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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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 Posted: Mon Jul 02, 2007 8:18 pm Post subject: 2 July VH |
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| I found a couple of xy wings for this one - 15 & 19 Block 2 with 59 (C4) eliminated 9 in R2C4 - then much later 23(R6C7), 28(R4C8) & 38 (R8C7) eliminated 8 in R7C8. Hope I got that right. Couldn't see any other ways. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Jul 03, 2007 1:10 am Post subject: |
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cgordon,
I believe your first XY-Wing is not necessary. Basic methods get you all the way to your second XY-Wing, which solves the puzzle.
I thought that "Very Hard" was an exaggeration for this one. |
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Lynnda
Joined: 07 Jun 2007
Posts: 3
Location: Sydney, Australia
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| Posted: Tue Jul 03, 2007 2:53 am Post subject: |
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"I believe your first XY-Wing is not necessary. Basic methods get you all the way to your second XY-Wing, which solves the puzzle."
Well, I needed the first XY-Wing as my "basic methods" couldn't get me past this point and I searched for quite a while!
And then with a lot of struggling I got the secomd XY-Wing and it was easy from there. But I would DEFINITELY say I thought that "Very Hard" was the correct classification - at least for my brain on the day  |
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jLo
Joined: 30 Apr 2007
Posts: 55
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| Posted: Tue Jul 03, 2007 5:23 am Post subject: |
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| Any of a couple of XY-wings, an XYZ-wing, or a W-wing break this one open. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Tue Jul 03, 2007 11:44 am Post subject: |
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[quote]Any of a couple of XY-wings, an XYZ-wing, or a W-wing break this one open. | Quote: |
Since I read up on W wings, I can never find the things. In fact the odds seem pretty remote. Certainly don't see any here. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Jul 03, 2007 5:11 pm Post subject: |
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I have checked and rechecked and always get to this point without having to use any advanced techniques:
| Code: | +------------+-----------+-----------+
| 7 128 3 | 15 6 4 | 28 9 258 |
| 289 289 4 | 359 7 359 | 6 1 258 |
| 169 169 5 | 2 8 19 | 4 3 7 |
+------------+-----------+-----------+
| 4 7 9 | 6 5 23 | 1 28 238 |
| 238 5 28 | 13 4 123 | 9 7 6 |
| 236 26 1 | 7 9 8 | 23 5 4 |
+------------+-----------+-----------+
| 5 19 28 | 4 3 6 | 7 28 19 |
| 18 4 7 | 59 2 59 | 38 6 138 |
| 29 3 6 | 8 1 7 | 5 4 29 |
+------------+-----------+-----------+ |
At this point, the XY-Wing previously noted (pivot in R6C7) solves the puzzle.
Am I not seeing something others are seeing? |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Tue Jul 03, 2007 6:26 pm Post subject: |
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| No, you are right - I missed the pair of 28s in row 7. The 23 pivot is all that is needed. |
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jLo
Joined: 30 Apr 2007
Posts: 55
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| Posted: Tue Jul 03, 2007 9:47 pm Post subject: |
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| Quote: |
Since I read up on W wings, I can never find the things. In fact the odds seem pretty remote. Certainly don't see any here.
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W-wings are probably more common than X-wings, XYZ-wings, or Skyscrapers when
you reach the point in a puzzle in which advanced techniques have to be applied.
While XY-Wings are more common than W-wings, if you learn what you are lookinig for
they are usually much easier to spot since you are looking for identical pairs rather than
complimentary pairs. There are three steps involved.
1. Find two identical pairs that occupy different boxes and do not share a row
or column (otherwise you have a naked pair).
2. Examine the block (or blocks) that both pair cells can see (ignorinig the blocks
which hold our pair cells). There will be exactly one or exactly two such blocks.
If one of the values from our pair appears in the block, but only in cells that
can be seen by one or both of the pair cells, then we have a possible W-wing.
The other value becomes our "target" value and we continue to step 3.
3. Look at the cells that both pairs can see (there will be either exactly six or exactly
two on these "common buddy" cells. If the "target" value appears in one of these
"common buddy" cells, it can be eliminated.
In the July 2 puzzle there is a W-Wing with the pair "19". See if you can find it using
the steps above. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Jul 04, 2007 5:50 pm Post subject: |
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| Asellus wrote: | I have checked and rechecked and always get to this point without having to use any advanced techniques:
| Code: | +------------+-----------+-----------+
| 7 128 3 | 15 6 4 | 28 9 258 |
| 289 289 4 | 359 7 359 | 6 1 258 |
| 169 169 5 | 2 8 19 | 4 3 7 |
+------------+-----------+-----------+
| 4 7 9 | 6 5 23 | 1 28 238 |
| 238 5 28 | 13 4 123 | 9 7 6 |
| 236 26 1 | 7 9 8 | 23 5 4 |
+------------+-----------+-----------+
| 5 19 28 | 4 3 6 | 7 28 19 |
| 18 4 7 | 59 2 59 | 38 6 138 |
| 29 3 6 | 8 1 7 | 5 4 29 |
+------------+-----------+-----------+ |
At this point, the XY-Wing previously noted (pivot in R6C7) solves the puzzle.
Am I not seeing something others are seeing? |
Asellus:
You can remove <8> from R2C1 (the <8> in C2 is in B1). This reveals a pair <29> in C1. Which brings you to:
| Code: | +-------------+-------------+-------------+
| 7 128 3 | 15 6 4 | 28 9 258 |
| 29 289 4 | 359 7 359 | 6 1 258 |
| 16 169 5 | 2 8 19 | 4 3 7 |
+-------------+-------------+-------------+
| 4 7 9 | 6 5 23 | 1 28 238 |
| 38# 5 28 | 13 4 123 | 9 7 6 |
| 36@ 26 1 | 7 9 8 | 23@ 5 4 |
+-------------+-------------+-------------+
| 5 19 28 | 4 3 6 | 7 28 19 |
| 18% 4 7 | 59 2 59 | 38# 6 138 |
| 29 3 6 | 8 1 7 | 5 4 29 |
+-------------+-------------+-------------+ |
1. There is a swordfish which takes out <2> in R4C9.
2. There is an XY-wing which takes out <9> in R8C6 and R2C4.
3. An XY-wing overlaid on the first takes out <5> in R8C4 and R2C6.
4. An XY-wing takes out <2> in R4C8.
5. An XY-wing overlaid on this one takes out <8> in R7C8.
6. A W-wing takes out <8> from R8C1. I only looked for one of these, there may be more.
Here is my explanation: Two cells have the same two candidates <XY>, but they do not form a naked pair. There is a strong link (in either of the candidate values) that lines up with these two cells. Then, the two cells cannot have the same value. We can eliminate <X> and <Y> from any cell that sees both of them.
The two cells are #. The strong link is @. The elimination is in %.
Best wishes,
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Jul 04, 2007 7:04 pm Post subject: |
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Keith,
I certainly did miss that <8>. Basic methods produce an even simpler result than I thought!
Regarding W-Wings...
I find Keith's definition to be what is essential: Two identical bivalue cells without a direct link (i.e. that are not buddies) that can each see the ends of a strong link in _one_ of those digits somewhere else on the board. In such cases, the _other_ digit can be removed from all buddies of the bivalue pair.
I have trouble following JLo's procedure and am not sure it is correct. Keith's example of a W-Wing above seems not to meet jLo's procedure since one of the digits in the "pivoting" strong link lies in the same Box as one of the bivalue cells. (Maybe a "block" isn't the same as a "box"?) To me, that doesn't matter. I'm also not sure it is possible to have a W-Wing if the bivalue cells can see only one instance of one of the digits. Where would the strong link be?
They do seem to be quite common, though I don't look for them that much. (I seem to have a knack for spotting XY-Wings with ease.) |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Jul 04, 2007 7:13 pm Post subject: |
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P.S.:
I just noticed...
Keith, in your W-Wing definition, I don't believe it is correct to say that both <X> and <Y> can be eliminated from the buddies. If the external strong link is in <X>, then <Y> can be eliminated from the buddies but not <X>. The bivalue cells are not themselves linked (a requirement for W-Wing), so it is possible that both are <Y>.
In your example, there happens also to be strong links on <3> between the external strong link and the two bivalue cells, allowing elimination of <3> in such a case (though there weren't any). But, that isn't always the case. |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Wed Jul 04, 2007 8:24 pm Post subject: |
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Not that anybody asked but I interpreted Keith's explanation to be if the strong link is on <x> then <y> can be eliminated or if the strong link is on <y> the <x> can be, not that both <xy> can be, regardless of which is the strong link.
(But I interpreted incorrectly)
Last edited by TKiel on Wed Jul 04, 2007 9:20 pm; edited 1 time in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Jul 04, 2007 8:52 pm Post subject: |
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| TKiel wrote: | | Not that anybody asked but I interpreted Keith's explanation to be if the strong link is on <x> then <y> can be eliminated or if the strong link is on <y> the <x> can be, not that both <xy> can be, regardless of which is the strong link. |
Tracy, that's what I thought until I read Keith's post and thought about it. Using the W-Wing pair of 38, the two cells have to be 38 or 83, thus both are removed from cells that see both, much like remote pairs. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Wed Jul 04, 2007 9:31 pm Post subject: |
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Marty R.,
You're right. Since there is an even number of cells, the bivalue cells will have opposite solutions, effectively eliminating both values from any common cells. I've been thinking of these things as like an XY-wing, which they are not. They're more like multi-digit coloring chains; I suspect if Myth Jellies got a whiff of this thread he could show it but I know I can't. |
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jLo
Joined: 30 Apr 2007
Posts: 55
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| Posted: Wed Jul 04, 2007 10:20 pm Post subject: |
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| Quote: |
As the saying goes: "A picture is worth a 1000 words." The only explanation on W wings I understood was given diagrammatically by Texcat in the discussion at
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I agree. That diagram really brought it home. Here's the type-2 that wasn't pictured.
| Code: |
+---------+---------+---------+ Type 2
| ~W |GW | |
|~g ~g | | | if GW and (~g or ~G) then ~W
|~g ~g | | |
+---------+---------+---------+
| | | |
| | | |
| | | |
+---------+---------+---------+
| GW |~W | |
| | ~G ~G | |
| | ~G ~G | |
+---------+---------+---------+
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It doesn't pop up quite as often, |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Jul 04, 2007 11:15 pm Post subject: |
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| Code: | +--------------+-------------+-------------+
| 7 128# 3 | 15# 6 4 | 28 9 258 |
| 29 28 94 | 359 7 359 | 6 1 258 |
| 16 169$ 5 | 2 8 19@ | 4 3 7 |
+-------------+-------------+-------------+
| 4 7 9 | 6 5 23 | 1 28 238 |
| 38 5 28 | 13# 4 123#| 9 7 6 |
| 36 26 1 | 7 9 8 | 23 5 4 |
+--------------+-------------+-------------+
| 5 19@ 28 | 4 3 6 | 7 28 19 |
| 18 4 7 | 59 2 59 | 38 6 138 |
| 29 3 6 | 8 1 7 | 5 4 29 |
+--------------+-------------+-------------+ |
jLo said: | Quote: | | In the July 2 puzzle there is a W-Wing with the pair "19" |
So far as I can see, correct, but not so simple.
There is a coloring chain on <1>, marked #. It is three links (four cells). The cells <19> are marked @, and the ends of the # chain line up with the @ cells.
Pick either @ cell. If it is <1>, the other must be <9>. So, you can eliminate <9> from their common buddies. In particular, the cell marked $ must be <16>. Which solves the puzzle.
Note that you CANNOT eliminate <1> from the $ cell. This is because if one @ cell is <9>, you cannot conclude the other is <1>. The logic is: One, OR BOTH, of them is <9>.
This is pretty cool!
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Jul 04, 2007 11:57 pm Post subject: |
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Perhaps everyone sees this, but just to be sure...
The 19 W-Wing can be seen as an example of jLo's "Type 2", it seems to me, since an Empty Rectangle can provide the external strong link, in this case the ER on <1> in Box 1.
As Keith notes, the W-Wing can also be "excited" by the coloring on <1>.
Two ways to skin the cat, which is, no doubt, what Keith finds so cool!
As I understand the logic of W-Wing, it can only justify elimination of one of the two digits. Sometimes (as in the 38 example above) there is some other logic present (coloring on <3> in that case) that affects the other digit. But, it is unrelated to the W-Wing. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 05, 2007 12:19 am Post subject: |
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| Asellus wrote: | P.S.:
I just noticed...
Keith, in your W-Wing definition, I don't believe it is correct to say that both <X> and <Y> can be eliminated from the buddies. If the external strong link is in <X>, then <Y> can be eliminated from the buddies but not <X>. The bivalue cells are not themselves linked (a requirement for W-Wing), so it is possible that both are <Y>.
In your example, there happens also to be strong links on <3> between the external strong link and the two bivalue cells, allowing elimination of <3> in such a case (though there weren't any). But, that isn't always the case. |
Asellus,
You are correct, I was being sloppy. The logic is:
<XY> --- <X-Strong link-X> -- <XY>
If one of the end cells is <X>, the other must be <Y>. They cannot both be <X>. One, OR BOTH, must be <Y>.
You can see this in the <19> example.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 05, 2007 12:31 am Post subject: |
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| Quote: | | ... what Keith finds so cool! |
is that this is a human-recognizable pattern that is actually useful.
I asked Mike Barker about this, he said it is a special case of "Nice Loops". Maybe so. |
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