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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Mar 15, 2008 1:27 pm Post subject: Another interesting Menneske |
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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
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| Posted: Sat Mar 15, 2008 3:40 pm Post subject: Another |
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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
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| Posted: Sat Mar 15, 2008 6:09 pm Post subject: |
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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
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| Posted: Sat Mar 15, 2008 6:14 pm Post subject: |
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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
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| Posted: Sat Mar 15, 2008 7:58 pm Post subject: |
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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
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| Posted: Sat Mar 15, 2008 9:21 pm Post subject: |
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| 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
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| Posted: Sat Mar 15, 2008 9:53 pm Post subject: |
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| 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
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| Posted: Sat Mar 15, 2008 11:27 pm Post subject: |
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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
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| Posted: Sat Mar 15, 2008 11:46 pm Post subject: |
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| Thanks Keith. |
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