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DB Saturday Puzzle: September 15, 2007

 
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sat Sep 15, 2007 11:40 am    Post subject: DB Saturday Puzzle: September 15, 2007 Reply with quote

I have not yet completed it ...
Code:
Puzzle: DB091507  ******
+-------+-------+-------+
| . . . | . . . | . 5 . |
| . 2 7 | . . . | 3 . 4 |
| . 5 . | . . 3 | 1 9 7 |
+-------+-------+-------+
| . . 1 | 2 . 4 | . . . |
| 4 7 . | . . . | . 2 8 |
| . . . | 8 . 9 | 7 . . |
+-------+-------+-------+
| 5 4 6 | 3 . . | . 1 . |
| 7 . 3 | . . . | 5 6 . |
| . 9 . | . . . | . . . |
+-------+-------+-------+
Keith
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Earl



Joined: 30 May 2007
Posts: 546
Location: St Louis MO

PostPosted: Sat Sep 15, 2007 3:12 pm    Post subject: DB Saturday Sept 15 Reply with quote

I's stuck here. Help!

Earl


*-----------------------------------------------------------*
| 139 13 49 | 7 148 18 | 2 5 6 |
| 16 2 7 | 9 156 156 | 3 8 4 |
| 68 5 48 | 46 2 3 | 1 9 7 |
|-------------------+-------------------+-------------------|
| 89 68 1 | 2 7 4 | 69 3 5 |
| 4 7 59 | 156 3 156 | 69 2 8 |
| 23 36 25 | 8 56 9 | 7 4 1 |
|-------------------+-------------------+-------------------|
| 5 4 6 | 3 9 7 | 8 1 2 |
| 7 18 3 | 14 148 2 | 5 6 9 |
| 12 9 28 | 156 1568 1568 | 4 7 3 |
*-----------------------------------------------------------*
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Sep 15, 2007 3:58 pm    Post subject: Reply with quote

From earl's position there is an extended XY-wing with <13> pivot in r1c2 that excludes 8 from r4c1.

(Edit: Sorry about the wrong cell reference.)


Last edited by TKiel on Sat Sep 15, 2007 10:26 pm; edited 3 times in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5179
Location: Rochester, NY, USA

PostPosted: Sat Sep 15, 2007 4:00 pm    Post subject: Reply with quote

Earl's grid:

Code:
---------------------------------------
| 139 13  49 | 7   148  18   | 2  5 6 |
| 16  2   7  | 9   156  156  | 3  8 4 |
| 68  5   48 | 46  2    3    | 1  9 7 |
|--------------------------------------
| 89  68  1  | 2   7    4    | 69 3 5 |
| 4   7   59 | 156 3    156  | 69 2 8 |
| 23  36  25 | 8   56   9    | 7  4 1 |
|-------------------------------------
| 5   4   6  | 3   9    7    | 8  1 2 |
| 7   18  3  | 14  148  2    | 5  6 9 |
| 12  9   28 | 156 1568 1568 | 4  7 3 |
---------------------------------------


Two XY-Chains and a W-Wing did it for me.

Quote:
From earls; position there is an extended XY-wing (<13> pivot in r1c3 that excludes 8 from r4c1


Tracy, I guess you mean r1c2. I'm not seeing how an extension works here.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sat Sep 15, 2007 5:21 pm    Post subject: Reply with quote

From Earl's grid there is a 5-cell xy-chain that eliminates <8> in R4C1
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Sep 15, 2007 9:25 pm    Post subject: Reply with quote

XY-wing with pivot in r1c2 <13>, pincers at r2c1 <16> and r6c2 <36>. R2c1 extends to r3c1 <68>, r6c2 extends to r4c2 <68>. Probably same XY-chain used by Johan.
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Marty R.



Joined: 12 Feb 2006
Posts: 5179
Location: Rochester, NY, USA

PostPosted: Sat Sep 15, 2007 10:04 pm    Post subject: Reply with quote

TKiel wrote:
XY-wing with pivot in r1c2 <13>, pincers at r2c1 <16> and r6c2 <36>. R2c1 extends to r3c1 <68>, r6c2 extends to r4c2 <68>. Probably same XY-chain used by Johan.


In my perpetual state of confusion, I confused Extended XY-Wing with that thing you posted about a couple of days ago, which I seem to recall was an XY-Wing and you called it W-Wing with Coloring, or something like that, but it involved a three-cell chain starting with one of the pincer cells.
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Ruud



Joined: 18 Jan 2006
Posts: 31

PostPosted: Sat Sep 15, 2007 10:28 pm    Post subject: Reply with quote

It would be interesting to know how earl eliminated 8 from r9c1. The best move I could find is a Sue-De-Coq on box 1 and column 1. A rare, but beautiful move.

Ruud
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sat Sep 15, 2007 10:35 pm    Post subject: Reply with quote

The 5-cell xy-chain could also be defined like Tracy said as an extended xy-wing.
But you can also define the xy-wing as a short 3-cell xy-chain, either both ways uses the pincer-cells effect, to eliminate a candidate that can be seen by both cells.

The 5-cell xy-chain, which erases <8> in R4C1, starting with <6> in R3C1.

[86][61][13][36][68]





Code:
+-----------+---------------+--------+
|139 C13 49 | 7   148  18   | 2  5 6 |
|B16  2  7  | 9   156  156  | 3  8 4 |
|A68  5  48 | 46  2    3    | 1  9 7 |
+-----------+---------------+--------+
|-89 E68 1  | 2   7    4    | 69 3 5 |
| 4   7  59 | 156 3    156  | 69 2 8 |
| 23 D36 25 | 8   56   9    | 7  4 1 |
+-----------+---------------+--------+
| 5   4  6  | 3   9    7    | 8  1 2 |
| 7   18 3  | 14  148  2    | 5  6 9 |
| 128 9  28 | 156 1568 1568 | 4  7 3 |
+-----------+---------------+--------+

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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Sep 15, 2007 10:43 pm    Post subject: Reply with quote

Ruud,

I'm not sure how earl did it, but there is a lowly old XY-chain that does it.

<82><25><56><63><31><18> (forgive my improper notation).
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Earl



Joined: 30 May 2007
Posts: 546
Location: St Louis MO

PostPosted: Sun Sep 16, 2007 1:20 am    Post subject: DB puzzle Sept 15 Reply with quote

I used the (8) pincers of R3C1 and R8C2 (by an xy-chain 1-4-6-8) to eliminate 8 from R9C1. But I failed to see the xy-chain from R3C1 to R4C2 (6-1-3-6-8) that eliminates 8 from R4C1 and solves the puzzle.

Earl

(Edited by keith to disable smilies)
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sun Sep 16, 2007 8:39 pm    Post subject: What is this called? Reply with quote

I've been away for the weekend, driving by Tracy's town, to Chicago and back. I apologize if this has been covered. This is the pinch point:
Code:
+----------------+----------------+----------------+
| 139  13   49   | 7    148  18   | 2    5    6    |
| 16   2    7    | 9    156  156  | 3    8    4    |
| 68   5    48   | 46   2    3    | 1    9    7    |
+----------------+----------------+----------------+
| 89   68   1    | 2    7    4    | 69   3    5    |
| 4    7    59   | 156  3    156  | 69   2    8    |
| 23   36   25   | 8    56   9    | 7    4    1    |
+----------------+----------------+----------------+
| 5    4    6    | 3    9    7    | 8    1    2    |
| 7    18   3    | 14   148  2    | 5    6    9    |
| 128  9    28   | 156  1568 1568 | 4    7    3    |
+----------------+----------------+----------------+
The shortest chain seems to be in the rectangle R18C25. Sudoku Susser says:
Code:
Found a 4-link Comprehensive Chain.  If we assume that square R1C5 is <1> then we can make the following chain of conclusions:

   R8C5 must be <4> (C5 pin), which means that
   R8C2 must be <8> (R8 pin), which means that
   R1C2 must be <1> (C2 pin), which means that
   R1C5 can't be <1> (buddy contradiction).

Since this is logically inconsistent, R1C5 cannot be <1>.
What would you experts call this chain?

Keith
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Mon Sep 17, 2007 12:50 am    Post subject: Reply with quote

I'd call it an AIC (Alternate Implication Chain) that uses end-to-end strong ("conjugate") links. In Eureka notation it can be written:

[1-4]R1C5=[4-8]R8C5=[8-1]R8C2=[1]R1C2-[1]R1C5; R1C5<>1

The three links are 4=4 in C5, 8=8 in R8, and 1=1 in C2.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Mon Sep 17, 2007 1:08 am    Post subject: Reply with quote

Medusa coloring easily produces an interesting result with Keith's grid:
Code:
+-----------------+----------------+----------------+
|#13r9r 1r3g 49   | 7    148  18   | 2    5    6    |
| 16    2    7    | 9    156  156  | 3    8    4    |
| 68    5    48   | 46   2    3    | 1    9    7    |
+-----------------+----------------+----------------+
| 8r9g  6r8g 1    | 2    7    4    | 69   3    5    |
| 4     7    59   | 156  3    156  | 69   2    8    |
| 23    3r6g 25   | 8    56   9    | 7    4    1    |
+-----------------+----------------+----------------+
| 5     4    6    | 3    9    7    | 8    1    2    |
| 7     18   3    | 14   148  2    | 5    6    9    |
| 128   9    28   | 156  1568 1568 | 4    7    3    |
+-----------------+----------------+----------------+

We quickly get two "red" values in R1C1, which is not possible. So all the "r" values are eliminated (a "Medusa Wrap") and the puzzle is solved.
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