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Set XY_03 Puzzle 049

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sat Oct 31, 2009 6:10 pm    Post subject: Set XY_03 Puzzle 049 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:
 +-----------------------+
 | 8 . 2 | 6 9 . | . 4 . |
 | . . . | 2 . . | . 9 . |
 | 9 . . | . 5 . | . . . |
 |-------+-------+-------|
 | 2 9 . | 5 . 6 | . . 4 |
 | 6 . 3 | . . 9 | . . . |
 | . . . | 4 1 . | 9 6 . |
 |-------+-------+-------|
 | . . . | . . 5 | 4 . . |
 | 1 5 . | . . 2 | . 7 3 |
 | . . . | 1 . . | . 5 6 |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site

Halloween Hint wrote:
grouped 6/7-cell gM-Wing ... now that's scary!
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
PostPosted: Sun Nov 01, 2009 1:58 pm    Post subject: Reply with quote
This one was fun. I used the ?? sink. Smile
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon Nov 02, 2009 7:57 am    Post subject: Reply with quote
Code:
.------------------.------------------.------------------.
| 8     137   2    | 6     9     17   | 135   4     157  |
|*3457  1367  457  | 2     347   1478 | 136   9     178  |
| 9     1367  47   |*38    5     1478 | 136   2     178  |
:------------------+------------------+------------------:
| 2     9     1    | 5     8     6    | 7     3     4    |
| 6     4     3    | 7     2     9    | 15    8     15   |
| 57    78    578  | 4     1     3    | 9     6     2    |
:------------------+------------------+------------------:
|*37    2     678  |*38    367   5    | 4     1     9    |
| 1     5     46   | 9     46    2    | 8     7     3    |
|#347   378   9    | 1     347   478  | 2     5     6    |
'------------------'------------------'------------------'

the cells marked with a * show a skyscraper on 3's, if the 3 at the # is false.
this skyscraper would eliminate the 3 in r2c5 and r3c2.
(3)r2c1 = (3)r7c1 - (3)r7c4 = (3)r3c4

if the 3 is true at #, then
(3-4)r9c1 = (4)r9c56 - (4=6)r8c5 - (6)r8c3 = (6-8)r7c3 = (8-3)r7c4 = (3)r3c4

so either the skyscraper is true or the 3 is true in r9c1. the 3 true at r9c1 results in the 3 being true at r3c4.

put it all together into one big branched chain...
[(3)r2c1 = (3)r7c1 - (3)r7c4 = (3)r3c4] = (3-4)r9c1 = (4)r9c56 - (4=6)r8c5 - (6)r8c3 = (6-8)r7c3 = (8-3)r7c4 = (3)r3c4; r3c2 and r2c5 <> 3

this leaves skyscraper on 4 to finish.

Code:
+----------------+--------------+-------------+
| 8     13  2    | 6  9     17  | 135  4  157 |
| 7(4)  36  5    | 2  7(4)  18  | 36   9  18  |
| 9     16  7-4  | 3  5     478 | 16   2  78  |
+----------------+--------------+-------------+
| 2     9   1    | 5  8     6   | 7    3  4   |
| 6     4   3    | 7  2     9   | 15   8  15  |
| 5     7   8    | 4  1     3   | 9    6  2   |
+----------------+--------------+-------------+
| 37    2   67   | 8  367   5   | 4    1  9   |
| 1     5   6(4) | 9  6(4)  2   | 8    7  3   |
| 37-4  8   9    | 1  347   47  | 2    5  6   |
+----------------+--------------+-------------+
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Mon Nov 02, 2009 3:02 pm    Post subject: Reply with quote
My three step solution was more of the "routine" variety.

skyscraper on 4 in r38c3, which opens a
w-wing 37 in r2c5 & r7c1; a pincer transport gets an addition deletion

This results in the following code:
Code:
*-----------------------------------------------------------*
 | 8     137   2     | 6     9     17    | 135   4     157   |
 | 345#  1367  457   | 2     37    1478  | 136   9     178   |
 | 9     1367  47    | 38    5     1478  | 136   2     178   |
 |-------------------+-------------------+-------------------|
 | 2     9     1     | 5     8     6     | 7     3     4     |
 | 6     4     3     | 7     2     9     | 15    8     15    |
 | 57    78    578   | 4     1     3     | 9     6     2     |
 |-------------------+-------------------+-------------------|
 | 37#   2     678   | 38@   36    5     | 4     1     9     |
 | 1     5     46    | 9     46    2     | 8     7     3     |
 | 34#   38@   9     | 1     347   78    | 2     5     6     |

We now have a w-wing 38 marked @ in r7c4 & r9c2. In col1, we have three occurrences of digit 3, marked #. I do not know what this strong link configuration is called, but
if r9c1=3 then r9c2=8,
if r7c1=3 then r7c4=8 and r9c2=8,
if r2c1=3 then r2c5<>3, then r3c4=3, then r7c4=8
so it is possible to delete 8 inr7c3 and r9c6 to complete the puzzle.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Nov 02, 2009 4:00 pm    Post subject: Reply with quote
I'm glad to see everyone having fun with my Halloween puzzle. Here's the scary grouped 6/7-cell gM-Wing that my solver found.

Code:
 r2  b1  Locked Candidate 1              <> 5    [r2c79]
   c3b7  Locked Candidate 1              <> 6    [r23c3]

 r38c3   Skyscraper                      <> 4    [r2c5],[r9c6]

         XY-Wing  [r7c4]/[r7c1]+[r9c6]   <> 7    [r7c5],[r9c12]

 (8=3)r9c2 - r79c1 = r2c2 - r2c5 = (3-8)r3c4 = (8)r7c4 => r7c3,r9c6<>8
 +--------------------------------------------------------------+
 |  8     137   2     |  6     9     17    |  135   4     157   |
 | #347   136   5     |  2    @37    1478  |  136   9     178   |
 |  9     1367  47    | @38    5     1478  |  136   2     178   |
 |--------------------+--------------------+--------------------|
 |  2     9     1     |  5     8     6     |  7     3     4     |
 |  6     4     3     |  7     2     9     |  15    8     15    |
 |  5     78    78    |  4     1     3     |  9     6     2     |
 |--------------------+--------------------+--------------------|
 | #37    2     67-8  | *38    36    5     |  4     1     9     |
 |  1     5     46    |  9     46    2     |  8     7     3     |
 | #34   *38    9     |  1     347   7-8   |  2     5     6     |
 +--------------------------------------------------------------+
 # 47 eliminations remain

The chain could also be viewed as a grouped eW-Wing:

Code:
(8=3)r9c2 - r79c1 = r2c2 - r2c5 = r3c4 - (3=8)r7c4 => r7c3,r9c6<>8


eW-Wing: extended (by internal digit) W-Wing
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
PostPosted: Mon Nov 02, 2009 5:35 pm    Post subject: Reply with quote
I can see the x-chain forming the 38 W-wing, shown above. I see a shorter one making a "built-up" 37 W-wing.

Code:
.------------------.------------------.------------------.
| 8     137   2    | 6     9     1-7  | 135   4     157  |
|#345   1367  457  | 2    @37    148-7| 136   9     178  |
| 9     1367  47   | 38    5     148-7| 136   2     178  |
:------------------+------------------+------------------:
| 2     9     1    | 5     8     6    | 7     3     4    |
| 6     4     3    | 7     2     9    | 15    8     15   |
| 57    78    578  | 4     1     3    | 9     6     2    |
:------------------+------------------+------------------:
|#37    2     678  | 38    36    5    | 4     1     9    |
| 1     5     46   | 9     46    2    | 8     7     3    |
|#34   @38    9    | 1     34-7 @78   | 2     5     6    |
'------------------'------------------'------------------'
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oaxen



Joined: 10 Jul 2006
Posts: 96
PostPosted: Tue Nov 03, 2009 9:48 am    Post subject: Reply with quote
The 6's on row 8 looks interesting. 6 on r8c5 gives the solution in one step.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Wed Nov 04, 2009 2:04 am    Post subject: Reply with quote
I used the Type 4 UR on 15, ER on 4, Hidden UR on 57 and X-Wing on 8. Obviously, not all those steps prior to the X-Wing were necessary.
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