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VH but no xy-wing

 
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nataraj



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

PostPosted: Wed Jul 02, 2008 3:12 pm    Post subject: VH but no xy-wing Reply with quote

This one requires more than x-wing or xy-wing:

Code:

+-----------+-----------+-----------+
|  .  .  2  |  .  .  7  |  3  .  .  |
|  .  3  8  |  .  .  2  |  .  5  .  |
|  .  .  .  |  3  .  .  |  .  7  .  |
+-----------+-----------+-----------+
|  6  .  .  |  4  .  .  |  .  3  .  |
|  4  .  .  |  .  .  .  |  .  .  6  |
|  .  8  .  |  .  .  6  |  .  .  1  |
+-----------+-----------+-----------+
|  .  9  .  |  .  .  5  |  .  .  .  |
|  .  2  .  |  9  .  .  |  1  4  .  |
|  .  .  1  |  7  .  .  |  9  .  .  |
+-----------+-----------+-----------+

play online
I used what I believe is an m-wing (28-28-28 in r5 and col 8, and a strong link on 2 in box 5, removing 2 in r9c5)
But coloring is also possible, on 2 and 8 (kite, skyscraper) ...
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Jul 02, 2008 7:27 pm    Post subject: Reply with quote

nataraj,
that pattern on {2,8} happens to be the only pattern than can be classified by:
m-wing
w-wing
xy-chain
coloring on both 2 and 8
remote naked pair...remote pair

the name I know it as is the classic remote naked pair.

consider circles of influence that are given the names of techiques above. if you were to lay them out so that each were to overlap just little. the classic remote naked pair would be the area in the center where all of techniques overlap because it satisfies all rules.



Last edited by storm_norm on Wed Jul 02, 2008 7:54 pm; edited 2 times in total
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Wed Jul 02, 2008 7:40 pm    Post subject: Reply with quote

storm_norm wrote:
nataraj,
that pattern on {2,8} happens to be a very unique pattern which can be classified by:


You can add sashimi x-wing (or skyscraper) to that as the 28 pair form a double sky that does all the eliminations that the remote pairs do.

Nice puzzle!
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nataraj



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

PostPosted: Wed Jul 02, 2008 8:05 pm    Post subject: Reply with quote

Oh, I agree that the 28-28-28-28 pattern can be called many names.

I find it interesting that the m-wing I mentioned does not end in that boring 28 cell but in a cell with THREE candidates and still makes the elimination. That is because, for the final strong link in an m-wing, the cell does not have to be bi-value. Only that there are only 2 occurrences of the candidate (in this case, "2") in that house
Code:

+--------------------------+--------------------------+--------------------------+
| 9       45      2        | 6       458     7        | 3       1       48       |
| 7       3       8        | 1       49      2        | 6       5       49       |
| 1       45      6        | 3       4589    489      | 28      7       2489     |
+--------------------------+--------------------------+--------------------------+
| 6       17      59       | 4       289*    189      | 2578    3       278      |
| 4       17      59       | 28#     39      139      | 57      28#     6        |
| 2       8       3        | 5       7       6        | 4       9       1        |
+--------------------------+--------------------------+--------------------------+
| 38      9       4        | 28      1       5        | 278     6       2378     |
| 358     2       7        | 9       6       38       | 1       4       358      |
| 358     6       1        | 7      -2348    348      | 9       28*     2358     |
+--------------------------+--------------------------+--------------------------+


Of course, the full 2-s skyscraper/w-wing/remote pair etc. in cols 4 and 8 makes the same elimination and the 8-s skyscraper eliminates some more ....
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Wed Jul 02, 2008 10:30 pm    Post subject: Reply with quote

Norm,

I like the idea of your diagram!

nataraj wrote:
I find it interesting that the m-wing I mentioned does not end in that boring 28 cell but in a cell with THREE candidates and still makes the elimination. That is because, for the final strong link in an m-wing, the cell does not have to be bi-value. Only that there are only 2 occurrences of the candidate (in this case, "2") in that house.


Nataraj,

To be pedantic, only two cells in an M-wing need to be bivalue: The pair that makes it (relatively) easy to recognize. Your example is:

28=28=28=2x

where x is any number of candidates. It eliminates <2> from any cell that sees both ends (pincers).

All you really need is

28=8y=28=2x

where y is also any number of candidates.

Of course the 28=28=28 fragment is very cool, because you can look for four possible M-wings: A strong link on either <2> or <8> at either end.

Or, they may turn out to be three corners of an X-wing or UR!)

Keith
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nataraj



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

PostPosted: Thu Jul 03, 2008 6:36 am    Post subject: Reply with quote

keith wrote:
Nataraj,

To be pedantic, only two cells in an M-wing need to be bivalue: The pair that makes it (relatively) easy to recognize.


Keith, I fully appreciate the value of the m-wing for my search strategies as one pattern that can be very easily recognized. When I start looking for wings, it is usually those cells that are bi-value and occur more than once in the grid where I look first for possible w- or m-wings. Only then do I widen the search to include other bi-values and start looking for an xy-wing. It is in that early stage when it helps to know that one does not need three consecutive pairs like the 28-28-28 here, but that the link between the first and third 28 can be any cell containing one of the pair (2 or 8 ) as long as there is a weak link (in one of the two candidates) between the first pair and that middle cell and a strong link between the middle cell and the other pair. And thank you very much indeed for pointing it out, that is a thing to remember and use in the future for sure.

Now thinking about that "...need to be bivalue" some more, I got an idea how to improve my other search strategy, namely the (multi-) coloring search using individual small sketches in the margin of the paper (Keith even provides those pre-printed in his templates, that's a cool idea).

In those sketches, I mark strong links and other occurrences of a single candidate. It looks like this (sketch for candidate 8 )

Code:

++++
       *-------#
               
               
               
       o oo   o
++++
       o oo   o
               
     #-------# 
     |      | 
     |      | 
++|+|+
o    #    o | o
            | 
o        o  | o
            | 
o      o o  # o
++++

The skyscraper (the 28-28-28-28 chain) is clearly visible, but I am trying to get to a different point altogether: If we'd mark those cells where there is only one other candidate (those bi-values) with that digit instead of a simple dot, we'd have the beginnings of all possible "generalized" m-wings. (I guess I should not call them m-wings, but in fact what we are looking for, here, is a pattern for a short AIC).

I'll give it a try, and (for this experiment, I assume that r5c4 contains an extra candidate 3:
Code:

++++
       *-------4
               
               
               
       o o2   o
++++
       o oo   o
               
     *-------2 
     |      | 
     |      | 
++|+|+
3    2    o | o
            | 
o        3  | o
            | 
o      o o  2 o
++++

In that case, we would have a small handful of possible AICs to check for eliminations:
- Starting in box 3: the "target" candidate (the one we are going to make the elimination on) would be 2 in cell r3c7. After the weak link - strong link sequence (8)r3c7-r1c9=r1c5 we would need a strong link in 2 starting from r1c5. There is no 2 in r1c5 so no such luck.
- Next possibility: 2 in r5c8. The weak link/strong link sequence leads to r7c4 and this time we can see that there is a "2" in that cell. (that would be the "classic" start of an m-wing. Look for a strong link on 2 starting at r7c4. There is indeed such a link, but the resulting m-wing (between r5c8 and r9c5) doesn't do much.
- next possibility: 3 in r7c1. weak/strong to r5c4, but no strong link from there (box 5 has 3 in 2 other cells already)
- 2 in r7c4. w/s to r5c8, strong link to r9c8 and we've got a winner.
- 3 in r8c6. w/s to r5c4, but again there is no strong link from there in 3
- last one to check: 2 in r9c8. w/s to r5c4, strong link in 2 to r4c5 or to r7c4 and in both cases a winner.

What I like in this approach is that it is very structured and it fits well with my usual search pattern for coloring (looking for x-wings, swordfish, jellyfish, kite, skyscraper and other flotsam and jetsam). I always hate it when I have to decide rather early whether to go looking for coloring patterns (and spend some time on the little sketches) or to look for wings right away. Including the m- and w- wings and even some not-quite-wings definitely improves the attractiveness of my little sketches ...

I shall experiment in the next couple of weeks and see how it works out (expect to be confronted with all sorts of chains, some not even xy-chains). Just thought I'd share this idea with you people here, maybe some of you have improved on this or a similar method already Smile ...
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cgordon



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

PostPosted: Thu Jul 03, 2008 5:17 pm    Post subject: Reply with quote

I'm into the history of science. That diagram of Norm's reminded me of Ptolemy's 2nd cent maps for the movements of the sun and planets around the earth. Coming down to earth a bit - I just used a skyscraper on <4> and an ER on <2>.
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Thu Jul 03, 2008 8:51 pm    Post subject: Reply with quote

Nataraj:
Quote:
If we'd mark those cells where there is only one other candidate (those bi-values) with that digit instead of a simple dot, we'd have the beginnings ...

An interesting idea! I'll try it myself.

I learned the idea of these diagrams from Marty R. They are easy to use, and much simpler than it might appear from your figures. (It is hard to type a simple sketch.)

What I am thinking is, suppose you have the sketches for both 2 and 8 (in this example) side by side. And, we have your idea that the other candidate in a bivalue cell is written in.

Suppose, on the diagram for 8, there are two unconnected cells that have 2. A glance at the sketch for 2 will tell me if there is a W-wing.

Suppose, on the diagram for 8 there are 3 connected cells 2=o=2. Look for an M-wing!

Food for thought.

Keith
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nataraj



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

PostPosted: Fri Jul 04, 2008 8:10 am    Post subject: Reply with quote

I know how easy it is to use the diagrams (have been using them for a long time), and also how awfully complicated it all seems when I include one in my posts. sometimes I am tempted to use photos of the real sketches I make, but they look too messy.

I was thinking about using a regular empty sudoku grid and have the boxes represent a whole grid for one candidate. So top left box would mean candidate 1 and it might look loke this:


oops forgot to add the line between r4c78. AND the line in box 3. AND then there would be a box/line and the rest of row 1 goes away ... Actually these little sketches help a lot to verify that I'm really done with basics ... sometimes I do not see box/line interactions until I do the sketches.

Oh! and ... there is a hidden single in r8c5 ... (of course I made it all up, no real sudoku behind that drawing...)
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nataraj



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

PostPosted: Fri Jul 04, 2008 1:04 pm    Post subject: Reply with quote

I've used the neighbouring thread "underrated VH" as a test case.
This is what the UR 57 looks like (grid shown for candidate 5, not that anyone would need a separate sketch to identify a type 1 Laughing)
Code:

++++
               
               
               
               
               
++++
  7---------*   
  |       |   
  |  7-4  |   
  |  | |  |   
  7---------7   
++||++
     *-4       
               
               
               
               
++++

The UR type 1 stands out with 3 corners filled in and a possibility for 7 in the top right.

After that, we come to the w-wing situation:
If we look at candidate "8", there is a strong link in row 8 and links to "1" from either end:
Code:

++++
          1---3
              |
       *-*    |
         |    |
         |    |
++|+|+
    1---1 |    |
   / /  |    |
  /  |  |    |
/    /  |    |
1-----1   |    |
+|+|+|+
|   oo   *    6
|              
7-----------7   
               
    oo o  o   
++++

So far, I am suffering from information overload when I look at the little sketches. But then again, what I'm trying to do here is to combine all advanced techniques (at least those used more commonly in this forum) into one single, structured, repeatable, non-invasive, pencil-and-paper solving process...

Maybe a bit too much for one afternoon

getting some rest now Smile
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Mon Jul 07, 2008 10:51 pm    Post subject: Reply with quote

This thread is continued in the "Solving Techniques" forum:

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=12167

Keith
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