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UR+SL: Mike Barker's UR+3C/2SL

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Nov 01, 2011 6:27 pm    Post subject: UR+SL: Mike Barker's UR+3C/2SL Reply with quote

My previous posts (obviously) used 1x SL for one UR value. There are other UR patterns that use 1x SL, but I'm not going to post them because I feel they are too complicated (for me) to ever spot. This is the first post using 2x SLs for one UR value.

===== ===== ===== ===== Mike Barker's UR+3C/2SL

Code:
2x SL in [c3] and [r2] for 1x value   (aka Hidden Unique Rectangle)
+--------------+
|  .   .   .   |
| 12X  .  1Y-2 |<  SL on <1>
|  .   .   .   |
+--------------+
|  .   .   .   |
| 12   .  12Z  |
|  .   .   .   |
+--------------+
           ^       SL on <1>

Puzzle from Mike Barker's "zoo" collection:

Code:
..2.9......46.7....9...43..7.8.....9.4..2.8...5..3.1.....5.......6..89.........37

 +-----------------------------------------------------+
 |  5    6    2    |  1    9    3    |  7    4    8    |
 |  3    1    4    |  6    8    7    |  5    9    2    |
 |  8    9    7    |  2    5    4    |  3    16   16   |
 |-----------------+-----------------+-----------------|
 |  7    3    8    |  4    1    5    |  26   26   9    |
 |  6    4    1    |  7    2    9    |  8    5    3    |
 |  2    5    9    |  8    3    6    |  1    7    4    |
 |-----------------+-----------------+-----------------|
 |  9    27   3    |  5   *46+7 12   | *46+2 8    16   | <  SL on <4>
 |  14   27   6    |  3    47   8    |  9    12   5    |
 |  14   8    5    |  9   *46   12   | *46+2 3    7    |
 +-----------------------------------------------------+
 # 20 eliminations remain               ^                   SL on <4>

 r79c57  <46> UR via s-link              <> 6    r7c7

Ironically, even though the puzzle is practically solved, this elimination does not crack the puzzle.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Nov 01, 2011 11:03 pm    Post subject: Reply with quote

I was all prepared to post this pattern separately, but RonK was kind enough to inform me that it was essentially equivalent to the above pattern because the implied X-Wing pattern would force an SL in [c3] if it didn't already exist. Ron was also kind enough to provide me with an example puzzle.

===== ===== ===== ===== Mike Barker's UR+3E/2SL

Code:
2x SL in [r2] and [r5] for 1x value   (essentially equivalent to UR+3C/2SL)
+--------------+
|  .   .   .   |
| 12X  .  1Y-2 |<  SL on <1>
|  .   .   .   |
+--------------+
|  .   .   .   |
| 12   .  12Z  |<  SL on <1>
|  .   .   .   |
+--------------+

Puzzle from Ron's collection: (Ron's analysis included)

Code:
.6..2...3...........3...4.5...8..7.2.1...4...8..23..9..4...3.5.78......19...8.2..

 *-----------------------------------------------------------------------------*
 | 45      6       789     | 14579   2       15789   | 189     178     3       |
 | 45      279     789     | 3       145679  156789  | 1689    12678   6789    |
 | 1       279     3       | 679     679     6789    | 4       2678    5       |
 |-------------------------+-------------------------+-------------------------|
 | 36      59      469     | 8       1569    1569    | 7       1346    2       |
 |*236     1      *2679    | 5679    5679    4       | 3568    368     68      |<  SL on <2>
 | 8       57      467     | 2       3       1567    | 156     9       46      |
 |-------------------------+-------------------------+-------------------------|
 |*26      4      *126     | 1679    1679    3       | 689     5       6789    |<  SL on <2>
 | 7       8       56      | 4569    4569    2       | 369     346     1       |
 | 9       3       156     | 14567   8       1567    | 2       467     467     |
 *-----------------------------------------------------------------------------*
____________________________________________________________________________________________

UR(26)r57c13 with SLs on <2> in r5 & r7 (or c1 & c3) for r5c3<>6
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