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Another Menneske, with a tough first step!

 
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sun Oct 18, 2009 3:48 pm    Post subject: Another Menneske, with a tough first step! Reply with quote

Code:
Puzzle: M6798876sh(17)
+-------+-------+-------+
| . . . | . 8 5 | 7 . . |
| . . . | . . . | . . . |
| . 3 9 | 6 . . | . 4 . |
+-------+-------+-------+
| . 6 . | . . . | . 3 . |
| 5 . . | . . . | 2 . . |
| 3 9 . | . 7 . | . . 4 |
+-------+-------+-------+
| . 2 . | . . 3 | . . . |
| . . . | 7 . . | . 1 9 |
| 6 . 8 | . . 4 | . . 5 |
+-------+-------+-------+

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5061
Location: Rochester, NY, USA

PostPosted: Sun Oct 18, 2009 8:23 pm    Post subject: Reply with quote

Two steps.

Quote:
Finned X-Wing on 8 exposed a W-Wing on 12. The latter created locked candidates on 1 which finished it off
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sun Oct 18, 2009 8:36 pm    Post subject: Reply with quote

Marty R. wrote:
Two steps.

Quote:
Finned X-Wing on 8 exposed a W-Wing on 12. The latter created locked candidates on 1 which finished it off


This is from Multi-step Marty Question Shocked My solution is much more complicated!
Keith Very Happy Very Happy
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keith



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

PostPosted: Sun Oct 18, 2009 8:43 pm    Post subject: Reply with quote

Marty,

That is very elegant!

Keith
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Sun Oct 18, 2009 9:30 pm    Post subject: Reply with quote

Keith, what is the starting point for this 1st step? Is it the SSTS position? There are the usual singles and whatnot from the position above.
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Mon Oct 19, 2009 12:39 am    Post subject: Reply with quote

Don,

After basics, I get here:
Code:
+-------------------+-------------------+-------------------+
| 12    14    6     | 1234  8     5     | 7     9     123   |
| 1278  148   5     | 12349 12349 1279  | 168   68    12368 |
| 1278  3     9     | 6     12    127   | 5     4     128   |
+-------------------+-------------------+-------------------+
| 18    6     47    | 12458 1245  128   | 9     3     178   |
| 5     18    47    | 13489 13469 1689  | 2     678   1678  |
| 3     9     2     | 18    7     168   | 168   5     4     |
+-------------------+-------------------+-------------------+
| 9     2     1     | 58    56    3     | 4     678   678   |
| 4     5     3     | 7     26    268   | 68    1     9     |
| 6     7     8     | 19    19    4     | 3     2     5     |
+-------------------+-------------------+-------------------+
By first step, I meant, after basics.

I will post my solution in a few minutes.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5061
Location: Rochester, NY, USA

PostPosted: Mon Oct 19, 2009 12:42 am    Post subject: Reply with quote

Quote:
That is very elegant!

Thank you. Keep in mind the old saying, "Even a blind pig finds an acorn once in a while." Laughing
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Mon Oct 19, 2009 1:05 am    Post subject: Reply with quote

Code:
+-------------------+-------------------+-------------------+
| 12    14    6     |-1234  8     5     | 7     9     123   |
| 1278  148   5     |-12349 -1-2349 1279| 168   68    12368 |
| 1278  3     9     | 6     12a   127   | 5     4     128   |
+-------------------+-------------------+-------------------+
| 18    6     47    |-1245-8 -1-245 128 | 9     3     178   |
| 5     18    47    |-134-89 -134-69 1689| 2     678   1678  |
| 3     9     2     | 18d   7     168   | 168   5     4     |
+-------------------+-------------------+-------------------+
| 9     2     1     | 58e   56e   3     | 4     678   678   |
| 4     5     3     | 7     26f   2-68  | 68    1     9     |
| 6     7     8     | 19c   19b   4     | 3     2     5     |
+-------------------+-------------------+-------------------+

abcdef..a is an XY-loop. a and f are pincers of an XY-chain, but since they are in the same house, they make a reversible loop. Any two adjacent cells in the chain are pincers in their common candidate. Therefore, you can make the eliminations shown.

Maybe my notation in the diagram is not entirely correct, but it should show:
Quote:

One of R3C5 and R8C5 must be <2>.
One of R8C5 and R7C5 must be <6>.
One of R7C5 and R7C4 must be <5>.
One of R7C4 and R6C4 must be <8>.
One of R6C4 and R9C4 must be <1>.
One of R9C4 and R9C5 must be <9>.
One of R9C5 and R3C5 must be <1>.

Thus:

R2C5 - cannot contain <2> because of R3C5 and R8C5.
R4C5 - cannot contain <2> because of R3C5 and R8C5.
R8C6 - cannot contain <6> because of R8C5 and R7C5.
R5C5 - cannot contain <6> because of R8C5 and R7C5.
R4C4 - cannot contain <8> because of R7C4 and R6C4.
R5C4 - cannot contain <8> because of R7C4 and R6C4.
R1C4 - cannot contain <1> because of R6C4 and R9C4.
R2C4 - cannot contain <1> because of R6C4 and R9C4.
R4C4 - cannot contain <1> because of R6C4 and R9C4.
R5C4 - cannot contain <1> because of R6C4 and R9C4.
R2C5 - cannot contain <1> because of R9C5 and R3C5.
R4C5 - cannot contain <1> because of R9C5 and R3C5.
R5C5 - cannot contain <1> because of R9C5 and R3C5.


Leading to here:
Code:
+-------------------+-------------------+-------------------+
| 12    14    6     | 234   8     5     | 7     9     123   |
| 1278  148   5     | 2349  349   1279  | 168   68    12368 |
| 1278  3     9     | 6     12    127   | 5     4     128   |
+-------------------+-------------------+-------------------+
| 18    6     47    | 245   45    128   | 9     3     178   |
| 5     18    47    | 349   349   1689  | 2     678   1678  |
| 3     9     2     | 18    7     168   | 168   5     4     |
+-------------------+-------------------+-------------------+
| 9     2     1     | 58    56    3     | 4     678   678   |
| 4     5     3     | 7     26    28    | 68    1     9     |
| 6     7     8     | 19    19    4     | 3     2     5     |
+-------------------+-------------------+-------------------+
which still has a few advanced steps to a solution.

What amazes me is that Marty's finned 8 X-wing is still in the above grid, and is a completely different path. Here it is:
Code:
+-------------------+-------------------+-------------------+
| 12    14    6     | 234   8     5     | 7     9     123   |
| 1278  148   5     | 2349  349   1279  | 168   68    12368 |
| 1278  3     9     | 6     12    127   | 5     4     128   |
+-------------------+-------------------+-------------------+
| 18    6     47    | 245   45    12-8  | 9     3     178   |
| 5     18    47    | 349   349   16-89 | 2     678   1678  |
| 3     9     2     | 18#   7     168@  | 168@  5     4     |
+-------------------+-------------------+-------------------+
| 9     2     1     | 58    56    3     | 4     678   678   |
| 4     5     3     | 7     26    28@   | 68@   1     9     |
| 6     7     8     | 19    19    4     | 3     2     5     |
+-------------------+-------------------+-------------------+

Either the X-wing @ is true, or # is true. Either way, R45C6 cannot be 8.

Keith


Last edited by keith on Mon Oct 19, 2009 1:07 am; edited 1 time in total
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Mon Oct 19, 2009 1:06 am    Post subject: Reply with quote

Marty R. wrote:
Quote:
That is very elegant!

Thank you. Keep in mind the old saying, "Even a blind pig finds an acorn once in a while." Laughing

In this case, more like a truffle!

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Oct 19, 2009 1:59 am    Post subject: Reply with quote

After basics and Marty's excellent finned X-Wing, there's his W-Wing and this XY-Chain:

Code:
 XY-Chain a-b-c-d-e
 +-----------------------------------------------------------------------+
 |  12     14     6      |  1234   8      5      |  7      9      123    |
 |  1278   148    5      |  12349  12349  1279   |  168    68     12368  |
 |  1278   3      9      |  6      12     127    |  5      4      128    |
 |-----------------------+-----------------------+-----------------------|
 |  18     6      47     |  12458  145-2 a12     |  9      3      178    |
 |  5      18     47     |  13489  13469  169    |  2      678    167    |
 |  3      9      2      | b18     7      168    |  168    5      4      |
 |-----------------------+-----------------------+-----------------------|
 |  9      2      1      | c58    d56     3      |  4      678    678    |
 |  4      5      3      |  7     e26     68-2   |  68     1      9      |
 |  6      7      8      |  19     19     4      |  3      2      5      |
 +-----------------------------------------------------------------------+
 # 83 eliminations remain

In addition, there's the shortest SIN (Single Implication Network) that I recall seeing in some time:

Code:
                        [r4c6]=1
             /                   \
 [r8c6]=2 =>                       contradiction; => [r8c6]<>2
             \                   /
               [r6c6]=8 [r6c4]=1
 +-----------------------------------------------------------------------+
 |  12     14     6      |  1234   8      5      |  7      9      123    |
 |  1278   148    5      |  12349  12349  1279   |  168    68     12368  |
 |  1278   3      9      |  6      12     127    |  5      4      128    |
 |-----------------------+-----------------------+-----------------------|
 |  18     6      47     |  12458  1245   12     |  9      3      178    |
 |  5      18     47     |  13489  13469  169    |  2      678    167    |
 |  3      9      2      |  18     7      168    |  168    5      4      |
 |-----------------------+-----------------------+-----------------------|
 |  9      2      1      |  58     56     3      |  4      678    678    |
 |  4      5      3      |  7      26     268    |  68     1      9      |
 |  6      7      8      |  19     19     4      |  3      2      5      |
 +-----------------------------------------------------------------------+
 # 83 eliminations remain

Yes, it can be represented as a short chain, but the simplicity is lost.
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Mon Oct 19, 2009 10:47 pm    Post subject: Reply with quote

Code:
+-------------------+-------------------+-------------------+
| 12    14    6     | 1234  8     5     | 7     9     123   |
| 1278  148   5     | 12349 12349 1279  | 168   68    12368 |
| 1278  3     9     | 6     12    127   | 5     4     128   |
+-------------------+-------------------+-------------------+
| 18    6     47    | 12458 1245  128   | 9     3     178   |
| 5     18    47    | 13489 13469 1689  | 2     678   1678  |
| 3     9     2     | 18    7     168   | 168   5     4     |
+-------------------+-------------------+-------------------+
| 9     2     1     | 58    56    3     | 4     678   678   |
| 4     5     3     | 7     26    268   | 68    1     9     |
| 6     7     8     | 19    19    4     | 3     2     5     |
+-------------------+-------------------+-------------------+


Here's a 2-step pattern-solving ALS-chain alternative (rc=restricted common):

Step 1: Dual-linked ALS:
Set A(1589)r679c4 -> rc5 & rc9 -> Set B(12569)r3789c5

Elims: 1 in r1245c4, 1 in r245c5, 8 in r45c4, 2 in r24c5, 6 in r5c5

Step 2: 3-set ALS chain:
Set A(123489)r12569c4 -> rc2 -> Set B(123459)r23459c5 -> rc5 -> Set C(2568)r7c5/r8c56

Thus: r7c4<>8=5
stte
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Thu Oct 22, 2009 1:14 am    Post subject: Reply with quote

Marty R. wrote:
Two steps.

Quote:
Finned X-Wing on 8 exposed a W-Wing on 12. The latter created locked candidates on 1 which finished it off


Great move Marty! I love to see those finned and Kraken solutions.

Ted
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