Why isn't this a remote pair?

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Why isn't this a remote pair?

Postby JeJ » Thu Feb 10, 2011 12:03 am

I have this game that starts as:
Code: Select all
2 4 .|5 . 1|. 3 .
. . 8|. . .|. 2 .
7 . .|. . .|. . 9
-----------------
. . .|6 . 5|. . .
1 3 .|. 7 .|. 6 5
. . .|3 . 8|. . .
-----------------
5 . .|. . .|. . 6
. 7 .|. . .|1 . .
. 6 .|8 . 4|. 9 7

And that I have taken to:

Code: Select all
2    4    6   |5    9    1   |7    3    8
9    15   8   |7    346  36  |456  2    14
7    15   3   |24   8    26  |456  145  9
---------------------------------------------
48   289  7   |6    124  5   |2349 14   1234
1    3    24  |249  7    29  |8    6    5
6    29   5   |3    124  8   |249  7    124
---------------------------------------------
5    289  249 |1    23   7   |234  48   6
48   7    24  |29   2356 2369|1    458  234
3    6    1   |8    25   4   |25   9    7

The definition of a remote pair is: "The Remote Pairs technique uses a XY-Chain involving an even number of bivalue cells, and all the cells have the same two digits as their candidate." Why r8c1 and r7c8 do not comply with this definition?

Thanks.

P.S.:I just want to learn about this specific technique, I do not need help to complete this puzzle.
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Re: Why isn't this a remote pair?

Postby JasonLion » Thu Feb 10, 2011 1:48 am

Remote pairs involve a chain of cell which all contain the same pair of candidates, in this example 48. R4C1 is linked to R8C1, since they share column 1. The only other occurrence of 48 is in R7C8, which does not share a house with either of the other two, and so does not link to them. Thus, the longest chain you can form is two cells. That isn't long enough to qualify as a remote pair, which has a minimum chain length of four.
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Re: Why isn't this a remote pair?

Postby JeJ » Thu Feb 10, 2011 2:23 am

Thanks for the clarification.

I am pretty sure that with some conditions (that this game doesn't have) similar pairs can be considered remote pairs even if they are not on the same house, I've seen them in the hints for the games in www.enjoysoduku.com
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Re: Why isn't this a remote pair?

Postby JasonLion » Thu Feb 10, 2011 2:44 am

If you post an example I would be happy to evaluate it for you.

The cells at either end of the chain should not share houses with each other. Each cell in a remote pair chain only has to share a house with the cell before it and the cell after it in the chain.
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Re: Why isn't this a remote pair?

Postby JeJ » Thu Feb 10, 2011 3:09 am

Next time I come across one of these, I'll post it.
Thanks for the offer.
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Re: Why isn't this a remote pair?

Postby JeJ » Mon Feb 14, 2011 11:52 pm

Here's one puzzle with the type of remote naked pair I had mentioned before (pairs not sharing any house), from today's Devious puzzle from www.enjoysudoku.com
The puzzle starts as:
Code: Select all
5 . 1|6 4 .|. . .
. . .|9 . .|. . .
8 2 .|. . 3|. . 7
-----------------
. 8 .|. 7 .|2 4 .
. . .|. . .|. . .
. 6 3|. 8 .|. 1 .
-----------------
1 . .|7 . .|. 9 8
. . .|. . 4|. . .
. . .|. 6 1|4 . 5


Which with some eliminations and placements you can get it to:

Code: Select all
5   9   1  |6   4   7  |38  38  2
367 37  67 |9   2   8  |1   5   4
8   2   4  |5   1   3  |9   6   7
-----------------------------------
9   8   5  |1   7   6  |2   4   3
247 1   27 |34  35  9  |578 78  6
47  6   3  |24  8   25 |57  1   9
-----------------------------------
1   4   26 |7   35  25 |36  9   8
236 5   8  |23  9   4  |367 237 1
237 37  9  |8   6   1  |4   23  5

I was stuck there and I asked a hint and the hint I got says:
"W-Wing (type D): the yellow cells form a remote naked pair, because the green cells can't be 3." The link to the explanation of the W-wing is broken.

The hint continues:
"One of the blue cells (referring to r8c123 and r9c123) must be 3. Thus, one of the yellow cells (referring to r8c4 and r9c8) must be 2. Therefore, the pink cells (r8c789 and r9456) can't be 2."

So could you please explain this situation?
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Re: Why isn't this a remote pair?

Postby JasonLion » Tue Feb 15, 2011 2:29 am

First, a W-WIng contains two cells with the same candidates, which Enjoy Sudoku calls a "remote naked pair", and others sometimes call an "almost naked pair", but neither of those names is exactly right and there isn't really a standard name. In any case, this is not the same thing as a "remote pair". A remote pair has a chain of cells containing the same pair of candidates between the cells, while a W-Wing has a more complex structure, typically an AIC using grouped cells.

In this specific example, R8C4 and R9C8 both contain 23. They aren't a naked pair and they aren't a remote pair, but they do share a chute (group of three rows covering three blocks). Further none of R7C1, R7C2, and R7C3 can contain a 3. There must be a 3 in box 7, and since it can't appear in row 7, it must appear either in row 8 or row 9. That means that one of R8C4 or R9C8 must contain a 2. Thus, no neighbor of both R8C4 and R9C8 can contain 2.

The chain in this example runs from R8C4 to R8C1 to the grouped pair of cells R9C1 and R9C2, to R9C8. That chain can be understood as a AIC using grouped cells, or you can simply use the explanation I gave in the previous paragraph, and not bothering understanding how the chain works.
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Re: Why isn't this a remote pair?

Postby JeJ » Tue Feb 15, 2011 12:47 pm

Thanks that kind of makes sense for me now :-)
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Re: Why isn't this a remote pair?

Postby keith » Tue Mar 29, 2011 2:17 am

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Re: Why isn't this a remote pair?

Postby keith » Tue Mar 29, 2011 3:44 am

JasonLion wrote: A remote pair has a chain of cells containing the same pair of candidates between the cells ...


Well, maybe. That is what I have called a classic remote pair. If = is a strong link (which it must be here) then the ends of the chain
XY = XY = XY = XY
are a remote pair.

However, two cells XY not in the same house can be pincers on both X and Y in a number of circumstances. For example:
XY = aX = bX = XY
where = is a strong link on X and a, b are any candidates.

There are other scenarios. One that is actually quite common, but commonly not useful, is the double W-wing:

A W-wing is two cells connected as
XY - aX = bX - XY
where - is a weak link on X. The end cells are pincers on Y: One OR BOTH is Y.

But you can often find the same cells also connected in Y (through different intermediate cells):
XY - cY = dY - XY
The end cells are pincers on X: One OR BOTH is X.

The only possibility for this combination is that the end cells are (by my definition) a remote pair: One is X and one is Y. This is often not useful to make immediate eliminations in both X and Y, but it can be very useful as a component in another logic chain.

I prefer the definition that a remote pair is any two cells XY not in the same house that are pincers on both X and Y.

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Re: Why isn't this a remote pair?

Postby keith » Tue Mar 29, 2011 4:56 am

JeJ wrote: ...
Which with some eliminations and placements you can get it to:

Code: Select all
5   9   1  |6   4   7  |38  38  2
367 37  67 |9   2   8  |1   5   4
8   2   4  |5   1   3  |9   6   7
-----------------------------------
9   8   5  |1   7   6  |2   4   3
247 1   27 |34  35  9  |578 78  6
47  6   3  |24  8   25 |57  1   9
-----------------------------------
1   4   26 |7   35  25 |36  9   8
236 5   8  |23  9   4  |367 237 1
237 37  9  |8   6   1  |4   23  5

I was stuck there and I asked a hint and the hint I got says:
"W-Wing (type D): the yellow cells form a remote naked pair, because the green cells can't be 3." The link to the explanation of the W-wing is broken.

The hint continues:
"One of the blue cells (referring to r8c123 and r9c123) must be 3. Thus, one of the yellow cells (referring to r8c4 and r9c8) must be 2. Therefore, the pink cells (r8c789 and r9456) can't be 2."

So could you please explain this situation?

First, there is an XY-wing that is ignored. Second, yes, there is a W-wing with a grouped link, but that is a bizarre way to explain it.
Code: Select all
+-------------+-------------+-------------+
| 5   9   1   | 6   4   7   | 38  38  2   |
| 367 37  67  | 9   2   8   | 1   5   4   |
| 8   2   4   | 5   1   3   | 9   6   7   |
+-------------+-------------+-------------+
| 9   8   5   | 1   7   6   | 2   4   3   |
| 247 1   27  | 34  35  9   | 578 78  6   |
| 47  6   3   | 24  8   25  | 57  1   9   |
+-------------+-------------+-------------+
| 1   4   26  | 7   35# 25  | 36# 9   8   |
| 236 5   8   | 23@ 9   4   |367 -237 1   |
| 237 37  9   | 8   6   1   | 4   23@ 5   |
+-------------+-------------+-------------+

The cells @ are a W-wing connected by the strong link # on 3 in R7. They eliminate 2 in all their peers.

I do not see how to connect them in 2 to make them a remote pair. (Which they turn out to be.)

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Re: Why isn't this a remote pair?

Postby JasonLion » Tue Mar 29, 2011 11:55 am

keith wrote:However, two cells XY not in the same house can be pincers on both X and Y in a number of circumstances. For example:
XY = aX = bX = XY
where = is a strong link on X and a, b are any candidates.
Common usage these days seems to be to call this form an extended or generalized remote pair. Andrew Stuart's original 2005 essay, Sudopedia, and nearly about every other source easily found on the web only cover cases of remote pairs where all of the cells contain the same pair of digits.

Those of us who speak freely of strong and weak links certainly appreciate the various extensions to remote pairs that you have discovered and documented. But attempting to teach that to a Sudoku novice or early intermediate does little but alienate them from the simpler form, which they can actually handle.
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Re: Why isn't this a remote pair?

Postby keith » Tue Mar 29, 2011 12:22 pm

(edited)

Jason, I think that is a very condescending response. Not to me (I have a very thick skin), but to those who are trying to learn.

By the way, Sudopedia is hardly a current reference source. My comment on the Sudopedia discussion page on exactly this point on remote pairs (to which you provide a link) has gone unanswered for three years.

There is no entry for M-wings.

The entry for W-wings is pretty marginal, and the discussion suggests most of it should be deleted.

And, by the way, I was very careful to be specific about my preferred terminology, since I know it is not the same as that preferred by some others. I don't think terminology, if explained, is a topic for debate.

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