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April 21 VH
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Mon Apr 21, 2008 10:13 pm    Post subject: Reply with quote

The way Clement describes his elimination of <5> in r1c2, it does sound like "forcing" reasoning. However, it isn't necessary to see it this way. Instead, the strong inference induced by the 48 UR between <5> in r1c3 and <3> in r1c5 is added to the end of a straightforward ALS Chain to provide the AIC elimination:
(5)r1c2-(5)r1c3=(3)r1c5-(3=5)r8c5-(5=8)r9c5-(8=7)r9c1-({17}=5)r79c2-(5)r1c2; r1c2<>5

In ordinary language: If r1c2 is <5>, then r1c3 is not <5> and r1c5 must be <3> (to kill the DP), then we XY Chain (via c5 and r9) to the <7> at r9c1. This "kills" the potential {17} pair in the r79c2 ALS, so one of those cells must be <5> and r1c2 cannot be. (This is the same as saying that the ALS becomes a {15} pair.) This contradiction means that r1c2 cannot be <5>.

[That ALS step could also be written -(7={15})r79c2-, which is easier to see following the chain in the direction I've written it. But, in the reverse direction, the "({17}=5)" notation is clearer. Either notation is valid and works. I chose the second to conform to Clement's reasoning.]

We have two different examples in this puzzle of how a UR/DP induced strong inference can be exploited in an AIC. While this is definitely overkill for these VH puzzles, exploiting such strong inferences can be very useful in more difficult puzzles.

AICs such as this are not really forcing, especially if uncovered by studying the alternating links. Medusa multi-coloring is, for instance, one way to do so. And without coloring, if one is comfortable with ALS Chains and strong links, then it is a tiny leap to either of these AICs.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Mon Apr 21, 2008 10:46 pm    Post subject: Reply with quote

Quote:
I believe it is more correctly related to the Kite in r2 and c1 that pivots in b1.

Asellus: I looked at this again and have posted this grid of available 8's. I now agree the skyscraper in R27 is not related to my ER solution which used the L shaped hinge in Box 7 and the two 8's in R2 to eliminate the 8 in R9C5.
But what's a Kite? Never heard of one - and I've been around !!

Code:
            
+-------+-------+-------+   
| . . 8 | 8 8 . | . . 8 |   
| . . 8 | . 8 . | . . . |   
| 8 . . | . . . | 8 . 8 |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . . | 8 . 8 | . . 8 |   
| . . . | . . 8 | 8 . 8 |   
+-------+-------+-------+   
| . . 8 | 8 . . | . . . |   
| . . . | . . . | . . . |   
| 8 . . | . 8 8 | . . . |
+-------+-------+-------+
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 21, 2008 10:47 pm    Post subject: Reply with quote

Did this get explained?
Code:
+--------------------------+--------------------------+--------------------------+
| 1       57      458      | 38      348     2        | 6       9       78       |
| 27      6       48       | 9       48      5        | 3       1       27       |
| 28      3       9        | 16      7       16       | 48      45      258      |
+--------------------------+--------------------------+--------------------------+

The <48> UR is in R12C35. <4> must be in R1C35 (there is no other <4> in R1), so <8> cannot be in R1C35. This is a Type 4.

Sudoku Susser explains:

Quote:
Squares R2C3, R2C5, R1C3 and R1C5 form a Type-4B Unique Rectangle on <48>. Because they share two rows, two columns, and two blocks, if they all had possibilities <48> then the puzzle would have two solutions; you could simply exchange the <4>s with the <8>s in the squares to get the other solution, and their common rows, columns and blocks would still contain one of each value. If you look carefully, you'll see that the only squares in row 1 that can contain <4> are the "roof" squares -- R1C3 and R1C5. Since one of these squares must be <4>, the only way to avoid the "deadly pattern" is if neither of them can contain <8>.

R1C3 - can remove <8> from <458> leaving <45>.
R1C5 - can remove <8> from <348> leaving <34>.


But, since we know that this puzzle can be solved without a UR, I didn't use it. I actually had four or five XY-wings, which I now see are surrogates for line-box interactions. It turns out to be a one-trick pony. After basics:
Code:
+-------------+-------------+-------------+
| 1   57  458 | 38  348 2   | 6   9   78  |
| 27  6   48  | 9   48  5   | 3   1   27  |
| 28  3   9   | 16  7   16  | 48  45  258 |
+-------------+-------------+-------------+
| 3   8   6   | 7   1   4   | 5   2   9   |
| 5   2   1   | 368 9   368 | 47  47  68  |
| 9   4   7   | 5   2   68  | 18  3   168 |
+-------------+-------------+-------------+
| 4  15-7 58# | 138 6   9   | 2   57# 135 |
| 6   9   2   | 4   35  137 | 17  8   135 |
| 78# 157 3   | 2   58  178 | 9   6   4   |
+-------------+-------------+-------------+

and the <78 58 57> XY-wing takes out <7> in R7C2, solving the puzzle.

Very enjoyable!

Keith
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 21, 2008 11:01 pm    Post subject: Reply with quote

cgordon wrote:
Asellus: But what's a Kite? Never heard of one - and I've been around !!

I believe a Kite is a Turbot Fish, also a Skyscraper where the two towers are in one row and one column, their "ground" cells being in a common box.

Keith
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Mon Apr 21, 2008 11:07 pm    Post subject: Reply with quote

keith wrote:
... a Skyscraper where the two towers are ...
Keith


Keith, you just answered my question from earlier tonight. I was seeing the two strong links of different size as two faces of one skyscraper. And I was wondering why they all looked like the Citicorp building... Now I know: two towers!

Smile
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 21, 2008 11:50 pm    Post subject: Reply with quote

nataraj wrote:
keith wrote:
... a Skyscraper where the two towers are ...
Keith


Keith, you just answered my question from earlier tonight. I was seeing the two strong links of different size as two faces of one skyscraper. And I was wondering why they all looked like the Citicorp building... Now I know: two towers!

Smile


Of course, but Nataraj' and my comments are quite serious. Any way people can get to visualize and recognize these patterns is, I believe, worth explaining.

Keith
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George Woods



Joined: 28 Mar 2006
Posts: 231
Location: Dorset UK

PostPosted: Mon Apr 21, 2008 11:52 pm    Post subject: Vh and W wings Reply with quote

This is the 3rd Vh in succession (I think) that can be solved by a W wing, when an XY or XYZ gave preety much the same next number!!
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Apr 22, 2008 4:33 am    Post subject: Reply with quote

cgordon,

Keith probably answered your question. But, if it helps you or others, the Kite in your <8> grid is marked below:
Code:
+-------+-------+-------+   
| . . 8 | 8 8 . | . . 8 |   
| # . 8c| . 8p. | . . . |   
| 8c. . | . . . | 8 . 8 |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . . | 8 . 8 | . . 8 |   
| . . . | . . 8 | 8 . 8 |   
+-------+-------+-------+   
| . . 8 | 8 . . | . . . |   
| . . . | . . . | . . . |   
| 8p. . | .-8v8 | . . . |
+-------+-------+-------+

The perpendicular pair of strong links are in r2 and c1. The "common" ends, marked "c", share box 1. The pincer ends, marked "p", eliminate the victim, "v", in r9c5. As an extra comment: any of the other cells in box 1 can contain an <8> candidate except the cell at the intersection of our row and column, in this case r1c2, marked "#", and the Kite is still valid. (Those sorts of Kites are a bit trickier to spot. Technically, they involve "grouped strong links".)

The names are not used consistently, so there is confusion. Turbot Fish is probably the general term for these sorts of techniques. They all involve a pair of strong links that have "common ends" in a single house with the other ends serving as pincers.

Skyscraper is commonly used to refer to the case where the two strong links are parallel (with the common ends sharing a row or a column). Kite is commonly used for the case, as above, where the strong links are perpendicular (with the common ends sharing a box).

There is another possible configuration in which the strong links are at an angle. One of the links is confined to a box and the common ends are in a row or column. Here are a couple of graphical examples:
Code:
+-------+-------+-------+   +-------+-------+-------+
| ~ ~ ~ | . ~ . | . . . |   | . . . | p ~ ~ | . v . |
| ~ ~ c | . c . | . . . |   | . . . | ~ ~ ~ | . . . |
| p ~ ~ | . ~ . | . . . |   | . . . | ~ ~ c | . . . |
+-------+-------+-------+   +-------+-------+-------+
| . . . | . ~ . | . . . |   | . . . | . . . | . . . |
| . . . | . ~ . | . . . |   | . . . | . . . | . . . |
| . . . | . ~ . | . . . |   | . . . | . . . | . . . |
+-------+-------+-------+   +-------+-------+-------+
| v . . | . p . | . . . |   | ~ ~ ~ | ~ ~ c | ~ p ~ |
| . . . | . ~ . | . . . |   | . . . | . . . | . . . |
| . . . | . ~ . | . . . |   | . . . | . . . | . . . |
+-------+-------+-------+   +-------+-------+-------+

The cells marked "~" cannot contain the candidate digit involved in the Turbot Fish. The cells marked "." can be anything.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Tue Apr 22, 2008 4:23 pm    Post subject: Reply with quote

Asellus/Keith – thanks for the low-down on Kites or Turbot fish. I probably ignored investigating these before because I figured they were part of the family of Swordfish, Jellyfish etc - which I always found too difficult to locate. These kites however are remarkably simple – just a couple of skyscrapers at right angles originating from the same box. Even the diagonal variant isn’t that complex. Sometimes the solutions offered on this forum look like proofs for quantum physics. These kites however are definitely easy to follow.
PS: What was the original obsession with fish: Swordfish, Jellyfish, Squirmbags, Finned Fish, Turbot Fish ???


Last edited by cgordon on Tue Apr 22, 2008 8:05 pm; edited 1 time in total
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stevieboy



Joined: 25 Jan 2008
Posts: 31
Location: Michigan

PostPosted: Tue Apr 22, 2008 5:04 pm    Post subject: Reply with quote

Hi Everyone! I'm new at posting, but have been attempting the VH Sudoku puzzles here for awhile. In trying to solve this puzzle, I came across an XY-Wing which (I'm not sure) is really a legitimate XY-Wing??(!)
Is the 16-68-18 found in R3C4, R6C6 and R6C7 REALLY an XY-Wing eliminating the '8' in R5C4 ?? If not, why?

Thank you everyone for your constant daily mind-boggling output!! Laughing
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Apr 22, 2008 7:58 pm    Post subject: Reply with quote

stevieboy wrote:
Hi Everyone! I'm new at posting, but have been attempting the VH Sudoku puzzles here for awhile. In trying to solve this puzzle, I came across an XY-Wing which (I'm not sure) is really a legitimate XY-Wing??(!)
Is the 16-68-18 found in R3C4, R6C6 and R6C7 REALLY an XY-Wing eliminating the '8' in R5C4 ?? If not, why?

Thank you everyone for your constant daily mind-boggling output!! Laughing


Code:
1      57     458    | 38     348    2      | 6      9      78
27     6      48     | 9      48     5      | 3      1      27
28     3      9      | 16     7      16     | 48     45     258
------------------------------------------------------------------
3      8      6      | 7      1      4      | 5      2      9
5      2      1      | 368    9      368    | 47     47     68
9      4      7      | 5      2      68     | 18     3      168
------------------------------------------------------------------
4      157    58     | 138    6      9      | 2      57     135
6      9      2      | 4      35     137    | 17     8      135
78     157    3      | 2      58     178    | 9      6      4


first of all, welcome.

secondly, no, this is not an xy-wing.

you do have two premises correct with the three cells that you have pointed out.

#1... the three cells are bivalue cells, meaning they contain only two candidates per cell

#2...the three cells share three candidates. {1,6,8} in this case

BUT!! the 3rd rule for an xy-wing is that there must be a pivot cell, or (you might want to consider this cell as the vertex)...
very importantly, this pivot cell must see the other two "pincer" cells...
the reason they are called pincer cells is because the candidate they share will eliminate any candidate they both "see".

in your example, the r3c4 (1,6) cell does not "see" (share a box, share a row, share a column ) either of the other two cells.

once you get the hang of this technique, these VH puzzles will become more like a hunt. If you have read any of nataraj's postings, he has made hunting a form of science.
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Tue Apr 22, 2008 8:16 pm    Post subject: Reply with quote

stevieboy wrote:
Hi Everyone! I'm new at posting, but have been attempting the VH Sudoku puzzles here for awhile. In trying to solve this puzzle, I came across an XY-Wing which (I'm not sure) is really a legitimate XY-Wing??(!)
Is the 16-68-18 found in R3C4, R6C6 and R6C7 REALLY an XY-Wing eliminating the '8' in R5C4 ?? If not, why?


Nope, sorry. The pincer 16 must "see" the pivot 68 which must see the other pincer 18. This is not true. If it was true, the logic is the pivot is 6 or 8; one of the pincers must be 1; any cell that sees both pincers cannot be 1.

There is a useless XY-wing in the same area. It would eliminate 1 in R3C7. Can you see it?

Keith
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Tue Apr 22, 2008 8:19 pm    Post subject: Reply with quote

To make matters worse (or maybe help by way of illustration), there is a valid xy-wing 168 in the puzzle. Look at r3c6, r6c6, r6c7.

The "pivot" cell in this case would be r6c6 (68), since it connects the other two.

The pincers are r3c6 (16) and r6c7 (18).

In an xy-wing, the digit present in both pincers ("1") can be eliminated from any cell that "sees" both pincers. The pivot cell sees both pincers and must contain the other two digits (6 and 8).

Unfortunately, in this puzzle, no cells that see both pincers contain any "1"s.

This is what is sometimes called a "useless" xy-wing.
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Tue Apr 22, 2008 8:20 pm    Post subject: Reply with quote

synchronicity
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Apr 22, 2008 8:23 pm    Post subject: Reply with quote

Asellus, Keith, cgordon, nataraj... anyone who follows the coloring discussions,

wouldn't it be nice to have a "coloring function" on the Draw/play screen??

even if that isn't possible, maybe a function to only show a particular candidate, like all the 1's or 2's etc.
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Tue Apr 22, 2008 8:42 pm    Post subject: Reply with quote

storm_norm wrote:
Asellus, Keith, cgordon, nataraj... anyone who follows the coloring discussions,

wouldn't it be nice to have a "coloring function" on the Draw/play screen??



Since I do not use the draw/play screen, I have no serious opinion on the matter. My theory is that no, it would not be nice: it would not add to the pleasure of solving sudoku but take away.

For other purposes, like answering questions in the forum, or to solve very difficult puzzles and make sure to avoid stupid errors or oversights in the early phases I endorse every sensible use of computer programs, as long as there is still enough challenge for the brain... Smile
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Tue Apr 22, 2008 8:45 pm    Post subject: Reply with quote

storm_norm wrote:
Asellus, Keith, cgordon, nataraj... anyone who follows the coloring discussions,

wouldn't it be nice to have a "coloring function" on the Draw/play screen??

even if that isn't possible, maybe a function to only show a particular candidate, like all the 1's or 2's etc.


I will pass the suggestion on to Sam. Maybe we should collect some suggestions in another part of the forum. I'll post a message.

Keith
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keith



Joined: 19 Sep 2005
Posts: 3136
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PostPosted: Tue Apr 22, 2008 8:48 pm    Post subject: Reply with quote

synchronicity
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DennyOR



Joined: 12 Sep 2007
Posts: 33
Location: Portland, Oregon

PostPosted: Wed Apr 23, 2008 6:47 am    Post subject: Reply with quote

Since I like to look for xy chains, from nataraj's position I solved the puzzle with what I would notate as (r3c8) 54-48-87-75=458=58 (r7c3), or what maybe would be called an xy chain with a coloring extension. Somebody a while back suggested looking for a coloring extension (my words) on an otherwise useless xy-wing (or chain), and that's turned out to be pretty useful.
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stevieboy



Joined: 25 Jan 2008
Posts: 31
Location: Michigan

PostPosted: Wed Apr 23, 2008 7:27 pm    Post subject: Reply with quote

Thank you Keith, nataraj, and my "neighbor" in Michigan, storm_norm for educating me on the "pincer" concept...the XY-Wing examples I've seen were more like the ones you all described...I was "reaching" wrongly, no doubt about it!

There should be college classes on this stuff; sometimes wannabes, such as myself, need to have the solving methods drilled in our heads!
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