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VanHegan 4-16200063

 
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Wed Jun 11, 2014 8:46 am    Post subject: VanHegan 4-16200063 Reply with quote

Interesting ending. Something Danny Jones suggested a long time ago.

Code:

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

Play this puzzle online at the Daily Sudoku site

Keith
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JC Van Hay



Joined: 13 Jun 2010
Posts: 370
Location: Charleroi, Belgium

PostPosted: Wed Jun 11, 2014 9:33 am    Post subject: Reply with quote

Code:
+-----------------+-----------------+-----------------+
| 5(6)  1     2   | 3     4    9    | 5(6)  7   8     |
| 9     7     56  | 568   158  16   | 2     3   4     |
| 8     4     3   | 56    2    7    | 1     59  (69)  |
+-----------------+-----------------+-----------------+
| 1     2     568 | 5678  589  3    | 4     59  679   |
| 34    9     568 | 5678  158  146  | 568   2   367   |
| (34)  5-6   7   | 2     589  (46) | 568   1   (369) |
+-----------------+-----------------+-----------------+
| 2     3     4   | 1     7    8    | 9     6   5     |
| 5(6)  5(6)  9   | 4     3    2    | 7     8   1     |
| 7     8     1   | 9     6    5    | 3     4   2     |
+-----------------+-----------------+-----------------+
[6r8c2=6r8c1-6r1c1=6r1c9-(6=9)r3c9-(9=346)r6c169]-(6=5)r6c2; ste
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arkietech



Joined: 31 Jul 2008
Posts: 1723
Location: Northwest Arkansas USA

PostPosted: Wed Jun 11, 2014 11:22 am    Post subject: Reply with quote

Code:
  *-----------------------------------------------------------*
 |a56    1     2     | 3     4     9     |b56    7     8     |
 | 9     7     56    | 568   158   16    | 2     3     4     |
 | 8     4     3     | 56    2     7     | 1     59   b69    |
 |-------------------+-------------------+-------------------|
 | 1     2     568   | 5678  589   3     | 4     59    679   |
 | 34    9     568   | 5678  158   146   | 568   2     367   |
 | 34   c56    7     | 2     589  c46    | 568   1    c369   |
 |-------------------+-------------------+-------------------|
 | 2     3     4     | 1     7     8     | 9     6     5     |
 | 5-6  d56    9     | 4     3     2     | 7     8     1     |
 | 7     8     1     | 9     6     5     | 3     4     2     |
 *-----------------------------------------------------------*
6=5)r1c1-(5=9)r1c7,r3c9-(9=5)r6c269-(5=6)r8c2 => -6r8c1; ste
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 12, 2014 8:09 am    Post subject: Reply with quote

After basics:
Code:
+----------------+----------------+----------------+
|d56   1    2    | 3    4    9    |e56   7    8    |
| 9    7    56   | 568  158  16   | 2    3    4    |
| 8    4    3    | 56   2    7    | 1    59  f69   |
+----------------+----------------+----------------+
| 1    2    568  | 5678 589  3    | 4    59   679  |
| 34   9    568  | 5678 158  146  | 568  2    367  |
| 34  a56   7    | 2    589  46   | 568  1    3-69 |
+----------------+----------------+----------------+
| 2    3    4    | 1    7    8    | 9    6    5    |
|c56  b56   9    | 4    3    2    | 7    8    1    |
| 7    8    1    | 9    6    5    | 3    4    2    |
+----------------+----------------+----------------+

Coloring on 6: af are pincers taking out 6 in R6C9.
Code:
+----------------+----------------+----------------+
|#56   1    2    | 3    4    9    |*56   7    8    |
| 9    7    56   | 568  158  16   | 2    3    4    |
| 8    4    3    | 56   2    7    | 1    59  d69   |
+----------------+----------------+----------------+
| 1    2    568  | 5678 589  3    | 4    59   679  |
| 34   9    568  | 5678 158  146  | 568  2    367  |
|b34  *56   7    | 2    589 a46   | 568  1   c39   |
+----------------+----------------+----------------+
| 2    3    4    | 1    7    8    | 9    6    5    |
|*56  #56   9    | 4    3    2    | 7    8    1    |
| 7    8    1    | 9    6    5    | 3    4    2    |
+----------------+----------------+----------------+

Extended XY-wing: ad are pincers on 6.
*# Coloring on 5. * must be 5.

Danny suggested this years ago: Pincers on 6 here make pincers on 5.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Thu Jun 12, 2014 3:24 pm    Post subject: Reply with quote

I don't know what an Extended XY-Wing is. A-b-c-d looks to be an XY-Chain and transporting the 6 from a to r1c1 solves it. Also don't understand how pincers on 6 create pincers on 5. But then, there's all sorts of stuff I don't understand.

(6=5)r1c1-r2c3=r45c3-(5=6)r6c2-(6=4)r6c6-(4=3)r6c1-(3=9)r6c9-(9=6)r3c9=>r1c7<>6

Code:
+----------------+----------------+----------------+
|#56   1    2    | 3    4    9    |*56   7    8    |
| 9    7    56   | 568  158  16   | 2    3    4    |
| 8    4    3    | 56   2    7    | 1    59  d69   |
+----------------+----------------+----------------+
| 1    2    568  | 5678 589  3    | 4    59   679  |
| 34   9    568  | 5678 158  146  | 568  2    367  |
|b34  *56   7    | 2    589 a46   | 568  1   c39   |
+----------------+----------------+----------------+
| 2    3    4    | 1    7    8    | 9    6    5    |
|*56  #56   9    | 4    3    2    | 7    8    1    |
| 7    8    1    | 9    6    5    | 3    4    2    |
+----------------+----------------+----------------+
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 12, 2014 10:36 pm    Post subject: Reply with quote

Marty,

If pincers on 6 both see cells 56, those 56 cells must be pincers on 5.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Fri Jun 13, 2014 1:54 am    Post subject: Reply with quote

OK, Thanks, I think I understand.
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arkietech



Joined: 31 Jul 2008
Posts: 1723
Location: Northwest Arkansas USA

PostPosted: Fri Jun 13, 2014 2:18 am    Post subject: Reply with quote

keith wrote:
Marty,

If pincers on 6 both see cells 56, those 56 cells must be pincers on 5.

Keith


What if both pincers were 6?
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Fri Jun 20, 2014 7:49 am    Post subject: Reply with quote

arkietech wrote:
keith wrote:
Marty,

If pincers on 6 both see cells 56, those 56 cells must be pincers on 5.

Keith


What if both pincers were 6?

The logic is, one or both pincers are 6. If they each see a cell 56, then one or both of those 56 cells is 5. They are pincers on 5.

There is a more subtle discussion if it is known that one, but not both, of the pincers is 6. You get into the possibility that the 56 cells are a remote pair, which is not the case here.

In this case, we know the 56 cells are the same: They must both be 5.

Keith
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