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Jan 24 DB

 
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
PostPosted: Sat Jan 24, 2009 1:15 pm    Post subject: Jan 24 DB Reply with quote
The Jan 24 DB is a poser. An xy-chain opened an xy-wing which solved it. Another more direct route?

Earl

Code:

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

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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sat Jan 24, 2009 6:39 pm    Post subject: Reply with quote
I couldn't find the XY-Chain, but I'm sure it's solvable with Medusa. But there's a trial-and-error method that isn't very satisfying, a Finned XY-Wing.

Code:

+---------+------------+-------------+
| 7  6  4 | 8   5  39  | 29  23  1   |
| 3  9  1 | 6   4  2   | 7   8   5   |
| 2  8  5 | 39  1  7   | 469 346 469 |
+---------+------------+-------------+
| 1  7  3 | 2   69 45  | 8   456 469 |
| 69 45 8 | 7   69 1   | 3   45  2   |
| 69 45 2 | 45  3  8   | 69  1   7   |
+---------+------------+-------------+
| 4  2  6 | 159 8  59  | 15  7   3   |
| 5  3  9 | 14  7  6   | 124 24  8   |
| 8  1  7 | 345 2  345 | 456 9   46  |
+---------+------------+-------------+

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There is a Finned XY-Wing on 593, pivoted in r7c6. If r9c4 = 35, then the 3 and the one in r1c6 are pincers of an XY-Wing. However, using this Wing leads to an invalidity. Thus, r9c4 must = 4, which solves the puzzle.
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
PostPosted: Sat Jan 24, 2009 8:23 pm    Post subject: Reply with quote
I'd use an ALS to do it in one from the posted markup.
Code:

.---------------.---------------.----------------.
| 7    6    4   | 8    5    39  |@29    3-2   1  |
| 3    9    1   | 6    4    2   | 7     8    5   |
| 2    8    5   | 39   1    7   | 469   346  469 |
:---------------+---------------+----------------:
| 1    7    3   | 2    69   45  | 8    #456  469 |
| 69   45   8   | 7    69   1   | 3    #45   2   |
| 69   45   2   | 45   3    8   |@69    1    7   |
:---------------+---------------+----------------:
| 4    2    6   | 159  8    59  | 15    7    3   |
| 5    3    9   | 14   7    6   | 14-2 #24   8   |
| 8    1    7   | 345  2    345 | 456   9    46  |
'---------------'---------------'----------------'


I didn't spot this as an ALS, I was looking for xy-chains.
The cells 456 and 45 can have at most one five. That makes the two cells an effective 46 one cell, for column 8. The 24 pair in column 8 completes the xy. OK, I did it from the other end and was looking for an xy-wing. Mentally I made the 456-45 pair a single 46 and the 29-69 pair a 26. To me that seems a "normal" xy-wing. Did I tell you I'm not "normal"? Smile
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sat Jan 24, 2009 9:53 pm    Post subject: Reply with quote
wapati wrote:
Did I tell you I'm not "normal"?

Nothing abnormal about that to me! But then, maybe that makes two of us.

Any ALS contains a strong inference between all instances of any two of its digits. In a bivalue ALS, this is easy: there are only two digits with only one instance each. But, it isn't really all that more complicated in larger ALS.

First, consider that ALS elimination. The 3-cell 2456 ALS in r458c7 contains the strong inference (2)r8c8=(6)r4c8 and the 2-cell 269 ALS contains (6)r6c7=(2)r1c7. Put them together and:
ALSr458c7[(2)r8c8=(6)r4c8] - ALS[(6)r6c7=(2)r1c7]; r1c8|r8c7<>2

The weakly linked <6>s are the "restricted common" (or "shared exclusive") digit, and the <2>s are the "shared common" pincers. I don't bother showing the cell references for the second ALS since the cell references inside the brackets fully describe the ALS.

Next, that ALS chain (or "XY Wing" with two "pseudocells"):
(2=4)r8c8 - ALS[(4)r45c7=(6)r4c7] - (6=9)r6c7 - (9=2)r1c7; r1c8|r8c7<>2
The only difference here is that the <4>s in the 2-cell 456 ALS must be grouped together: (4)r45c7. And, it is important that both of those <4>s, as a group, can "see" the <4> at r8c8.

Also, to write it as the "XY Wing" we combine the two last bivalues into a single ALS (as we did in the first case, above):
(2=4)r8c8 - ALS[(4)r45c7=(6)r4c7] - ALS[(6)r6c7=(2)r1c7]; r1c8|r8c7<>2

These are all various ways of seeing the same thing.
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