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Mar 3 - uh hum

 
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Mon Mar 03, 2008 7:10 am    Post subject: Mar 3 - uh hum Reply with quote

Bad start into the week.

How hard is it to solve a puzzle, when after basics (I mean real easy basics) there is just a handful of cell left. When there are mostly those candidate combinations left: 36, 37 and 67 (ok, there is also 69 and three tri-values)

I am sure there are a lot of fancy ways to take the last step. That does not take my frustration away, right now. Sad
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Mon Mar 03, 2008 2:06 pm    Post subject: VH Reply with quote

I agree. Just an xy-wing pivoted at R8C2.

Earl
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Mon Mar 03, 2008 4:43 pm    Post subject: Reply with quote

One W-Wing on the 37s was all that was needed.
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KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Mon Mar 03, 2008 4:59 pm    Post subject: Reply with quote

Hi
Can someone point me to a link that explains w-wings! Thanks.
Kathy
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Mon Mar 03, 2008 5:50 pm    Post subject: Reply with quote

Kathy, a W-wing occurs when there are two cells with the same pair and they are connected by a strong link on one of the numbers. Then the other numbers become pincers, working like the pincers of an XY-Wing.

The fourth post here gives an example. If it's not enough information, just ask for more detail and someone will be happy to answer.

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Mon Mar 03, 2008 10:35 pm    Post subject: Reply with quote

xy-wing for me
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KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Mon Mar 03, 2008 11:10 pm    Post subject: Reply with quote

Marty

I understood the link you mentioned and could follow the w-wing as described. I don't know if I ever will be able to spot one. In particular, I cannot see the w-wing based on 37. Can you point it out to me.
Thanks

Kathy
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Tue Mar 04, 2008 12:33 am    Post subject: Reply with quote

KSipher wrote:
Marty

I understood the link you mentioned and could follow the w-wing as described. I don't know if I ever will be able to spot one. In particular, I cannot see the w-wing based on 37. Can you point it out to me.
Thanks

Kathy

I'm sorry Kathy, I can't help. There are no grids thus far in this thread and I don't have my intermediate position since I'm a pencil-and-paper guy. Do you have a grid you can post?
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KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Tue Mar 04, 2008 2:12 am    Post subject: Reply with quote

Marty

Here is my grid at the point where I started looking for the elusive w-wing.

Kathy

Code:

+-----------+------------+-------+
| 5 4   37  | 367 367 8  | 9 1 2 |
| 6 37  2   | 37  1   9  | 4 8 5 |
| 9 1   8   | 5   4   2  | 6 3 7 |
+-----------+------------+-------+
| 3 2   5   | 9   8   7  | 1 4 6 |
| 7 69  69  | 4   5   1  | 3 2 8 |
| 1 8   4   | 36  2   36 | 7 5 9 |
+-----------+------------+-------+
| 4 379 379 | 8   37  5  | 2 6 1 |
| 8 36  1   | 2   9   36 | 5 7 4 |
| 2 5   67  | 1   67  4  | 8 9 3 |
+-----------+------------+-------+

Play this puzzle online at the Daily Sudoku site
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Stanley P



Joined: 27 Feb 2008
Posts: 20
Location: Tennessee, USA

PostPosted: Tue Mar 04, 2008 3:00 am    Post subject: Where's the w-wing? Reply with quote

I am pretty new to this forum. I saw the xy-wing for rows 1,8,9 and cols 2,3 which eliminated the 3 in r2c2. With a previous x-wing I think, that did it for me. Like KSipher I missed the w-wing and would like to know where it occurs.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Tue Mar 04, 2008 4:52 am    Post subject: Reply with quote

KSipher wrote:
Marty

Here is my grid at the point where I started looking for the elusive w-wing.

Kathy

Code:

+-----------+------------+-------+
| 5 4   37  | 367 367 8  | 9 1 2 |
| 6 37  2   | 37  1   9  | 4 8 5 |
| 9 1   8   | 5   4   2  | 6 3 7 |
+-----------+------------+-------+
| 3 2   5   | 9   8   7  | 1 4 6 |
| 7 69  69  | 4   5   1  | 3 2 8 |
| 1 8   4   | 36  2   36 | 7 5 9 |
+-----------+------------+-------+
| 4 379 379 | 8   37  5  | 2 6 1 |
| 8 36  1   | 2   9   36 | 5 7 4 |
| 2 5   67  | 1   67  4  | 8 9 3 |
+-----------+------------+-------+

Play this puzzle online at the Daily Sudoku site

Kathy and Stanley, note the 37 pairs in boxes 1 and 8 and the strong link on 7 in row 9. Each 7 sees one of the 37 pairs so the 3s become pincers and take out the 3 from r1c5 and r7c3.

P.S. Welcome to the forum Stanley.

P.P.S. There's another neat little move which doesn't do much. Note the 3-cell chain of 36 pairs in boxes 5 and 8. Each end of the chain taken together can be used as the XY cell in an XY-Wing. One end of the chain (r6c4) sees the 37 in r2c4 and the other end (r8c6) sees the 67 in r9c5. Those pincers on 7 take out the 7 from r1c5.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Tue Mar 04, 2008 6:47 am    Post subject: Reply with quote

Some more things to see in the grid posted by KSipher:

The xy-wings in boxes 1 and 7 can be seen either as 37-36-67 pivoted on r8c2 (as Earl remarked) which takes out the 7 in r1c3, or as 36-67-37 pivoted on r9c3, in which case it takes out the 3 in r2c2 (Stanley's).

Furthermore, in box 8, "7" is restricted to col r79c5, thus 7 can be removed from cell r1c5.
We now have another xy-wing 36-37-67 pivoted on r1c3 which takes out 6 in r9c5.

The 36 and 37 cells form a ring
Code:

   37...|.....36
37      |      .
.       |      .
36      |      .
   67...|.....67

Starting at any cell (e.g. r1c3), one can follow the ring in both directions, one for each of the two candidates in the cell:
case a: r1c3=3 going clockwise, we get r1c5=6, r9c5=7, r9c3=6, r8c2=3, r2c2=7
case b: r1c3=7 going couterclockwise - r2c2=3, r8c2=6, r9c3=7,r9c5=6,r1c5=3
Either way, the common candidate(s) in both ends of a link can be removed from all cells that see both ends of the link, that is
3 from row 1 (r1c4)
6 from c5 (none)
6,7 from row 9 (none, we already did that, it is a naked pair)
6 from box 7 (none)
3 from col 2 (r7c2)
3,7 from box 1 (nope, naked pair)

Plus, of course, r7c2, r7c3 and r1c4 being the only cells with three candidates the situation looks suspiciously like a BUG+3
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KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Thu Mar 06, 2008 2:29 am    Post subject: Reply with quote

Thanks for the comments. Marty, I finally can see the w-wing - I finally got it. I even think I can recognize it in the future, with a little practice.

Now I need to spend a little time trying to digest all the comments nataraj made. It's been a busy day, so tomorrow I will work on following it.

I love this group - so many generous offers of help!

Kathy
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Thu Mar 06, 2008 11:23 am    Post subject: Reply with quote

KSipher wrote:
Thanks for the comments. Marty, I finally can see the w-wing - I finally got it. I even think I can recognize it in the future, with a little practice.
As a first exercise you can try to find other w-wings with 37-pairs in this grid Smile (Another possible link for Marty's pairs and 2 possible links for another pair of 37's)
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Mar 06, 2008 12:24 pm    Post subject: Reply with quote

To complete the zoo of wings, there is also an x-wing (on 3, in cols 3 and 5) which turns the situation into a BUG+1, easily recognized by having only one cell with more than 2 candidates:

Code:

+--------------------------+--------------------------+--------------------------+
| 5       4       37       | 67      36      8        | 9       1       2        |
| 6       37      2        | 37      1       9        | 4       8       5        |
| 9       1       8        | 5       4       2        | 6       3       7        |
+--------------------------+--------------------------+--------------------------+
| 3       2       5        | 9       8       7        | 1       4       6        |
| 7       69      69       | 4       5       1        | 3       2       8        |
| 1       8       4        | 36      2       36       | 7       5       9        |
+--------------------------+--------------------------+--------------------------+
| 4       79      379      | 8       37      5        | 2       6       1        |
| 8       36      1        | 2       9       36       | 5       7       4        |
| 2       5       67       | 1       67      4        | 8       9       3        |
+--------------------------+--------------------------+--------------------------+

In r7c3, "7" is the number that occurs 3 times in col 3 and 3 times in row 7.
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Asellus



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

PostPosted: Fri Mar 07, 2008 4:00 am    Post subject: Reply with quote

I was wondering if anyone was going to find the X-Wing and BUG+1. That's how I happened to solve it.
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