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Aug 30 DB

 
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
PostPosted: Sat Aug 30, 2008 3:03 pm    Post subject: Aug 30 DB Reply with quote
I needed three tricks for this August 30 DB: A UR demanded a 5 in R2C4, then two xy-chains finished it. Any one-trick wonders out there?


Earl

Code:

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

Play this puzzle online at the Daily Sudoku site
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Sat Aug 30, 2008 3:34 pm    Post subject: Reply with quote
Good puzzle! Found a ur then an xy-chain to solve it. Smile
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sat Aug 30, 2008 4:23 pm    Post subject: Reply with quote
1) Hidden UR
2) Type 1 UR
3) W-Wing
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Aug 30, 2008 7:55 pm    Post subject: Reply with quote
After a Type-1 UR on <25>:
Code:
+-------------+-------------+-------------+
| 3   2   6   | 7   158 18  | 458 9   45  |
| 4   1   7   | 58  9   3   | 568 2   56  |
| 8   5   9   | 46  46  2   | 7   1   3   |
+-------------+-------------+-------------+
| 2   7   4   | 9   3   158 | 56  568 156 |
| 6   8   13a | 2   14b 15  | 345 7   9   |
| 5   9   1-3 | 48c 7   6   | 2   38c 14  |
+-------------+-------------+-------------+
| 1   6   5   | 3   2   7   | 9   4   8   |
| 7   4   8   | 1   56  9   | 356 356 2   |
| 9   3   2   | 568 568 4   | 1   56  7   |
+-------------+-------------+-------------+
The two cells c act like <34>. There is thus an extended XY-wing abc that takes out <3> in R6C3 and solves the puzzle.

Keith
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ravel



Joined: 21 Apr 2006
Posts: 536
PostPosted: Sun Aug 31, 2008 12:01 pm    Post subject: Re: Aug 30 DB Reply with quote
Earl wrote:
Any one-trick wonders out there?
You could do it with a kind of extended w-wing. But i never would have looked for such a pattern.

In Keith's grid the w-wing 14 solves the puzzle.
When we spool it back before the UR we still can use it.
Code:
 *-----------------------------------------------------------*
 | 3     25    6     | 7     158   1258  | 458   9     45    |
 | 4     1     7     | 58    9     3     | 568   2     56    |
 | 8     25    9     | 46    46    25    | 7     1     3     |
 |-------------------+-------------------+-------------------|
 | 2     7     4     | 9     3    #158   | 56    568  #156   |
 | 6     8     13    | 2    @145  @15    | 3-45  7     9     |
 | 5     9     13    |-48    7     6     | 2     38   @14    |
 |-------------------+-------------------+-------------------|
 | 1     6     5     | 3     2     7     | 9     4     8     |
 | 7     4     8     | 1     56    9     | 356   356   2     |
 | 9     3     2     | 568   568   4     | 1     56    7     |
 *-----------------------------------------------------------*

The 1 in r4c6 implies 4 in r5c5 via the ALS 145 in r5c56.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Aug 31, 2008 3:41 pm    Post subject: Re: Aug 30 DB Reply with quote
Earl wrote:
Any one-trick wonders out there?

Before UR Type 1 and Locked Candidate 2: SIN in (abcde)

Code:
 SIN: -3r5c3  1r5c3  5r5c6  4r5c5  8r6c4  3r6c8  =>  [r5c7],[r6c3]<>3
 *-----------------------------------------------------------*
 | 3     25    6     | 7     158   1258  | 458   9     45    |
 | 4     1     7     | 58    9     3     | 568   2     56    |
 | 8     25    9     | 46    46    25    | 7     1     3     |
 |-------------------+-------------------+-------------------|
 | 2     7     4     | 9     3     158   | 56    568   156   |
 | 6     8    a13    | 2    c145  b15    | 45-3  7     9     |
 | 5     9     1-3   |d48    7     6     | 2    e38    14    |
 |-------------------+-------------------+-------------------|
 | 1     6     5     | 3     2     7     | 9     4     8     |
 | 7     4     8     | 1     56    9     | 356   356   2     |
 | 9     3     2     | 568   568   4     | 1     56    7     |
 *-----------------------------------------------------------*

After UR Type 1 and Locked Candidate 2: XY-Chain in (acde)
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada
PostPosted: Sun Aug 31, 2008 8:20 pm    Post subject: Reply with quote
Quote:
The two cells c act like <34>. There is thus an extended XY-wing abc that takes out <3> in R6C3 and solves the puzzle.


I understand extended XY-wings (are they now also called xy-chains?). But for the life of me I can't see how "The two cells c act like <34>."

Actually I don't wanna know - it's all far too abstruse and esoteric. Good words eh!
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Sun Aug 31, 2008 9:28 pm    Post subject: Reply with quote
keith wrote:
The two cells c act like <34>. There is thus an extended XY-wing abc that takes out <3> in R6C3 and solves the puzzle.


I thought I understood pseudo-cells in UR situations; basically they are confined to the row/column/box that contained it. In this situation, the digits <3> & <4> are in r6 but boxes <6> & <5> respectively. Is the pseudo-cell <34> visible in all three boxes (4,5,6)? If so, please provide the logical process to support this.

Ted
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sun Aug 31, 2008 11:38 pm    Post subject: Reply with quote
Ted,

They are a pseudo {34} because they are in peer bivalue cells with a common third digit. In this case, the <8>s happen to be conjugate, but that doesn't matter. All that matters is that the <8>s are weakly linked, which causes the <3> and <4> to be strongly linked, as they would be if they were a bivalue pair:
(3=8)cell_A - (8=4)cell_B
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sun Aug 31, 2008 11:47 pm    Post subject: Reply with quote
Danny,

I recognize your one-step method as an ALS elimination (and a nice one), but what does "SIN" stand for?
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Sep 01, 2008 12:24 am    Post subject: Reply with quote
Asellus wrote:
Danny,

I recognize your one-step method as an ALS elimination (and a nice one), but what does "SIN" stand for?

SIN: Single Implication Network

It's like a chain, except side-effect eliminations are allowed to affect cells later in the implication stream. It always ends in a contradiction, forcing the initial assumption to be false. In this case, the contradiction is [r6c3]=EMPTY. However, I felt the conjugate relationship on <3> was more important, and skipped listing the contradiction.

http://www.sudoku.com/boards/viewtopic.php?t=2859
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Tue Sep 02, 2008 2:33 am    Post subject: Reply with quote
Ouch! That other thread gave me an instant headache. It seems way overly and unnecessarily complex.

I'll stick with seeing those <3> eliminations as a 2-ALS elimination, which is, or course, just a very short ALS Chain.
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