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Another interesting one

 
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keith



Joined: 19 Sep 2005
Posts: 3341
Location: near Detroit, Michigan, USA

PostPosted: Wed Feb 23, 2011 1:24 pm    Post subject: Another interesting one Reply with quote

Another interesting one.
Code:
Puzzle: M3799253sh(16)
+-------+-------+-------+
| . 7 3 | . . 4 | . . 1 |
| . . 9 | . . 6 | . 4 . |
| . 5 . | . 2 . | . 6 . |
+-------+-------+-------+
| . . . | . . . | 5 3 6 |
| . . . | . . . | . . . |
| 4 8 7 | . . . | . . . |
+-------+-------+-------+
| . 9 . | . 7 . | . 5 . |
| . 4 . | 5 . . | 6 . . |
| 3 . . | 4 . . | 9 8 . |
+-------+-------+-------+
Keith
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Marty R.



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

PostPosted: Wed Feb 23, 2011 7:52 pm    Post subject: Reply with quote

Whatever solution was there escaped me. I played an ER, M-Wing and W-Wing to no avail. A Medusa trap exposed a flightless XY-Wing with a couple of transports followed by a Medusa placement which finished things off.
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Asellus



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

PostPosted: Wed Feb 23, 2011 8:07 pm    Post subject: Reply with quote

[1] 6-cell 12DP B147[(8)r2c1=(8)r7c3] - (8)r7c6=(8)r8c5; r2c5<>8
(i.e. a simple transport of one of the <8>s in the DP)
[2] 289XYW; r6c7<>2
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keith



Joined: 19 Sep 2005
Posts: 3341
Location: near Detroit, Michigan, USA

PostPosted: Wed Feb 23, 2011 9:18 pm    Post subject: Reply with quote

After basics:
Code:
+----------------+----------------+----------------+
| 6    7    3    | 89   5    4    | 28@  29@  1    |
| 128% 12   9    | 178  38$  6    | 378  4    5    |
| 18   5    4    | 1789 2    378  | 378  6    389  |
+----------------+----------------+----------------+
| 9    12   12   | 78   4    78   | 5    3    6    |
| 5    3    6    | 2    9    1    | 48   7    48   |
| 4    8    7    | 3    6    5    | 12# -129  29   |
+----------------+----------------+----------------+
| 12   9    128% | 6    7    38   |-1234 5    234  |
| 7    4   12-8  | 5    38$  9    | 6    12#  23   |
| 3    6    5    | 4    1    2    | 9    8    7    |
+----------------+----------------+----------------+

DP noted by Asellus, I think. Either % R2C1 is 8 and/or R7C3 is 8. Note the strong link $8 in C5. Either way, R8C3 <>8. (Transport R2C1.)

Then a W-wing @# (noted by Marty?) in B369.

How sweet it is.

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Feb 23, 2011 9:32 pm    Post subject: Reply with quote

Asellus' <12> DP can be combined with coloring to perform two extra eliminations.

Code:
    Blue   Green  Blue               Green     Blue
 (8)r2c5 - r8c5 = r8c3 - <12> DP [(8)r7c3 = (8)r2c1]
 +--------------------------------------------------------------+
 |  6     7     3     |  89    5     4     |  28    29    1     |
 | B128   12    9     |  178  B38    6     |  378   4     5     |
 |  18    5     4     |  1789  2     378   |  378   6     389   |
 |--------------------+--------------------+--------------------|
 |  9     12    12    |  78    4     78    |  5     3     6     |
 |  5     3     6     |  2     9     1     |  48    7     48    |
 |  4     8     7     |  3     6     5     |  12    129   29    |
 |--------------------+--------------------+--------------------|
 |  12    9    G128   |  6     7     38    |  1234  5     234   |
 |  7     4    B128   |  5    G38    9     |  6     12    23    |
 |  3     6     5     |  4     1     2     |  9     8     7     |
 +--------------------------------------------------------------+
 # 45 eliminations remain

The Blue cells -- r2c1, r2c5, and r8c3 -- must be false. Singles complete the puzzle.

The five cell pattern connected by 4x strong links reminds me of a Broken Wing pattern where r2c4 and r2c7 act as guardian cells.
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keith



Joined: 19 Sep 2005
Posts: 3341
Location: near Detroit, Michigan, USA

PostPosted: Thu Feb 24, 2011 5:53 am    Post subject: Reply with quote

A different route: From the "after basics" grid above:

A grouped skyscraper in C67 takes out 3 in C39.

After an XY-wing -289 in C79 we are here:

Code:
+----------------+----------------+----------------+
| 6    7    3    | 89   5    4    | 28   29   1    |
| 128  12   9    | 178  38   6    | 37   4    5    |
| 18   5    4    | 1789 2    378  | 37   6    89   |
+----------------+----------------+----------------+
| 9    12   12   | 78   4    78   | 5    3    6    |
| 5    3    6    | 2    9    1    | 48   7    48   |
| 4    8    7    | 3    6    5    | 1    29   29   |
+----------------+----------------+----------------+
| 12   9    128  | 6    7    38   | 24   5    234  |
| 7    4    28   | 5    38   9    | 6    1    23   |
| 3    6    5    | 4    1    2    | 9    8    7    |
+----------------+----------------+----------------+

M-wing: 8 In R8C3 forces 8 in R1C7. R8C3 and R7C7 are pincers on 2, puzzle is solved.

Keith Cool
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Asellus



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

PostPosted: Thu Feb 24, 2011 9:29 am    Post subject: Reply with quote

daj95376 wrote:
Asellus' <12> DP can be combined with coloring to perform two extra eliminations.

Code:
    Blue   Green  Blue               Green     Blue
 (8)r2c5 - r8c5 = r8c3 - <12> DP [(8)r7c3 = (8)r2c1]
 +--------------------------------------------------------------+
 |  6     7     3     |  89    5     4     |  28    29    1     |
 | B128   12    9     |  178  B38    6     |  378   4     5     |
 |  18    5     4     |  1789  2     378   |  378   6     389   |
 |--------------------+--------------------+--------------------|
 |  9     12    12    |  78    4     78    |  5     3     6     |
 |  5     3     6     |  2     9     1     |  48    7     48    |
 |  4     8     7     |  3     6     5     |  12    129   29    |
 |--------------------+--------------------+--------------------|
 |  12    9    G128   |  6     7     38    |  1234  5     234   |
 |  7     4    B128   |  5    G38    9     |  6     12    23    |
 |  3     6     5     |  4     1     2     |  9     8     7     |
 +--------------------------------------------------------------+
 # 45 eliminations remain

The Blue cells -- r2c1, r2c5, and r8c3 -- must be false.

Danny,

I believe you were lucky in this case. Care must be taken when coloring from a DP-induced strong inference. This is actually multi-coloring:
Code:
 +--------------------------------------------------------------+
 |  6     7     3     |  89    5     4     |  28    29    1     |
 |  128B  12    9     |  178   38g   6     |  378   4     5     |
 |  18    5     4     |  1789  2     378   |  378   6     389   |
 |--------------------+--------------------+--------------------|
 |  9     12    12    |  78    4     78    |  5     3     6     |
 |  5     3     6     |  2     9     1     |  48    7     48    |
 |  4     8     7     |  3     6     5     |  12    129   29    |
 |--------------------+--------------------+--------------------|
 |  12    9     128G  |  6     7     38    |  1234  5     234   |
 |  7     4     128g  |  5     38G   9     |  6     12    23    |
 |  3     6     5     |  4     1     2     |  9     8     7     |
 +--------------------------------------------------------------+

I've revised your color markings. Two color groups, Bb and Gg, propagate from the DP strong inference. Only B and G can eliminate , or "trap," candidates (hence the elimination of <8> in r2c5). Note that bg is a weak inference pair and so cannot make eliminations. There is no "wrap" of two Bs in row 2 so we don't know the status of the <8> in r2c1 from this. (r8c3<>8 because the Gg group collapses from the elimination.)

Most multi-coloring exploits a weak inference "bridge" between two color groups. However a strong inference can also be used to bridge two groups, as was done here. In either case, one must be careful to distinguish the weak inference and strong inference color pairs and not to confuse the two separate color groups.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Feb 24, 2011 4:02 pm    Post subject: Reply with quote

Asellus: Yes, upon review, I realize that I'd applied coloring based on one direction of my logic. If I'd started at r2c1 with the assumption that Blue was true, then I could not then assume that cell r7c3 is Green. (In fact, I'd previously determined that r7c3 was always true.)

The <12> DP has a strong inference but not a weak inference!!! This is probably rephrasing your reply.

Thanks for catching my oversight.

Regards, Danny
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Fri Feb 25, 2011 3:40 pm    Post subject: Reply with quote

Three deadly pattern based steps.........

#1 6-cell ADP(12)r247[(8)r2c1=(8)r7c3-r7c6-(8)r8c5; r2c5<>8

#2. Type 1 UR(78)r34c69; r3c4<>78

#3: BUG+3: sis r2c1=1 or r6c8=2 or r7c7=2; r3c1<>1=8

Ted
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