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XY-wings (Nightmare March 17, 2006)

 
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keith



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

PostPosted: Tue Mar 21, 2006 1:31 am    Post subject: XY-wings (Nightmare March 17, 2006) Reply with quote

Similarly, the St. Patrick's Day puzzle is dripping with XY-wings. Here is the starting point:

Code:


+-------------------+-------------------+-------------------+
| 6     13489 1248  | 5     2489  189   | 7     38    18    |
| 12357 13789 12578 | 2789  6     1789  | 138   4     158   |
| 1457  1478  14578 | 478   478   3     | 168   9     2     |
+-------------------+-------------------+-------------------+
| 457   478   3     | 46789 45789 2     | 689   1     6789  |
| 9     178   15678 | 678   3578  5678  | 2368  23678 4     |
| 47    2     4678  | 1     34789 6789  | 5     3678  6789  |
+-------------------+-------------------+-------------------+
| 8     6     1247  | 3     2579  579   | 1249  257   1579  |
| 2347  5     247   | 26789 1     6789  | 24689 2678  6789  |
| 127   17    9     | 2678  2578  4     | 1268  25678 3     |
+-------------------+-------------------+-------------------+



And, if you wing on <7>, you may catch a swordfish!

Best wishes,

Keith
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Wed Mar 22, 2006 12:25 am    Post subject: I'm not good with xy-wings Reply with quote

Hi, Keith!

I liked this puzzle because I found a "6-star constellation" in it. I did have to find one xy-wing a bit later to finish it off entirely. dcb
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Marty R.



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

PostPosted: Wed Mar 22, 2006 5:43 pm    Post subject: Reply with quote

Keith, I was not able to find any XY-Wings or swordfish, but two X-Wings and two forcing chains did the trick.
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keith



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

PostPosted: Fri Mar 24, 2006 9:31 am    Post subject: Winging it Reply with quote

Using standard methods (pinned squares, naked sets, and intersections), you can get to this point:

Code:


+----------------+----------------+----------------+
| 6    39   2    | 5    4    19   | 7    38   18   |
| 7    39   8    | 2    6    19   | 13   4    5    |
| 1    4    5    | 78   78   3    | 6    9    2    |
+----------------+----------------+----------------+
| 5    78   3    | 4    789  2    | 89   1    6    |
| 9    178  167  | 678  3578 5678 | 238  2378 4    |
| 4    2    67   | 1    3789 678  | 5    378  789  |
+----------------+----------------+----------------+
| 8    6    14   | 3    2    57   | 149  57   19   |
| 3    5    47   | 9    1    678  | 248  2678 78   |
| 2    17   9    | 678  578  4    | 18   5678 3    |
+----------------+----------------+----------------+



There are three XY-wings in the puzzle:

Squares R9C2, R9C7 and R4C2 form an XY-Wing pattern on <8>.
R4C7 - can remove <8> from <89> leaving <9>.

Squares R2C7, R9C7 and R1C8 form an XY-Wing pattern on <8>.
R8C8 - can remove <8> from <2678> leaving <267>.
R9C8 - can remove <8> from <5678> leaving <567>.

Squares R9C7, R7C9 and R4C7 form an XY-Wing pattern on <9>.
R7C7 - can remove <9> from <149> leaving <14>.
R6C9 - can remove <9> from <789> leaving <78>.

Removing the <8>'s reveals another XY-wing:

Squares R9C7, R9C2 and R8C9 form an XY-Wing pattern on <7>.
R8C3 - can remove <7> from <47> leaving <4>.
R9C8 - can remove <7> from <567> leaving <56>.

Removing the <7>'s reveals a totally unneeded swordfish on <7> in rows R3, R4, and R9. Rather, simply note that R9C2 (in Block 7) must be <7>.

You do not have to find all of these to solve the puzzle.

Best wishes,

Keith
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Fri Mar 24, 2006 2:46 pm    Post subject: A five-star constellation Reply with quote

I didn't have to do anything too tricky to arrive at the following position.
Code:
  6    39     2     5     4    19     7    38    18*
  7    39     8     2     6    19    13     4     5
  1     4     5    78    78     3     6     9     2
  5    78     3     4    789    2    89     1     6
  9    178   167   678  3578  5678   238  2378    4
  4     2    67     1   3789   678    5    378   789
  8     6    14     3     2    57    149   57    19
  3     5    47     9     1    678   248  2678   78
  2    17     9    678   578    4    18   5678    3

The five-star constellation is rooted in r1c9:

A. r1c9 = 8 ==> r8c9 = 7 ==> r8c3 = 4 ==> r7c3 = 1 ==> r7c9 = 9
B. r1c9 = 1 ==> r7c9 = 9

So r7c9 = 9; after this discovery the puzzle presents no special difficulties, except for an XY-Wing from r8c9 that allows one to eliminate a "6". dcb
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