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Set A Puzzle 30

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Nov 28, 2008 10:36 pm    Post subject: Set A Puzzle 30 Reply with quote

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

Play this puzzle online at the Daily Sudoku site
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sat Nov 29, 2008 3:00 am    Post subject: Reply with quote

I found a three-step solution: An ER followed by two xy-wings.

Hint:
Quote:
ER on <6> in box2 with strong link on <6> in row6, a xy-wing on <289> and then on <689>.

Ted
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Dec 09, 2008 10:14 pm    Post subject: Reply with quote

that ER that Marty mentioned had me evaluating this puzzle again and this came up.

notice the "*" marked cells belown contain the almost UR {2,5} in r58c23
Code:
.------------------.------------------.------------------.
| 5     26    268  | 168   4     238  | 7     13    9    |
| 29    1     3    | 7     5     29   | 8     6     4    |
| 7     4     689  | 1689  16    389  | 5     13    2    |
:------------------+------------------+------------------:
| 689   3     169  | 4     16    89   | 2     7     5    |
| 28   *25   *125  | 18    3     7    | 4     9     6    |
| 4     7     69   | 69    2     5    | 3     8     1    |
:------------------+------------------+------------------:
| 3     8     4    | 5     9     6    | 1     2     7    |
| 26   *256  *256  | 3     7     1    | 9     4     8    |
| 1     9     7    | 2     8     4    | 6     5     3    |
'------------------'------------------'------------------'

notice also that an inference can be made.

if the 1 in r5c3 is not there then the 6's in r8c23 have to be true. and vice versa. this is a strong link, they both can't be false. (1)r5c3 = (6)r8c23...ok?

lets put this little chunk to work

Code:
.------------------.------------------.------------------.
| 5     26    268  | 168   4     238  | 7     13    9    |
| 29    1     3    | 7     5     29   | 8     6     4    |
| 7     4     689  | 1689  16    389  | 5     13    2    |
:------------------+------------------+------------------:
|#689   3     169  | 4    #16    89   | 2     7     5    |
| 28    25   #125  |-18    3     7    | 4     9     6    |
| 4     7     69   | 69    2     5    | 3     8     1    |
:------------------+------------------+------------------:
| 3     8     4    | 5     9     6    | 1     2     7    |
|#26   #256  #256  | 3     7     1    | 9     4     8    |
| 1     9     7    | 2     8     4    | 6     5     3    |
'------------------'------------------'------------------'

now we can form a w-wing Exclamation Exclamation Exclamation yep. see the strong links on 6 in column 1?

we now have a w-wing {1,6} via strong link on 6 in column 1. this connects our pseudocell {1,6} to the {1,6} in r4c5. 1's are the pincers eliminating the 1 in r5c4.

singles to finish.

hopefully this image will be helpful.


I circled the w-wing pair in green ! and I connected the links on 6 in blue, the red is the pincer elimination.

what this shows is how the {1,6} pseudocell is formed via the almost UR and how they can be encompassed because they are part of the UR structure thus forming the strong link necessary, like a bivalue cell Idea

I will take a shot at notating this.

(25UR)r58c23[(1)r5c3 = (6)r8c23] - (6)r8c1 = (6)r4c1 - (6=1)r4c5; r5c4 <> 1
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