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URs - an acquired taste

 
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nataraj



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

PostPosted: Sun Oct 28, 2007 4:09 pm    Post subject: URs - an acquired taste Reply with quote

Maybe it's just that I am getting the hang of it or that there were a few puzzles recently that didn't yield to "normal" means without resorting to uniqueness arguments, anyway - I am starting to like those UR, BUG+1 etc. techniques.

Here is one from last Wednesday at sudocue.net:
http://www.sudocue.net/olddaily.php?id=681&sol=0

After basics (and maybe an x-wing or two) I seemed stuck in this position:
Code:

+--------------------------+--------------------------+--------------------------+
| 7       1458    145      | 56      2       13       | 1346    9       138      |
| 28      6       14       | 39      7       139      | 134     28      5        |
| 125     9       3        | 56      4       8        | 167     127     127      |
+--------------------------+--------------------------+--------------------------+
| 346     47      9        | 2       1       5        | 8       34      67       |
| 16      17      8        | 34      9       34       | 5       27      267      |
| 345     45      2        | 7       8       6        | 19      34      19       |
+--------------------------+--------------------------+--------------------------+
| 458     458     6        | 1       3       479      | 2       57      789      |
| 9       2       147      | 48      5       47       | 137     6       1378     |
| 158     3       157      | 89      6       2        | 179     1578    4        |
+--------------------------+--------------------------+--------------------------+


But this being the Wednesday puzzle I went looking for a possible deadly pattern and - lo and behold - found a possible DP in r46c18 ("34").

To avoid the deadly pattern, r4c1=6 or r6c1=5.

But either assumption gives r4c1<>4 and r6c1<>4:


r4c1=6 => r6c1=3 (strong link on 3 in c1)
r6c1=5 => r4c1=3 (by the same strong link)

and thus r7c1=4 and the puzzle is solved.
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Marty R.



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

PostPosted: Sun Oct 28, 2007 5:12 pm    Post subject: Reply with quote

Nataraj,

Just as a point of information, that's a conventional "Type 4" rectangle. With a strong link of 3 on the corners, 4 must be removed from both cells.
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nataraj



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

PostPosted: Sun Oct 28, 2007 6:03 pm    Post subject: Reply with quote

Thanks, Marty!
I am just beginning to get into URs so I am not yet familiar with the different subtypes. As I understand it now, knowing the types obviously helps a lot in getting the result much faster - like all the other patterns I guess. So: time to do some reading ...
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sun Oct 28, 2007 6:48 pm    Post subject: Reply with quote

Some suggested reading:

Uniqueness Tests
----- Unique Rectangles http://www.sudoku.com/boards/viewtopic.php?p=29105#29105
---------- Types 1-4 http://www.setbb.com/phpbb/viewtopic.php?p=2441
----------------------- http://www.sudoku.com/boards/viewtopic.php?t=2000
---------- Diagonal and X-wing types http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?p=2894#2894
---------- Strong Link and Nice Loop Types http://www.sudoku.com/boards/viewtopic.php?p=26448#26448

(from Mike Barker's list of solving techniques)

Keith
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nataraj



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

PostPosted: Tue Oct 30, 2007 12:35 pm    Post subject: Reply with quote

Hail all nice people in this forum who have so patiently been pointing me in the right direction!

With your help (and especially Marty and keith providing information on URs other than type 1) I was able to solve last Friday's nightmare. It was a type 3 that did the trick, and (after the suggested reading) not too hard to find.

Gratefully yours
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