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Set XY_03 Puzzle 040

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri Oct 16, 2009 3:39 am    Post subject: Set XY_03 Puzzle 040 Reply with quote
Code:
XY puzzles can be solved using these techniques:

Basics:  Naked/Hidden Single, Naked Pair/Triple, Locked Candidates 1/2
Basics+: Naked Quad, Hidden Pair/Triple/Quad
VH:      BUG+1, UR Type 1, X-Wing, XY-Wing
VH+:     2-String Kite, Empty Rectangle, Remote Pair, Skyscraper,
         XYZ-Wing, finned X-Wing, UR Type 2/4
XY:      gM-Wing, W-Wing, XY-Chain, BUG+2, BUG+3, other URs

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

Play this puzzle online at the Daily Sudoku site

Last edited by daj95376 on Fri Oct 16, 2009 10:16 am; edited 1 time in total
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Fri Oct 16, 2009 6:48 am    Post subject: Reply with quote
there are two w-wings on the candidates {3,9} that can be extended and each will crack the puzzle.
in picture form

this one uses the strong link on 3's in column 8


and this one uses the strong link on 3 in row 8...
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Fri Oct 16, 2009 1:28 pm    Post subject: Reply with quote
Nice work Norm! Very Happy
Another way
Code:
 *-----------------------------------------------------------*
 | 3     9     5     | 7     4     6     | 2     8     1     |
 | 17    6     8     | 3     19    2     | 79    4     5     |
 | 147   2     14    | 18    5     89    | 6     79    3     |
 |-------------------+-------------------+-------------------|
 | 2     4     39    | 5     8     1     | 39    6     7     |
 | 6     1     7     | 9     3     4     | 5     2     8     |
 | 8     5     39    | 2     6     7     | 1349  139   49    |
 |-------------------+-------------------+-------------------|
 | 5     8     6     | 14    19    39    | 1347  137   2     |
 | 149   7     14    | 6     2     38    | 38    5     49    |
 | 49    3     2     | 148   7     5     | 1489  19    6     |
 *-----------------------------------------------------------*

XY-Chain
(1=8)r3c4-(8=9)r3c6-(9=3)r7c6(3=8)r8c6-(8=3)r8c7-(3=9)r4c7-(9=7)-r2c7-(7=1)r2c1
 => r2c5,r3c13<>1 singles remain
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Fri Oct 16, 2009 5:05 pm    Post subject: Reply with quote
Quote:
Nice work Norm

you as well.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri Oct 16, 2009 5:08 pm    Post subject: Reply with quote
arkietech wrote:
Code:
 XY-Chain
(1=8)r3c4-(8=9)r3c6-(9=3)r7c6(3=8)r8c6-(8=3)r8c7-(3=9)r4c7-(9=7)r2c7-(7=1)r2c1
 => r2c5,r3c13<>1 singles remain


I like Eureka notation because it is a nice way to see and verify all of the strong/weak inferences. But, there is a lot of redundant information being recorded -- especially for XY-Chains.

Although I plan to upgrade my solver's output to match Eureka notation (so I won't have to manually alter it for listing to the forums), I'll miss the shorthand notation it uses now.

Code:
 -1r3c4 8r3c4 9r3c6 3r7c6 8r8c6 3r8c7 9r4c7 7r2c7 1r2c1 <> 1    r2c5,r3c13
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri Oct 16, 2009 6:15 pm    Post subject: Reply with quote
Although there are a couple of URs that reduce the puzzle (included below), all that's needed is the 6-cell gM-Wing (XY-Chain) to crack the puzzle in one step.

Code:
 after basics
 *--------------------------------------------------------------*
 |  3     9     5     |  7     4     6     |  2     8     1     |
 |  17    6     8     |  3     19    2     |  79    4     5     |
 |  147   2     14    |  18    5     89    |  6     79    3     |
 |--------------------+--------------------+--------------------|
 |  2     4     39    |  5     8     1     |  39    6     7     |
 |  6     1     7     |  9     3     4     |  5     2     8     |
 |  8     5     39    |  2     6     7     |  1349  139   49    |
 |--------------------+--------------------+--------------------|
 |  5     8     6     |  14    19    39    |  1347  137   2     |
 |  149   7     14    |  6     2     38    |  38    5     49    |
 |  49    3     2     |  148   7     5     |  1489  19    6     |
 *--------------------------------------------------------------*

Code:
 r46c37  <39> UR Type 1                  <> 39   [r6c7]

 *** UR 2x bivalue cells:   <14> [r38c13]   cand count =  4/2,2,3,3

 strong link on <4> in [r3] +
 strong link on <1> in [r8] => [r3c3]=4 and [r8c3]=1
 +--------------------------------------------------------------+
 |  3     9     5     |  7     4     6     |  2     8     1     |
 |  17    6     8     |  3     19    2     |  79    4     5     |
 | *14+7  2    *14    |  18    5     89    |  6     79    3     |
 |--------------------+--------------------+--------------------|
 |  2     4     39    |  5     8     1     |  39    6     7     |
 |  6     1     7     |  9     3     4     |  5     2     8     |
 |  8     5     39    |  2     6     7     |  14    139   49    |
 |--------------------+--------------------+--------------------|
 |  5     8     6     |  14    19    39    |  1347  137   2     |
 | *14+9  7    *14    |  6     2     38    |  38    5     49    |
 |  49    3     2     |  148   7     5     |  1489  19    6     |
 +--------------------------------------------------------------+
 # 37 eliminations remain

 (3=9)r4c7 - r2c7 = r2c5 - r7c5 = (9-3)r7c6 = (3)r8c6  [gM-Wing ]  <> 3    r8c7
 +--------------------------------------------------------------+
 |  3     9     5     |  7     4     6     |  2     8     1     |
 |  17    6     8     |  3    #19    2     | #79    4     5     |
 |  17    2     4     |  18    5     89    |  6     79    3     |
 |--------------------+--------------------+--------------------|
 |  2     4     39    |  5     8     1     | *39    6     7     |
 |  6     1     7     |  9     3     4     |  5     2     8     |
 |  8     5     39    |  2     6     7     |  14    139   49    |
 |--------------------+--------------------+--------------------|
 |  5     8     6     |  14   @19   @39    |  1347  137   2     |
 |  49    7     1     |  6     2    *38    |  8-3   5     49    |
 |  49    3     2     |  148   7     5     |  1489  19    6     |
 +--------------------------------------------------------------+
 # 33 eliminations remain
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Fri Oct 16, 2009 6:45 pm    Post subject: Reply with quote
Danny,
nice gm-wing extending the inner 9's

using that UR you referenced UR(14)r38c13. there are strong links on the 1 in r3c4 and the 4 in r8c9


(3=8)r8c6 - (8)r9c4 = (8)r3c4 - UR14[(1)r3c4 = (4)r8c9] - (9)r8c9 = (9)r6c9 - (9=3)r4c7; r8c7 <> 3
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Tue Oct 20, 2009 3:04 pm    Post subject: Reply with quote
I just realized that this was a new puzzle (and so is NR_069).

Anyway, I found this chain while looking for an xy-wing extension; it also solves the puzzle in one step.

(9)r2c7 - (9=3)r4c7 - (3)r6c8 = (3)r7c8 - (3=9)r7c6 - (9)r7c5 = (9)r2c5; r2c7<>9

Ted
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