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Another interesting Menneske

 
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keith



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

PostPosted: Sat Mar 15, 2008 1:27 pm    Post subject: Another interesting Menneske Reply with quote

Can you solve it without the BUG?
Code:
Puzzle: M6733444sh(14)
+-------+-------+-------+
| . . 5 | . . . | . . . |
| 1 . . | 8 . 6 | . . . |
| . . . | 5 2 1 | . . 8 |
+-------+-------+-------+
| . 1 8 | . . . | 7 4 . |
| . . 4 | . 5 . | 9 . . |
| . 9 6 | . . . | 2 5 . |
+-------+-------+-------+
| . . . | 3 9 2 | . . . |
| . . . | 6 . 7 | . . 4 |
| . . 9 | . . . | 1 . . |
+-------+-------+-------+

Keith
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Sat Mar 15, 2008 3:40 pm    Post subject: Another Reply with quote

An xy-chain with pincers of 2 at R1C1 and R9C9, the R9C9 arm extended by coloring (R1C9, R2C8), eliminates 2 from R2C3 and opens the puzzle. Not very sophisticated, but it worked.

Earl
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sat Mar 15, 2008 6:09 pm    Post subject: Reply with quote

After basics the <2> in R2C3 can be eliminated using the strong links on <2> in R2 and C8 and the strong link on <3> in R9, which succumbs the puzzle.

R2C3=2 => R2C8≠2 => R9C8=2 => R9C2=3 => R8C3=2 <=> R2C3≠2

Code:
+-------------------------+-------------------------+------------------------+
| 268       2368      5   | 9         37        4   | 36        1        27  |
| 1         4        =237 | 8         37        6   | 5        ≠237      9   |
| 9         36        37  | 5         2         1   | 4         367      8   |
+-------------------------+-------------------------+------------------------+
| 5         1         8   | 2         6         9   | 7         4        3   |
| 27        27        4   | 1         5         3   | 9         8        6   |
| 3         9         6   | 7         4         8   | 2         5        1   |
+-------------------------+-------------------------+------------------------+
| 4         678       1   | 3         9         2   | 68        67       5   |
| 28        5        =23  | 6         1         7   | 38        9        4   |
| 67       =367       9   | 4         8         5   | 1        =2367     27  |
+-------------------------+-------------------------+------------------------+
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Marty R.



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

PostPosted: Sat Mar 15, 2008 6:14 pm    Post subject: Reply with quote

M-Wing (36) with coloring
Finned X-Wing (6)
XY-Wing (28-27-78 )
XY-Wing (37-27-23) with coloring

Or, starting with Johan's grid:

Code:
+-------------------------+-------------------------+------------------------+
| 268       2368      5   | 9         37        4   | 36        1        27  |
| 1         4        =237 | 8         37        6   | 5        ≠237      9   |
| 9         36        37  | 5         2         1   | 4         367      8   |
+-------------------------+-------------------------+------------------------+
| 5         1         8   | 2         6         9   | 7         4        3   |
| 27        27        4   | 1         5         3   | 9         8        6   |
| 3         9         6   | 7         4         8   | 2         5        1   |
+-------------------------+-------------------------+------------------------+
| 4         678       1   | 3         9         2   | 68        67       5   |
| 28        5        =23  | 6         1         7   | 38        9        4   |
| 67       =367       9   | 4         8         5   | 1        =2367     27  |
+-------------------------+-------------------------+------------------------+


The Finned X-Wing on 6 in rows 37 take out the 6 from r9c8 and r7c2, setting up the XY-Wing 78-28-27 pivoted in r7c2, leaving us here.

Code:
+-------------------------+-------------------------+------------------------+
| 28        368       5   | 9         37        4   | 36        1        27  |
| 1         4         237 | 8         37        6   | 5         237      9   |
| 9         36        37  | 5         2         1   | 4         367      8   |
+-------------------------+-------------------------+------------------------+
| 5         1         8   | 2         6         9   | 7         4        3   |
| 7         2         4   | 1         5         3   | 9         8        6   |
| 3         9         6   | 7         4         8   | 2         5        1   |
+-------------------------+-------------------------+------------------------+
| 4         78        1   | 3         9         2   | 68        67       5   |
| 28        5         23  | 6         1         7   | 38        9        4   |
| 6         37        9   | 4         8         5   | 1         237      27  |
+-------------------------+-------------------------+------------------------+


Now the XY-Wing on 37-23-27, pivoted in r9c2, and coloring the pincer from r8c3-->r8c1-->r1c1 takes out the 2 from r1c9.
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keith



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

PostPosted: Sat Mar 15, 2008 7:58 pm    Post subject: Reply with quote

After basics:
Code:
+----------------+----------------+----------------+
| 268  2368 5    | 9    37   4    | 36   1    27   |
| 1    4    237  | 8    37   6    | 5    237  9    |
| 9    36c  37   | 5    2    1    | 4    367  8    |
+----------------+----------------+----------------+
| 5    1    8    | 2    6    9    | 7    4    3    |
| 27   27   4    | 1    5    3    | 9    8    6    |
| 3    9    6    | 7    4    8    | 2    5    1    |
+----------------+----------------+----------------+
| 4   -678  1    | 3    9    2    | 68   67   5    |
| 28   5    23   | 6    1    7    | 38   9    4    |
| 67a  367b 9    | 4    8    5    | 1    2367 27   |
+----------------+----------------+----------------+

The XYZ-wing abc takes out <6> in R7C2. Leading to an XY-wing that takes out <2> in R5C1. Which brings us to:
Code:
+-------------+-------------+-------------+
| 28 -368 5   | 9   37@ 4   | 36  1   27# |
| 1   4   237 | 8   37  6   | 5   237 9   |
| 9   36  37  | 5   2   1   | 4   367 8   |
+-------------+-------------+-------------+
| 5   1   8   | 2   6   9   | 7   4   3   |
| 7   2   4   | 1   5   3   | 9   8   6   |
| 3   9   6   | 7   4   8   | 2   5   1   |
+-------------+-------------+-------------+
| 4   78  1   | 3   9   2   | 68  67  5   |
| 28  5   23  | 6   1   7   | 38  9   4   |
| 6   37@ 9   | 4   8   5   | 1   237 27# |
+-------------+-------------+-------------+

The cells <37> @ are a W-link with the strong link on <7> # in C9. Takes out <3> in R1C2. Leading to here:
Code:
+-------------+-------------+-------------+
| 28  68  5   | 9   37a 4   | 36b 1   27e |
| 1   4   237 | 8   37@ 6   | 5   237 9   |
| 9   36  37  | 5   2   1   | 4   367 8   |
+-------------+-------------+-------------+
| 5   1   8   | 2   6   9   | 7   4   3   |
| 7   2   4   | 1   5   3   | 9   8   6   |
| 3   9   6   | 7   4   8   | 2   5   1   |
+-------------+-------------+-------------+
| 4   78  1   | 3   9   2   | 68  67  5   |
| 28  5   23d | 6   1   7   | 38c 9   4   |
| 6   37@ 9   | 4   8   5   | 1   237 2-7 |
+-------------+-------------+-------------+

The cells <37> @ are a W-link with the strong links on <3> abcd. Coloring in R1 from a to e extends the pincer, taking out <7> in R9C9, solving the puzzle.

The first time I solved it there was a really nice half M-wing, but I do not see it now.

Keith
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Marty R.



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

PostPosted: Sat Mar 15, 2008 9:21 pm    Post subject: Reply with quote

Quote:

The first time I solved it there was a really nice half M-wing, but I do not see it now.

Keith,

Can you, without going to a lot of trouble, refresh my memory and tell me what an M-Wing ÷ 2 is?
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keith



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

PostPosted: Sat Mar 15, 2008 9:53 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:

The first time I solved it there was a really nice half M-wing, but I do not see it now.

Keith,

Can you, without going to a lot of trouble, refresh my memory and tell me what an M-Wing ÷ 2 is?


http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143

Look at the last post.

An M-wing starts with a complementary pair:

XY=X=XY

where = is a strong link. What you can say is, the end cells have the same value, they are a complementary pair. An M-wing is obtained by adding a strong link for Y on either end:

Y=XY=X=XY
or
XY=X=XY=Y

Any cell that sees both ends cannot be Y.

Ravel pointed out the "half" M-wing: Suppose you start with

XY-X=XY
a-b=c

where - is a weak link. If the first cell (a) is X, so is the last (c). But, the converse is NOT true. If c is X, you can make no statement about a.

So, you can add on the right a strong link for Y:

XY-X=XY=Y

Any cell that sees both ends cannot be Y. If you add a link on the left:

Y=XY-X=XY

there is no pincer. Hence, the "half" wing.

Keith
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sat Mar 15, 2008 11:27 pm    Post subject: Reply with quote

after basics, you can color on 3,
then multicolor on 6 which eliminates two 6's.

then the 2,7,8 xy-wing

which leaves you with the xy-chain, 27-37-36-28 removes 2 in r1c9
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Marty R.



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

PostPosted: Sat Mar 15, 2008 11:46 pm    Post subject: Reply with quote

Thanks Keith.
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