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No XY/XYZ-Wings: Set A Puzzle 1

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Oct 26, 2008 6:24 pm    Post subject: No XY/XYZ-Wings: Set A Puzzle 1 Reply with quote

I've only had moderate success generating puzzles for the forum. It seemed that every time I went beyond XY/XYZ-Wings then the puzzles weren't suitable. Then, a recent discussion about how an XY-Wing was too easy to solve a puzzle resulted in other techniques being used to find the solution.

I went back and generated a number of puzzles that could be solved using XY/XYZ-Wings. Then I checked them hoping to find some that could/might be solved with other techniques. See what you think about this puzzle!

BTW: no cheating and substituting 3-cell XY-Chains for XY-Wings Very Happy

Code:
 +-----------------------+
 | . . . | . . 2 | . . . |
 | . . . | 9 . . | 4 5 8 |
 | . . . | 4 . . | . . . |
 |-------+-------+-------|
 | . 9 4 | 6 3 . | . 8 . |
 | . . . | 5 4 . | . 3 . |
 | 5 . . | . . 8 | . . 4 |
 |-------+-------+-------|
 | . 3 . | . . . | 2 6 . |
 | . 6 . | 2 5 . | 7 4 . |
 | . 5 . | . . 6 | . . . |
 +-----------------------+
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Sun Oct 26, 2008 7:06 pm    Post subject: Reply with quote

A puzzle that can be solved without xy-wing. Just my cup of tea!

After basics, kite (7) row 6 and col 6: r2c2<>6

Then ... (you guessed, right?)
Code:

+--------------------------+--------------------------+--------------------------+
| 13689   4       5        | 138     168     2        | 39      7       16       |
| 12367   12      167      | 9       167     137#     | 4       5       8        |
| 136789  178     16789    | 4       1678    5        | 39      2       16       |
+--------------------------+--------------------------+--------------------------+
| 127     9       4        | 6       3       17*      | 5       8       27       |
| 2678    278     678      | 5       4       9        | 1       3       27       |
| 5       17      3        | 1-7     2       8        | 6       9       4        |
+--------------------------+--------------------------+--------------------------+
| 179     3       179      | 18      189     4        | 2       6       5        |
| 189     6       189      | 2       5       13#      | 7       4       39       |
| 4       5       2        | 37*     79      6        | 8       1       39       |
+--------------------------+--------------------------+--------------------------+

Using the strong link (3) in col 6, r9c4 and r4c6 work together:

if r9c4=3 then r2c6=3 then r4c6=7 and 7 in r6c4 is toast!

...singles after that.

Nice one!!
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keith



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

PostPosted: Sun Oct 26, 2008 7:41 pm    Post subject: Reply with quote

Quote:
BTW: no cheating and substituting 3-cell XY-Chains for XY-Wings Very Happy


We meet at dawn! I will slap you with my extended wing!

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Oct 26, 2008 8:56 pm    Post subject: Reply with quote

nataraj: Now try to solve it without using the XY-Wing cells.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sun Oct 26, 2008 11:15 pm    Post subject: Reply with quote

Two steps:

[1] Using the 16 UR in r13c59:
(8)r1c4|r7c2 - UR[(8)r13c5=(7)r3c5] - (7)r2c6=(7)r4c6 - (7=1)r6c4 - (1=8)r7c4 - (8)r1c4|r7c2; r1c4|r7c2<>8

This opens up a...

[2] 13 W-Wing, c46: r2c6|r9c4<>3
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