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		| nataraj 
 
 
 Joined: 03 Aug 2007
 Posts: 1048
 Location: near Vienna, Austria
 
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				|  Posted: Thu Sep 13, 2007 6:24 am    Post subject: sept 13 |   |  
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				| not very hard, when UR looking at it the right way. |  | 
	
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		| Mindwarp 
 
 
 Joined: 13 Sep 2007
 Posts: 25
 Location: St. Ives, England
 
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				|  Posted: Thu Sep 13, 2007 9:52 am    Post subject: |   |  
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				| A fairly easy puzzle.  On Draw/Play, first enter all numbers possible without sweep and after that just sweep and eliminate. |  | 
	
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		| TexCat 
 
 
 Joined: 07 Jul 2006
 Posts: 32
 
 
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				|  Posted: Thu Sep 13, 2007 3:07 pm    Post subject: |   |  
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				| I got stuck here: 
  	  | Code: |  	  | +------------+----------+---------+
 | 23  26  8  | 4  236 5 | 1  9  7 |
 | 257 267 9  | 1  26  8 | 25 4  3 |
 | 1   4   35 | 27 237 9 | 6  25 8 |
 +------------+----------+---------+
 | 25  1   7  | 9  8   4 | 25 3  6 |
 | 9   25  6  | 3  1   7 | 8  25 4 |
 | 8   3   4  | 6  5   2 | 7  1  9 |
 +------------+----------+---------+
 | 37  79  2  | 5  49  6 | 34 8  1 |
 | 6   59  35 | 8  49  1 | 34 7  2 |
 | 4   8   1  | 27 27  3 | 9  6  5 |
 +------------+----------+---------+
 
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 Play this puzzle online at the Daily Sudoku site
 
 What am I missing?
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		| sdq_pete 
 
 
 Joined: 30 Apr 2007
 Posts: 119
 Location: Rotterdam, NL
 
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				|  Posted: Thu Sep 13, 2007 3:29 pm    Post subject: |   |  
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				| The UR on 27 putting 3 at R3C5, presumably. Since we normally don't seem to have to rely on UR's I'm curious if anyone spotted an XY wing or such. 
 Peter
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		| duffy 
 
 
 Joined: 13 Sep 2007
 Posts: 26
 Location: Toronto Canada
 
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				|  Posted: Thu Sep 13, 2007 3:44 pm    Post subject: |   |  
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				| Since I learned about UR's (thanks, Keith!) a couple of months ago, I find them interesting and useful. After the previous one for 27's in boxes 2 and 8, there is immediately another one in boxes 1 and 2 on 26's. And for the record, I did not see any wings except for an earlier x-wing on 5's in rows 2 and 4. I am glad to be back here, after having to re-register since the server  problems a few months ago.
 
   Don D.
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		| cgordon 
 
 
 Joined: 04 May 2007
 Posts: 769
 Location: ontario, canada
 
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				|  Posted: Thu Sep 13, 2007 6:03 pm    Post subject: |   |  
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				|  	  | Quote: |  	  | What am I missing? | 
 
 Texcat:  From your grid there's a UR that leaves a 7 in R2C1.  Though when I did it there was another 257 in R4C1 which, according to Keith's UR post made the UR a Type 2.
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		| lkmckin 
 
 
 Joined: 25 May 2007
 Posts: 9
 
 
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				|  Posted: Thu Sep 13, 2007 6:06 pm    Post subject: |   |  
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				| You can use a finned fish on [2] in cols 1 and 7 to eliminate [2] from r2c2. 
 You can use an XY wing to eliminate [5] from r2c1.
 
 Now, r2c7 is forced to [5] and the rest comes easily after that.
 
 I hate URs because they assume something additional about the puzzle (that it has a unique solution).
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		| nataraj 
 
 
 Joined: 03 Aug 2007
 Posts: 1048
 Location: near Vienna, Austria
 
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				|  Posted: Thu Sep 13, 2007 6:09 pm    Post subject: |   |  
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				| sure thing, peter. 
 from this position
 
  	  | Code: |  	  | +--------------------------+--------------------------+--------------------------+
 | 23      26      8        | 4       236     5        | 1       9       7        |
 | 257     25679   579      | 1       267     8        | 25      4       3        |
 | 1       4       357      | 27      237     9        | 6       25      8        |
 +--------------------------+--------------------------+--------------------------+
 | 257     1       57       | 9       8       4        | 25      3       6        |
 | 9       25      6        | 3       1       7        | 8       25      4        |
 | 8       3       4        | 6       5       2        | 7       1       9        |
 +--------------------------+--------------------------+--------------------------+
 | 37      79      2        | 5       49      6        | 34      8       1        |
 | 6       59      359      | 8       49      1        | 34      7       2        |
 | 4       8       1        | 27      27      3        | 9       6       5        |
 +--------------------------+--------------------------+--------------------------+
 
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 an xwing in 5 cols 1 and 7,
 later on an xy-wing pivot r1c1 (23) with 35-23-25 getting rid of 5 in r2c1 which opens the puzzle.
 
 might have missed an intermediate step or two but those are the highlights I remember
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		| Marty R. 
 
 
 Joined: 12 Feb 2006
 Posts: 5770
 Location: Rochester, NY, USA
 
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				|  Posted: Thu Sep 13, 2007 6:15 pm    Post subject: |   |  
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				|  	  | TexCat wrote: |  	  | I got stuck here: 
  	  | Code: |  	  | +------------+----------+---------+
 | 23  26  8  | 4  236 5 | 1  9  7 |
 | 257 267 9  | 1  26  8 | 25 4  3 |
 | 1   4   35 | 27 237 9 | 6  25 8 |
 +------------+----------+---------+
 | 25  1   7  | 9  8   4 | 25 3  6 |
 | 9   25  6  | 3  1   7 | 8  25 4 |
 | 8   3   4  | 6  5   2 | 7  1  9 |
 +------------+----------+---------+
 | 37  79  2  | 5  49  6 | 34 8  1 |
 | 6   59  35 | 8  49  1 | 34 7  2 |
 | 4   8   1  | 27 27  3 | 9  6  5 |
 +------------+----------+---------+
 
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 Play this puzzle online at the Daily Sudoku site
 
 What am I missing?
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 There is a Type 6 rectangle in boxes 1 and 2, with the 26 pairs on the diagonal. The four corners are an X-Wing on 6, so the two bivalue cells must be 6 to preclude the deadly pattern. Then remote pairs on 25 take out the 2 from r2c2, leaving it solved with a 7. I don't know offhand if that finishes the puzzle.
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		| sdq_pete 
 
 
 Joined: 30 Apr 2007
 Posts: 119
 Location: Rotterdam, NL
 
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				|  Posted: Thu Sep 13, 2007 6:26 pm    Post subject: |   |  
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				|  	  | nataraj wrote: |  	  | an xwing in 5 cols 1 and 7, 
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 Thanks - I seem not very good at X-wings, or, at least, I think I tend to forget to look for them explicitly and to concentrate on XY and XYZ wings.
 Peter
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		| cgordon 
 
 
 Joined: 04 May 2007
 Posts: 769
 Location: ontario, canada
 
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				|  Posted: Thu Sep 13, 2007 7:34 pm    Post subject: |   |  
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				| I'm going bonkers with this one. According to Texcats grid (and my solution) there is a UR for 257 on R2C17 and R4C17.  That should make R2C1 a 7 and eliminate the 7 from R7C1 - but it doesn't - R7C1 is the 7. 
 Pls help!!
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		| Marty R. 
 
 
 Joined: 12 Feb 2006
 Posts: 5770
 Location: Rochester, NY, USA
 
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				|  Posted: Thu Sep 13, 2007 7:49 pm    Post subject: |   |  
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				|  	  | cgordon wrote: |  	  | I'm going bonkers with this one. According to Texcats grid (and my solution) there is a UR for 257 on R2C17 and R4C17.  That should make R2C1 a 7 and eliminate the 7 from R7C1 - but it doesn't - R7C1 is the 7. 
 Pls help!!
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 Craig, the problem is that it is not a rectangle. All the rectangle theories are based on the fact of the rectangle being in just two boxes; the 257 occupies four boxes. With four boxes, there is no "deadly pattern."
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		| cgordon 
 
 
 Joined: 04 May 2007
 Posts: 769
 Location: ontario, canada
 
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				|  Posted: Thu Sep 13, 2007 8:16 pm    Post subject: |   |  
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				| Marty. 
 I didn't know that!!  A week ago I thought I was an expert on URs.  I was gonna move on to Medusa Wraps. Then on Monday I found out you can't use 3 triples and a quad in a UR - and now the corners have to be in 2 boxes.  I should stick to naked-singles.
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		| TKiel 
 
 
 Joined: 22 Feb 2006
 Posts: 292
 Location: Kalamazoo, MI
 
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				|  Posted: Thu Sep 13, 2007 9:34 pm    Post subject: |   |  
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				| I'd clear that with the significant other first. |  | 
	
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		| TKiel 
 
 
 Joined: 22 Feb 2006
 Posts: 292
 Location: Kalamazoo, MI
 
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				|  Posted: Thu Sep 13, 2007 9:56 pm    Post subject: |   |  
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				| When I got here (a spot similar to Texcat's and nataraj's position) I saw but decided to ignore the <27> UR in hopes of finding something else, so I went hunting for wings.  I missed the (25)(23)(35) with pivot in r1c1 but noticed there was a (23)(35)(25) with pivot in r3c3.  Unfortunately, no exclusions were directly possible with it.  But applying W-wing with coloring logic (I hope) to the XY-wing, the strong links on <2> show that <2> can be excluded from r1c2. 
 
  	  | Code: |  	  | *--------------------------------------------------*
 | 23B  26   8    | 4    236  5    | 1    9    7    |
 | 257  67   9    | 1    26   8    | 25   4    3    |
 | 1    4    35   | 27   237  9    | 6    25A  8    |
 |----------------+----------------+----------------|
 | 25   1    7    | 9    8    4    | 25   3    6    |
 | 9    25A  6    | 3    1    7    | 8    25a  4    |
 | 8    3    4    | 6    5    2    | 7    1    9    |
 |----------------+----------------+----------------|
 | 37   79   2    | 5    49   6    | 34   8    1    |
 | 6    59   35   | 8    49   1    | 34   7    2    |
 | 4    8    1    | 27   27   3    | 9    6    5    |
 *--------------------------------------------------*
 
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 One of the cells marked A or B must be 2, because of the XY-wing.  Any cell that sees both can be excluded.
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		| Asellus 
 
 
 Joined: 05 Jun 2007
 Posts: 865
 Location: Sonoma County, CA, USA
 
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				|  Posted: Thu Sep 13, 2007 10:49 pm    Post subject: |   |  
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				| Tracy, 
 Your coloring based on the XY Wing is more interesting than you realize.
 
  	  | Code: |  	  | *--------------------------------------------------* |#2R3  26   8    | 4    236  5    | 1    9    7    |
 | 257  67   9    | 1    26   8    | 2r5  4    3    |
 | 1    4    35   | 27   237  9    | 6    2G5  8    |
 |----------------+----------------+----------------|
 |#2r5  1    7    | 9    8    4    | 2g5  3    6    |
 | 9    2g5  6    | 3    1    7    | 8    2r5  4    |
 | 8    3    4    | 6    5    2    | 7    1    9    |
 |----------------+----------------+----------------|
 | 37   79   2    | 5    49   6    | 34   8    1    |
 | 6    59   35   | 8    49   1    | 34   7    2    |
 | 4    8    1    | 27   27   3    | 9    6    5    |
 *--------------------------------------------------*
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 The <2>s on the ends of the XY Wing are a conjugate pair (strong link).  I've used R and G to mark them, then colored the other conjugates with r and g.  Not only is the <2> at R1C2 eliminated by the rg "trap," but there is a color "wrap" caused by having two "reds" in C1, marked #.
 
 So, all of the "red" <2>s can be removed and all the "green" <2>s placed.
 
 (Note: There is no W-Wing type of coloring logic, as discussed recently on another thread, involved here.)
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		| keith 
 
 
 Joined: 19 Sep 2005
 Posts: 3355
 Location: near Detroit, Michigan, USA
 
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				|  Posted: Thu Sep 13, 2007 10:52 pm    Post subject: |   |  
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				| The UR solves it. 
 Or, there is an XY-wing followed by an X-wing and then a remote pair.
 
 Keith
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		| cgordon 
 
 
 Joined: 04 May 2007
 Posts: 769
 Location: ontario, canada
 
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				|  Posted: Thu Sep 13, 2007 10:54 pm    Post subject: |   |  
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				| I'm into ERs (an advanced technique).  There's one on 5's from C7 that says R4C3 cannot be a 5.  This exposes the UR already alluded to. |  | 
	
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		| Mogulmeister 
 
 
 Joined: 03 May 2007
 Posts: 1151
 
 
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				|  Posted: Fri Sep 14, 2007 7:59 am    Post subject: |   |  
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				| Empty rectangles (ER) is a technique that (in my opinion) helps out at the early phase of a puzzle and is a nice visual tool.  Havard put it forward 
 http://www.sudoku.com/boards/viewtopic.php?t=3251&start=0
 
 and on his own board.
 
 I find these days that I don't encounter them nearly as much and can only conclude that it is because I am making those eliminations with other strong-link based techniques.
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		| TKiel 
 
 
 Joined: 22 Feb 2006
 Posts: 292
 Location: Kalamazoo, MI
 
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				|  Posted: Sat Sep 15, 2007 1:54 pm    Post subject: |   |  
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				|  	  | Asellus wrote: |  	  | The <2>s on the ends of the XY Wing are a conjugate pair (strong link). | 
 
 Are you saying that in all cases the end cells of an XY-wing are conjugate pairs?
 
 Or that in this case they just happen to be the end cells of an XY-wing and just happen to be conjugate?
 
 Cuz, I'm having a hard time seeing either one, but it wouldn't be the first time I missed something like that.  I can't think of anything inherent in the XY-wing that precludes them both being <2> and I can't find a simple coloring chain that strongly links them.  The cells are linked only in that we know from the XY-wing that at least one of them must be <2>.
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