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DB Saturday Puzzle: July 28, 2007

 
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keith



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

PostPosted: Sat Jul 28, 2007 9:50 am    Post subject: DB Saturday Puzzle: July 28, 2007 Reply with quote

Seems to me, this one requires a chain ...
Code:
Puzzle: DB072807  ******
+-------+-------+-------+
| . . 8 | . . . | 7 . . |
| . . . | 7 . 3 | . 2 5 |
| . . 7 | . 4 . | 1 9 . |
+-------+-------+-------+
| . . . | . 9 . | . . 7 |
| . 9 1 | . . . | 5 4 . |
| 3 . . | . 8 . | . . . |
+-------+-------+-------+
| . 4 2 | . 3 . | 9 . . |
| 7 1 . | 2 . 9 | . . . |
| . . 9 | . . . | 2 . . |
+-------+-------+-------+

Keith
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Earl



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

PostPosted: Sat Jul 28, 2007 5:52 pm    Post subject: DB July 28 Reply with quote

Basic technique got me here:

Code:

+---------+------------+-----------+
| 1  35 8 | 9  2   56  | 7 36   4  |
| 9  6  4 | 7  1   3   | 8 2    5  |
| 2  35 7 | 68 4   58  | 1 9    36 |
+---------+------------+-----------+
| 4  2  6 | 5  9   1   | 3 8    7  |
| 8  9  1 | 3  67  67  | 5 4    2  |
| 3  7  5 | 4  8   2   | 6 1    9  |
+---------+------------+-----------+
| 56 4  2 | 68 3   578 | 9 57   1  |
| 7  1  3 | 2  56  9   | 4 56   8  |
| 56 8  9 | 1  567 4   | 2 3567 36 |
+---------+------------+-----------+

Play this puzzle online at the Daily Sudoku site

Then I had to color 6's from R9C9 to R9C1 to eliminate some from R9; then a W-wing took care of the 7 in R9C8 and rest was a cake walk.

Perhaps there is a more direct solution.

Earl
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jLo



Joined: 30 Apr 2007
Posts: 55

PostPosted: Sat Jul 28, 2007 6:29 pm    Post subject: Re: DB July 28 Reply with quote

Earl wrote:
Basic technique got me here:

Code:

+---------+------------+-----------+
| 1  35 8 | 9  2   56  | 7 36   4  |
| 9  6  4 | 7  1   3   | 8 2    5  |
| 2  35 7 | 68 4   58  | 1 9    36 |
+---------+------------+-----------+
| 4  2  6 | 5  9   1   | 3 8    7  |
| 8  9  1 | 3  67  67  | 5 4    2  |
| 3  7  5 | 4  8   2   | 6 1    9  |
+---------+------------+-----------+
| 56 4  2 | 68 3   578 | 9 57   1  |
| 7  1  3 | 2  56  9   | 4 56   8  |
| 56 8  9 | 1  567 4   | 2 3567 36 |
+---------+------------+-----------+

Play this puzzle online at the Daily Sudoku site

Then I had to color 6's from R9C9 to R9C1 to eliminate some from R9; then a W-wing took care of the 7 in R9C8 and rest was a cake walk.

Perhaps there is a more direct solution.

Earl


You can eliminate the <5> from R7C6 because the <5> for column 8 must be
either R8C5 or R9C5. This opens up a W-wing on <56>s and solves R9C9
and reduces the puzzle to singles.
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sat Jul 28, 2007 8:49 pm    Post subject: Reply with quote

I solved it with five moves:

1) Eliminated a candidate to break up a potential deadly pattern in a rectangle

2) W-Wing

3) Type 4 rectangle

4) Skyscraper

5) W-Wing finishes it off

I make moves when I see them, so I don't know if every one of my moves was necessary.

I had a lot of fun with this one.
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Johan



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

PostPosted: Sat Jul 28, 2007 10:32 pm    Post subject: DB 28 JULY Reply with quote

It took me four steps to solve this one

1. XY-chain length 5

2. XY-chain length 4

3. Swordfish

4. XY-chain length 4
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keith



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

PostPosted: Sun Jul 29, 2007 12:47 am    Post subject: Reply with quote

In the position posted by Earl, there is a swordfish on <6> in R158.

Keith
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Asellus



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

PostPosted: Mon Jul 30, 2007 8:19 pm    Post subject: Reply with quote

Just got around to this puzzle...

I couldn't get to Earl's basic position. I needed a W-Wing on 16 in R79. That got me here:
Code:
+------------+---------------+-------------+
| 1   35   8 | 9    2   56   | 7 D36    4  |
| 9   6    4 | 7    1   3    | 8  2     5  |
| 2   35   7 |B68   4   5-68 | 1  9    C36 |
+------------+---------------+-------------+
| 4   2    6 | 5   9    1    | 3  8     7  |
| 8   9    1 | 3   67   67   | 5  4     2  |
| 3   7    5 | 4   8    2    | 6  1     9  |
+------------+---------------+-------------+
| 56  4    2 |A68  3   -678  | 9  5-67  1  |
| 7   1    3 | 2  F56   9    | 4 E56    8  |
| 56  8    9 | 1   5-67 4    | 2  35-67 36 |
+------------+---------------+-------------+

Next, there is a nice XY Loop (XY Chain that closes on itself to form a loop) which I have marked A through F. This produces all of the <6> eliminations shown.

After that, it is just a BUG+1. Done in 3 steps!
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Johan



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

PostPosted: Tue Jul 31, 2007 12:24 am    Post subject: XY-loop Reply with quote

Asellus,

I've encountered these endless XY-chains several times in puzzles.
But didn't know how to make the eliminations. So the eliminations you made on <6>, are they resulting from the strong links [AF], [BC], and [DE] in the loop, or maybe something else?
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Asellus



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

PostPosted: Tue Jul 31, 2007 6:01 pm    Post subject: Reply with quote

Johan,

Yes, it is the strong links you mention that cause the eliminations.

It is important to point out that the links in an open XY Chain are not strong links. It is only when the chain forms a closed XY Loop that strong links are formed along the chain.

In an open chain, one or both of the pincer ends may contain the shared digit. This is the basis of the eliminations from the "buddies" of the pincers. However, if the pincer ends share a common house, then the relationship becomes an either/or "strong link" and an XY Loop is formed. In such a Loop, all of the sequential links along the Loop chain are strong links and can, potentially, perform eliminations.

XY Loops are common, though often they are just circulations around related locked sets where all the eliminations have already been exploited. However, sometimes one turns up as in this puzzle where new eliminations can be exploited.
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Johan



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

PostPosted: Tue Jul 31, 2007 6:32 pm    Post subject: Reply with quote

Asellus,

Thanks for the useful info.
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