post subject:

Asellus · Posted: Wed Oct 31, 2007 2:49 am Post subject:

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.

nataraj · Posted: Wed Oct 31, 2007 8:40 am Post subject:

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

re'born · Joined: 28 Oct 2007 Posts: 80

nataraj · Posted: Wed Oct 31, 2007 3:07 pm Post subject:

keith · Posted: Wed Oct 31, 2007 8:43 pm Post subject:

Asellus · Posted: Wed Oct 31, 2007 8:57 pm Post subject:

Marty R. · Posted: Wed Oct 31, 2007 9:18 pm Post subject:

nataraj · Posted: Wed Oct 31, 2007 9:51 pm Post subject:

nataraj · Posted: Wed Oct 31, 2007 9:54 pm Post subject:

re'born · Joined: 28 Oct 2007 Posts: 80

storm_norm · Joined: 18 Oct 2007 Posts: 1741

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.