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Set XY_01 Puzzle 81 -- Advanced

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Apr 12, 2009 5:52 pm    Post subject: Set XY_01 Puzzle 81 -- Advanced Reply with quote
This puzzle turned out to be far more interesting than my solver's original solution indicated. For sure, bypassing the XY-Chain leaves two alternative solution paths that caught my eye. The UR path was the most interesting.

BTW: I hope you like turbot fish! Smile

Code:
 +-----------------------+
 | 3 . . | . . . | 2 . . |
 | . 8 . | . . . | . 7 . |
 | . . 6 | 2 1 . | . . 4 |
 |-------+-------+-------|
 | . . 3 | . 2 1 | . 6 . |
 | . . 5 | 3 . . | . . 7 |
 | . . . | 8 . 7 | . . 3 |
 |-------+-------+-------|
 | 1 . . | . . . | 3 . 5 |
 | . 3 . | 7 . . | . . . |
 | . . 4 | . 3 6 | 7 . 9 |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site

Code:
   c9b3  Naked  Pair                     <> 16   [r2c7]

         XY-Wing  [r5c6]/[r3c6]+[r4c4]   <> 5    [r12c4]

   c4b2  Naked  Pair                     <> 46   [r2c5]
 r2      Naked  Pair                     <> 59   [r2c13]

         turbot fish/ER r4b3             <> 9    [r1c2]
         turbot fish/ER r2b5             <> 9    [r5c7]
         turbot fish/ER r3b5             <> 9    [r6c2]
         turbot fish/ER c5b3             <> 9    [r6c8]

         Skyscraper c38                  <> 9    [r5c2],[r6c7]

   c2    Naked  Quad                     <> 1245 [r34c2]

----- ----- ----- ----- ----- ----- closing moves

 W-Wing: 4/9 in r4c7,r6c5 connected by 9 in r2c57 => r6c7<>4
 W-Wing: 2/5 in r6c8,r9c2 connected by 5 in r1c28 => r6c2<>2
 W-Wing: 1/4 in r5c7,r6c2 connected by 4 in r4c17 => r5c2,r6c7<>1

 <14> UR in [r56c27]
 [r56c2]=2             => [r6c3]<>2
 [r 6c7]=5 => [r6c8]=2 => [r6c3]<>2
 +-----------------------------------------------------+
 |  3    145  19   |  46   7    8    |  2    59   16   |
 |  24   8    12   |  46   59   3    |  59   7    16   |
 |  57   79   6    |  2    1    59   |  8    3    4    |
 |-----------------+-----------------+-----------------|
 |  47   79   3    |  5    2    1    |  49   6    8    |
 |  8    124  5    |  3    6    49   |  14   29   7    |
 |  6    124  129  |  8    49   7    |  145  25   3    |
 |-----------------+-----------------+-----------------|
 |  1    6    7    |  9    8    2    |  3    4    5    |
 |  9    3    8    |  7    45   45   |  6    1    2    |
 |  25   25   4    |  1    3    6    |  7    8    9    |
 +-----------------------------------------------------+
 # 35 eliminations remain

 -2r2c3  1r2c3  9r1c3  5r1c8  2r6c8  [XY-Chain] <> 2 [r6c3]


Last edited by daj95376 on Sun Apr 19, 2009 2:41 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Tue Apr 14, 2009 5:01 am    Post subject: Reply with quote
I never saw any UR possibilities that I could do anything with, nor did I bypass the XY-Chain. My typical scattershot approach took me through an XY-Wing (495), coloring, two multi-colorings and two ERs, all on 9, a W-Wing (25) with pincer transport and a finishing XY-Chain.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Tue Apr 14, 2009 1:04 pm    Post subject: Reply with quote
I had an experience similar to Marty, including a lack of useful URs.

Most steps involved digit <4> & <9>: a skyscraper <9>, kite <4>, w-wing <49>, and coloring <9> twice. I finished with a w-wing <25> and w-wing <14>.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Tue Apr 14, 2009 5:01 pm    Post subject: Reply with quote
Ted: Your <49> W-Wing destroyed a <4> present in my UR.

Marty: I didn't reconstruct your solution, but it's possible that you also eliminated a candidate in my UR.

Code:
 probable grid before W-Wing (or my 4-cell XY-Chain)

 <14> UR in [r56c27]
 [r56c2]=2             => [r6c3]<>2
 [r 6c7]=5 => [r6c8]=2 => [r6c3]<>2
 +-----------------------------------------------------+
 |  3    145  19   |  46   7    8    |  2    59   16   |
 |  24   8    12   |  46   59   3    |  59   7    16   |
 |  57   79   6    |  2    1    59   |  8    3    4    |
 |-----------------+-----------------+-----------------|
 |  47   79   3    |  5    2    1    |  49   6    8    |
 |  8    14+2 5    |  3    6    49   |  14   29   7    |
 |  6    14+2 19-2 |  8    49   7    |  14+5 25   3    |
 |-----------------+-----------------+-----------------|
 |  1    6    7    |  9    8    2    |  3    4    5    |
 |  9    3    8    |  7    45   45   |  6    1    2    |
 |  25   25   4    |  1    3    6    |  7    8    9    |
 +-----------------------------------------------------+
 # 35 eliminations remain
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