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M-wing puzzle

 
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon Dec 31, 2007 11:08 am    Post subject: M-wing puzzle Reply with quote

Also by TTHsieh:
Code:
 . 1 . | . . . | . 2 .
 2 3 . | . . . | . 4 5
 . . . | 4 . 2 | . . .
 - - - + - - - + - - -
 . . 6 | 1 7 5 | 3 . .
 . . . | 8 . 6 | . . .
 . . 8 | 2 3 4 | 1 . .
 - - - + - - - + - - -
 . . . | 5 . 7 | . . .
 5 4 . | . . . | . 7 9
 . 6 . | . . . | . 1 .
Two w-wings didn't help much, but a M-wing solved it (with UR or xy-wing).
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keith



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

PostPosted: Mon Dec 31, 2007 7:23 pm    Post subject: Reply with quote

Ravel,

I am stuck. So far i have had an XY-wing and then three W-wings:

on <79> taking out <9>
on <68> taking out <6>
on <28> taking out <2>.

But now, I am stuck:
Code:
+----------------+----------------+----------------+
| 678  1    4    | 3679 5    389  | 6789 2    678  |
| 2    3    79   | 679  168  189  | 6789 4    5    |
| 678  789  5    | 4    68   2    | 6789 3    1    |
+----------------+----------------+----------------+
| 4    29   6    | 1    7    5    | 3    89   28   |
| 13   27   13   | 8    9    6    | 47   5    247  |
| 79   5    8    | 2    3    4    | 1    69   67   |
+----------------+----------------+----------------+
| 1389 89   1239 | 5    1248 7    | 2468 68   346  |
| 5    4    123  | 36   1268 138  | 28   7    9    |
| 378  6    237  | 39   248  389  | 5    1    348  |
+----------------+----------------+----------------+

Keith
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keith



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

PostPosted: Mon Dec 31, 2007 7:33 pm    Post subject: Reply with quote

Aha!. Now I see it.

Color on the XY-wing to eliminate all except two candidates <8> in R7. That opens up the M-wing on <89> which takes out <9> in R3C1. {Edit: should be R3C2 - keith}

Then, the singles come slowly until you find the UR on <39> in C35.

Nice puzzle, thank you.

Keith


Last edited by keith on Thu Jan 03, 2008 10:49 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Mon Dec 31, 2007 10:35 pm    Post subject: Reply with quote

I did this twice. First time I used two M-Wings and finished it with the 39 UR. Second time was just one M-Wing and didn't use the UR. There were also Ws and XYs. I used pincer coloring with two of the XYs and on one of the Ws, I (for the first time) colored both pincers. A very good exercise.

Who or what is "TTHsieh"?
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keith



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

PostPosted: Mon Dec 31, 2007 10:50 pm    Post subject: Reply with quote

Marty R. wrote:
Who or what is "TTHsieh"?


Someone who posts beautiful puzzles on the sudoku.com site.

Keith
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Tue Jan 01, 2008 5:24 pm    Post subject: Reply with quote

Code:
 *--------------------------------------------------------------------*
 | 6789   1      4      | 3679   5      389    | 6789   2      678    |
 | 2      3      79     | 679    168    189    | 6789   4      5      |
 | 6789   78-9   5      | 4      68     2      | 6789   3      1      |
 |----------------------+----------------------+----------------------|
 | 4     D29     6      | 1      7      5      | 3     A89     28     |
 | 13     27     13     | 8      9      6      | 247    5      247    |
 | 79     5      8      | 2      3      4      | 1      69     67     |
 |----------------------+----------------------+----------------------|
 | 1389  C89     1239   | 5      12468  7      | 2468  B68     23468  |
 | 5      4      123    | 36     1268   138    | 268    7      9      |
 | 378    6      237    | 39     248    389    | 5      1      2348   |
 *--------------------------------------------------------------------*
Oops, i am sorry, after reading the definition now, what i meant is only a "half M-wing" Sad

It was there from the beginning. The strong link for 8 in column 8 connects A and C only in the sense, that if A=9, then C=9. In row 4 there is a strong link for 9 from A. That means, that either A and C or D must be 9.
Because r3c2 sees both C and D, the 9 can be eliminated there.
This only works with a strong link for 9 from A (using the one in column 8 to r6c8 a 9 could be eliminated from r6c2 and r7c8, but there is none).

r3c2<>9 opens an xy-wing, which solves the puzzle with triples and the UR 39 later.

What else is in the grid ?
An xy-wing to eliminate 8 from r7c9.
A w-wing 79 with strong link for 7 in column 2 to eliminate 9 from r13c1.
A w-wing 68 with strong link for 8 in column 2 to eliminate 5 from r7c5.

TTHsieh is currently the dominator in the patterns game. The goal is to find as much as possible (minimal) puzzles to a given "pattern", that have different ratings from the Sudoku Explainer program. Puzzles with rating between 4.2 (more than basics, x-wing and swordfish) and 7.3 are potentially interesting to solve.
It is fascinating, what the guys can find in shortest time for hard patterns. If you want to have any chances in the game you need a very good program, a fast computer and free time from the beginning to the end of the game (some days).
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Wed Jan 02, 2008 9:05 pm    Post subject: Reply with quote

Thanks, nice puzzle. And thanks too to Keith for the smart and attractive M-wing idea.
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