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Another not difficult (? ) Menneske

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Nov 30, 2008 3:19 am    Post subject: Another not difficult (? ) Menneske Reply with quote
This one is rated Very Hard (0). After an XYZ-wing, I am at a loss. Still working on it.

Code:
Puzzle: M543856vh
+-------+-------+-------+
| . . 6 | . . . | 2 . . |
| . 3 . | . 4 . | . 9 . |
| 2 8 . | . 7 . | . 3 1 |
+-------+-------+-------+
| . . . | . 2 4 | . . . |
| . 2 4 | 9 . 5 | 6 1 . |
| . . . | 6 1 . | . . . |
+-------+-------+-------+
| 1 9 . | . 6 . | . 4 5 |
| . 7 . | . 8 . | . 6 . |
| . . 2 | . . . | 1 . . |
+-------+-------+-------+


Keith
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Nov 30, 2008 3:33 am    Post subject: Reply with quote
After basics and the XYZ-wing:
Code:
+-------------------+-------------------+-------------------+
| 457   14    6     | 138   9     138   | 2     578   78    |
| 57    3     157   | 128   4     128   | 578   9     6     |
| 2     8     9     | 5     7     6     | 4     3     1     |
+-------------------+-------------------+-------------------+
| 36789 16    137   | 78    2     4     | 35789 578   39    |
| 78    2     4     | 9     3     5     | 6     1     78    |
| 3789  5     378   | 6     1     78    | 3789  2     4     |
+-------------------+-------------------+-------------------+
| 1     9     38    | 237   6     237   | 78    4     5     |
| 345   7     35    | 134   8     139   | 39    6     2     |
| 3468  46    2     | 347   5     379   | 1     78    39    |
+-------------------+-------------------+-------------------+

Quote:
Aha! A W-wing <78> taking out <7> in R6C7 R7C6.


Still working ...

Keith
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Nov 30, 2008 3:42 am    Post subject: Reply with quote
...

Quote:
A W-wing <78> taking out <8> in R4C8.

A W-wing <57> that takes out <7> in R4C1.

A W-wing <57> that (with coloring) takes out <5> in R2C3.


... working ...
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sun Nov 30, 2008 9:46 am    Post subject: Reply with quote
keith if you aren't done then close your eyes.

Code:
.---------------------.---------------------.---------------------.
|*457    14     6     | 138    9      138   | 2      578    78    |
|*57     3     #157   | 128    4      128   |5-78    9      6     |
| 2      8      9     | 5      7      6     | 4      3      1     |
:---------------------+---------------------+---------------------:
| 36789  16     1378  | 78     2      4     | 35789  578    39    |
|#78     2      4     | 9      3      5     | 6      1      78    |
| 3789   5      378   | 6      1      78    | 3789   2      4     |
:---------------------+---------------------+---------------------:
| 1      9      38    | 237    6      237   |#78     4      5     |
| 345    7      35    | 134    8      139   | 39     6      2     |
|#3468   46     2     | 347    5      379   | 1     #78     39    |
'---------------------'---------------------'---------------------'

1.extended w-wing (7)r2c3 = (7)r12c1 - (7=8)r5c1 - (8)r9c1 = (8)r9c8 - (8=7)r7c7; r2c7 <> 7

2. (8=5)r2c7 - (5=7)r2c1 - (7)r5c1 = (7)r5c9 - (7=8)r1c9; r1c8 <> 8
the same cells form a xy-chain

3. xy-wing {5,7,8}...(7=8)r7c7 - (8=5)r2c7 - (5=7)r1c8; r9c8 <> 7

gets it to here
Code:
.---------------------.---------------------.---------------------.
| 45     14     6     | 138    9      138   | 2     #57     78    |
|#57     3     1-57   | 128    4      128   |#58     9      6     |
| 2      8      9     | 5      7      6     | 4      3      1     |
:---------------------+---------------------+---------------------:
|36-789  16     137   | 78     2      4     | 3589  #57     39    |
|#78     2      4     | 9      3      5     | 6      1     #78    |
|3-789   5      37    | 6      1      78    | 389    2      4     |
:---------------------+---------------------+---------------------:
| 1      9      8     | 23     6      23    | 7      4      5     |
| 345    7      35    | 14     8      19    | 39     6      2     |
| 346    46     2     | 47     5      79    | 1      8      39    |
'---------------------'---------------------'---------------------'

extended w-wing loop since the ends end in the same row.
4. (5)r2c7 = (5)r1c8 - (5=7)r4c8 - (7)r5c9 = (7)r5c1 - (7=5)r2c1; r2c3 <> 5 and r46c1 <> 7

then

Code:
.------------------.------------------.------------------.
| 45    14    6    | 138   9     138  | 2     57    78   |
| 57    3     17   | 128   4     128  | 58    9     6    |
| 2     8     9    | 5     7     6    | 4     3     1    |
:------------------+------------------+------------------:
| 689   16   #137  | 78    2     4    | 3589  57   #39   |
| 78    2     4    | 9     3     5    | 6     1     78   |
| 89    5    #37   | 6     1    #78   | 389   2     4    |
:------------------+------------------+------------------:
| 1     9     8    | 23    6     23   | 7     4     5    |
| 34    7     5    | 14    8    1-9   |#39    6     2    |
| 346   46    2    | 47    5    #79   | 1     8    #39   |
'------------------'------------------'------------------'

5. (9=3)r8c7 - (3)r9c9 = (3)r4c9 - (3)r4c3 = (3-7)r6c3 = (7)r6c6 - (7=9)r9c6; r8c6 <> 9
this basically follows the useless m-wing on {3,9} around, but doesn't jump back to 9. instead follows 3 to 7
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Nov 30, 2008 6:34 pm    Post subject: Reply with quote
Nothing brilliant or even interesting.

Code:
XYZ-Wing, Skyscraper, short chain, long XY-Chain, short XY-Chain.

It sure would be nice to see a solution from the puzzle source. There appears to be plenty of potential for a UR or DP. Unfortunately, too much potential for me.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Tue Dec 02, 2008 12:47 am    Post subject: Reply with quote
daj95376 wrote:
There appears to be plenty of potential for a UR or DP.

You picqued my interest. After basics without the XYZ Wing:
Code:
+--------------------+-----------------+----------------+
| 457    14   6      | 138    9  138   | 2      578  78 |
| 57     3   $157    | 1[28]  4  1[28] | 578    9    6  |
| 2      8    9      | 5      7  6     | 4      3    1  |
+--------------------+-----------------+----------------+
| 36789  16   13[78] |[78]    2  4     | 35789  578  39 |
| 78     2    4      | 9      3  5     | 6      1    78 |
| 3789   5    3[78]  | 6      1 [78]   | 3789   2    4  |
+--------------------+-----------------+----------------+
| 1      9   $38     | 3[27]  6  3[27] | 78     4    5  |
| 345    7    35     | 134    8  139   | 39     6    2  |
| 3468   46   2      | 347    5  379   | 1      78   39 |
+--------------------+-----------------+----------------+

There is an 8-cell DP as marked. The <1> and <3> in the cells marked $ are weakly linked as a result since if they are both true, the DP results. (One might note that the potential 78 NP in r46c3 is invalid due to r5c1 so why not just use that? To do so, I would have to group the <3>s in r78c3, which isn't as useful.) This can be denoted as: DP[(1)r2c3-(3)r7c3]. A simple bit of Medusa multi-coloring using this weak link bridge reveals:
(8-6)r9c1=(6)r9c2 - (6=1)r4c2 - (1)r4c3=DP[(1)r2c3 - (3)r7c3]=(8)r7c3 - (8)r9c1; r9c1<>8

Most often it is an induced strong inference that is exploited in a DP. But this shows that the weak inference created between exterior candidates that force the DP can also be useful.

The grid becomes:
Code:
+----------------+-------------+--------------+
| 45     14  6   | 138  9  138 | 2     57  78 |
| 57     3   157 | 128  4  128 | 58    9   6  |
| 2      8   9   | 5    7  6   | 4     3   1  |
+----------------+-------------+--------------+
| 36789  16  137 | 78   2  4   | 3589  57  39 |
| 78     2   4   | 9    3  5   | 6     1   78 |
| 3789   5   37  | 6    1  78  | 389   2   4  |
+----------------+-------------+--------------+
| 1      9   8   | 23   6  23  | 7     4   5  |
| 345    7   35  | 14   8  19  | 39    6   2  |
| 346    46  2   | 47   5  79  | 1     8   39 |
+----------------+-------------+--------------+

At this point, those two 57 W-Wings with transport can be applied. They can also be viewed as a Remote Naked Pair with transport, since a "double W-Wing" is a RNP. Alternately, the same eliminations occur via a continuous AIC loop:
(7)r2c1=(7-1)r2c3=(1-4)r1c2=(4-5)r1c1=(5-7)r1c8=(7)r4c8 - (7)r5c9=(7)r5c1 - (7)r2c1:Loop; r46c1<>7, r2c3<>5

This gets us here where we can use a UR:
Code:
+---------------+-------------+----------------+
| 45    14  6   | 138  9  138 | 2      57   78 |
| 57    3   17  | 128  4  128 | 58     9    6  |
| 2     8   9   | 5    7  6   | 4      3    1  |
+---------------+-------------+----------------+
| 6[89] 16  137 |$78   2  4   | 35[89] 57  $39 |
| 78    2   4   | 9    3  5   | 6      1    78 |
| [89]  5   37  | 6    1  78  | 3[89]  2    4  |
+---------------+-------------+----------------+
| 1     9   8   | 23   6  23  | 7      4    5  |
| 34    7   5   | 14   8  19  | 39     6    2  |
| 346   46  2   | 47   5  79  | 1      8    39 |
+---------------+-------------+----------------+

In this case, we use an "almost Type 4" 89UR. If r4c9 is <3> the resulting Type 4 UR requires r4c4=8. If r4c9 is not <3>, then:
r9c9=3 => r9c12=46 => r9c4=7 => r4c4=8.
Thus, r4c4=8.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Tue Dec 02, 2008 1:09 am    Post subject: Reply with quote
Thank you, all!

I think I got more than I thought I was signing up for!

Keith
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