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Set XY_03 Puzzle 039

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Aug 23, 2009 3:03 pm    Post subject: Set XY_03 Puzzle 039 Reply with quote
Code:
 +-----------------------+
 | . 2 . | 8 5 . | 3 . . |
 | 8 . 4 | 9 . . | . . . |
 | . 1 . | . . 7 | . . 8 |
 |-------+-------+-------|
 | 1 8 . | 2 7 . | 4 . 9 |
 | 3 . . | 1 8 . | 2 . . |
 | . . 2 | . . 9 | . . . |
 |-------+-------+-------|
 | 2 . . | 5 9 . | 7 4 . |
 | . . . | . . . | 8 9 . |
 | . . 7 | 3 . . | . . 2 |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site

If the above is too easy, then we can always remove [r4c4]=2.

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

Play this puzzle online at the Daily Sudoku site
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon Aug 24, 2009 2:08 am    Post subject: Reply with quote
interestingly, both puzzles have a coloring move on 5 and 1 toward the beginning of the solving process.
then its curtains for the first puzzle with a xy-chain.

then it gets interesting again because the xy-chain that finishes the first puzzle ends up being the second xy-chain needed to finish the second puzzle.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Aug 24, 2009 5:59 am    Post subject: Reply with quote
First Puzzle:

Code:
 after basics and Skyscrapers in <1> and <5>
 *-----------------------------------------------------------*
 | 67    2     9     | 8     5     16    | 3     167   4     |
 | 8     567   4     | 9     12    3     | 56    12    567   |
 | 56    1     3     | 4     26    7     | 9     256   8     |
 |-------------------+-------------------+-------------------|
 | 1     8     6     | 2     7     5     | 4     3     9     |
 | 3     9     5     | 1     8     4     | 2     67    67    |
 | 47    47    2     | 6     3     9     | 15    8     15    |
 |-------------------+-------------------+-------------------|
 | 2     36    8     | 5     9     16    | 7     4     136   |
 | 456   3456  1     | 7     46    2     | 8     9     36    |
 | 9     46    7     | 3     146   8     | 156   56    2     |
 *-----------------------------------------------------------*


There is an alternative to the XY-Chain. However, it's two steps that I think are difficult.

Second Puzzle: I didn't notice a workaround for the first XY-Chain, but I also didn't look very hard. The alternative for the XY-Chain in the first puzzle also works for the second XY-Chain in this puzzle.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon Aug 24, 2009 6:24 am    Post subject: Reply with quote
first puzzle using your grid after the patterns on 1 and 5
Code:
.------------------.------------------.------------------.
| 67    2     9    | 8     5     16   | 3     167   4    |
| 8     567   4    | 9     12    3    | 56    12    567  |
| 56    1     3    | 4     26    7    | 9     256   8    |
:------------------+------------------+------------------:
| 1     8     6    | 2     7     5    | 4     3     9    |
| 3     9     5    | 1     8     4    | 2     67    67   |
|*47    47    2    | 6     3     9    | 15    8     15   |
:------------------+------------------+------------------:
| 2     36    8    | 5     9     16   | 7     4     136  |
|*456   3456  1    | 7     46    2    | 8     9     36   |
| 9    *46    7    | 3    *146   8    | 156   56    2    |
'------------------'------------------'------------------'

well, you can take this useless kite on 4's and extend it.
here is the 4's... r6c1 = r8c1 - r9c2 = r9c5

7's in col 2... r1c1 = r6c1

1's and 6's in box 8 and col 6... (1)r9c5 = (1)r7c6 - (1=6)r1c6

put it all together

(7)r1c1 = (7-4)r6c1 = (4)r8c1 - (4)r9c2 = (4-1)r9c5 = (1)r7c6 - (1=6)r1c6; r1c1 <> 6
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon Aug 24, 2009 8:26 am    Post subject: Reply with quote
second puzzle:
skyscraper on 1's and finned x-wing on 5 gets to here.
Code:
.------------------.------------------.------------------.
| 679   2     69   | 8     5    *16   | 3    *167   4    |
| 8     567   4    | 9     12    3    | 56    12    567  |
| 56    1     3    | 24    246   7    | 9     256   8    |
:------------------+------------------+------------------:
| 1     8     56   | 26    7     25   | 4     3     9    |
| 3     49    59   | 1     8     45   | 2     67    67   |
| 467   467   2    | 46    3     9    | 15    8     15   |
:------------------+------------------+------------------:
| 2     36    8    | 5     9    *16   | 7     4    *136  |
| 456   3456  1    | 7     246   24   | 8     9     356  |
| 4569  469   7    | 3     146   8    | 156   56    2    |
'------------------'------------------'------------------'

you can skip the xy-chain by going back to the skyscraper on 1's and extending it
(5=1)r6c9 - (1)r7c9 = (1)r7c6 - (1)r1c6 = (1-7)r1c8 = (7)r2c9; r2c9 <> 5

which leaves a xy-wing to finish it.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Aug 24, 2009 3:55 pm    Post subject: Reply with quote
I messed up!!! Here is what I needed to get around the XY-Chain in the first puzzle -- totally unacceptable!!!

Code:
 r78c29  <36> UR Type 6                  <> 3    r7c9,r8c2
                                         <> 6    r7c2,r8c9
 *-----------------------------------------------------------*
 | 67    2     9     | 8     5     16    | 3     167   4     |
 | 8     567   4     | 9     12    3     | 56    12    567   |
 | 56    1     3     | 4     26    7     | 9     256   8     |
 |-------------------+-------------------+-------------------|
 | 1     8     6     | 2     7     5     | 4     3     9     |
 | 3     9     5     | 1     8     4     | 2     67    67    |
 | 47    47    2     | 6     3     9     | 15    8     15    |
 |-------------------+-------------------+-------------------|
 | 2    *36    8     | 5     9     16    | 7     4    *36+1  |
 | 456  *36+45 1     | 7     46    2     | 8     9    *36    |
 | 9     46    7     | 3     146   8     | 156   56    2     |
 *-----------------------------------------------------------*

 *** <46> UR [r89c25]

 UR{ (5)r8c2 = (1)r9c5 } - (1=2)r2c5 - (2=6)r3c5 - (6=5)r3c1 - (5)r8c1 = (5)r8c2
 +-----------------------------------------------------+
 |  67   2    9    |  8    5    16   |  3    167  4    |
 |  8    567  4    |  9    12   3    |  56   12   567  |
 |  56   1    3    |  4    26   7    |  9    256  8    |
 |-----------------+-----------------+-----------------|
 |  1    8    6    |  2    7    5    |  4    3    9    |
 |  3    9    5    |  1    8    4    |  2    67   67   |
 |  47   47   2    |  6    3    9    |  15   8    15   |
 |-----------------+-----------------+-----------------|
 |  2    3    8    |  5    9    16   |  7    4    16   |
 |  456 *46+5 1    |  7   *46   2    |  8    9    3    |
 |  9   *46   7    |  3   *46+1 8    |  156  56   2    |
 +-----------------------------------------------------+
 # 34 eliminations remain

   c27   X-Wing                          <> 6    r2c9,r9c5

         BUG+1                           =  6    [r1c8]

Somehow, I misplaced the last two steps from the solution while manually adding the UR chain. Sorry!!!
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Tue Aug 25, 2009 5:00 pm    Post subject: Reply with quote
For the first version of the puzzle, I used
xy-wing -467 with pivot 67 in r1c1 and a strong link on 6 in col6 to access the 46 pincer in r8c5 and delete 4 in r8c1,
skyscraper 1 in r17c6,
x-wing on 6 in r38c15,
BUG+2 condition that requires r8c2=5 or r9c7=5; both imply r9c2<>5 to complete the puzzle.

A quick look at the second version did not prove fruitful.

Ted
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