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DB Saturday Puzzle: June 23, 2007

 
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keith



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

PostPosted: Sat Jun 23, 2007 2:52 pm    Post subject: DB Saturday Puzzle: June 23, 2007 Reply with quote

Code:
Puzzle: DB062307 ******
+-------+-------+-------+
| 8 . 5 | . . . | 9 3 . |
| . . . | 8 3 . | . 5 6 |
| . . . | . . 1 | . . . |
+-------+-------+-------+
| . . . | . . 6 | 8 . 5 |
| . . 1 | . . . | 6 . . |
| 9 . 2 | 4 . . | . . . |
+-------+-------+-------+
| . . . | 6 . . | . . . |
| 1 5 . | . 2 8 | . . . |
| . 2 8 | . . . | 3 . 9 |
+-------+-------+-------+
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Earl



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

PostPosted: Sun Jun 24, 2007 12:16 pm    Post subject: Sat June 23 DB Reply with quote

I solved this with two key moves;

After standard elimination, there is a UR (parallel pairs) at R2C1&7, R3C1&7 which yields a 3 in R3C1.

After subsequent elimination, there is a skyscraper of 9's R3C2&4, R8C3&4, which eliminates the 9 in R7C2. This opens up the puzzle for solution by simple eliminations.

Any one find a more direct solution?

Earl
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Sun Jun 24, 2007 12:45 pm    Post subject: Reply with quote

A w-wing with pincers (39) does the trick on this one.

Steve
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keith



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

PostPosted: Sun Jun 24, 2007 2:41 pm    Post subject: Reply with quote

Basic methods get you here:
Code:
+-----------------+----------------+----------------+
| 8    47    5    | 27   6    24   | 9    3    1    |
| 247  1     479@ | 8    3    49@  | 27   5    6    |
| 237  379   6    | 79   5    1    | 27   4    8    |
+-----------------+----------------+----------------+
| 347  347   347  | 1    9    6    | 8    2    5    |
| 5    8     1    | 23   7    23   | 6    9    4    |
| 9    6     2    | 4    8    5    | 1    7    3    |
+-----------------+----------------+----------------+
| 347  3479% 3479@| 6    1    39@  | 5    8    2    |
| 1    5     39#  | 39   2    8    | 4    6    7    |
| 6    2     8    | 5    4    7    | 3    1    9    |
+-----------------+----------------+----------------+

The UR on <27> takes out <7> in R23C1.

But, there is a nice "Finned X-wing" on <9>. Look at the cells marked @. In the columns: Either the X-wing is true, or the cell marked # is true. Either way, the cell marked % is not true.

You can make a similar argument in the rows: Either @ or % is true. Either way, # is not true.

This (take out <9> from % and #) solves the puzzle. The UR is not needed.

Keith
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Marty R.



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

PostPosted: Sun Jun 24, 2007 3:40 pm    Post subject: Reply with quote

Code:
+-----------------+----------------+----------------+
| 8    47    5    | 27   6    24   | 9    3    1    |
| 247  1     479@ | 8    3    49@  | 27   5    6    |
| 237  379   6    | 79   5    1    | 27   4    8    |
+-----------------+----------------+----------------+
| 347  347   347  | 1    9    6    | 8    2    5    |
| 5    8     1    | 23   7    23   | 6    9    4    |
| 9    6     2    | 4    8    5    | 1    7    3    |
+-----------------+----------------+----------------+
| 347  3479% 3479@| 6    1    39@  | 5    8    2    |
| 1    5     39#  | 39   2    8    | 4    6    7    |
| 6    2     8    | 5    4    7    | 3    1    9    |
+-----------------+----------------+----------------+


I get mixed up on the terminology. Note the strong links on 9 in column 2 and row 8. R3c2 and r8c4 act as pincers to zap the 9 from r3c4 which broke open the puzzle.

Is this:

Strong links
Multi-coloring
Turbot fish
None of the above?

(Having all sorts of troubles with the site since Saturday).
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keith



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

PostPosted: Sun Jun 24, 2007 4:59 pm    Post subject: Reply with quote

Quote:
Is this:

Strong links
Multi-coloring
Turbot fish
None of the above?


Marty,

All of the above. and also known as skyscraper, sometimes as a fork.

Keith

PS: I have not noticed any problems with the site.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Sun Jun 24, 2007 5:59 pm    Post subject: Reply with quote

Curiously, the x- and w- wings are almost the same here.

This is Keith’s grid again with the finned x-wing for 9 in rows 2 and 7 marked with x:

Code:
+-------------------+---------------+----------------+
| 8     47     5    | 27   6    24  | 9    3    1    |
| 247   1     x479  | 8    3   x49  | 27   5    6    |
| 237   379    6    | 79   5    1   | 27   4    8    |
+-------------------+---------------+----------------+
| 347   347    347  | 1    9    6   | 8    2    5    |
| 5     8      1    | 23   7    23  | 6    9    4    |
| 9     6      2    | 4    8    5   | 1    7    3    |
+-------------------+---------------+----------------+
| 347  x3479  x3479 | 6    1   x39  | 5    8    2    |
| 1     5      3-9  | 39   2    8   | 4    6    7    |
| 6     2      8    | 5    4    7   | 3    1    9    |
+-------------------+---------------+----------------+

It eliminates 9 from r8c3, placing 3 in the cell.

In this copy of the grid the conjugates in the w-wing are marked w and the pincers p:

Code:
+--------------------+---------------+----------------+
| 8     47     5     | 27   6    24  | 9    3    1    |
| 247   1     w479   | 8    3   w49  | 27   5    6    |
| 237   379    6     | 79   5    1   | 27   4    8    |
+--------------------+---------------+----------------+
| 347   347    347   | 1    9    6   | 8    2    5    |
| 5     8      1     | 23   7    23  | 6    9    4    |
| 9     6      2     | 4    8    5   | 1    7    3    |
+--------------------+---------------+----------------+
| 47-3  479-3  479-3 | 6    1   p39  | 5    8    2    |
| 1     5     p39    | 9-3  2    8   | 4    6    7    |
| 6     2      8     | 5    4    7   | 3    1    9    |
+--------------------+---------------+----------------+

It eliminates 3 from r7b7, again placing 3 in r8c3.

Steve
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Sun Jun 24, 2007 8:56 pm    Post subject: Reply with quote

Marty - take a look at this:

Using Colouring put in the conjugates for 9 in two different colours:



Notice that we use green and orange for the different polarities - notice also that we have two orange cells in the same house (box 7) QED orange MUST be false. What is also great is that orange is false throughout and therefore ALL orange cells here are eliminated..!



Hooray for colouring - strong links etc.


Last edited by Mogulmeister on Sun Jun 24, 2007 9:37 pm; edited 3 times in total
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Marty R.



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

PostPosted: Sun Jun 24, 2007 9:06 pm    Post subject: Reply with quote

Quote:
All of the above. and also known as skyscraper, sometimes as a fork.


I always thought that the skyscraper was the version of strong links that formed two parallel lines, because that looked like a tall building in someone's imagination.

This puzzle can also use simple coloring on 9 with the chain of four cells starting in r8c3. It's fascinating how many different things can be done with those 9s.

For 24 hours, sometimes I couldn't get to the site, other times I got here and couldn't get to a message box, and similar problems. Seems to be OK at the moment.
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Sun Jun 24, 2007 9:15 pm    Post subject: Reply with quote

Quote:
I always thought that the skyscraper was the version of strong links that formed two parallel lines


It is ! Two parallel lines of different length.

See the skyscraper which is formed by 9's in row 2 and 8. It is an horizontal skyscraper and makes the same single elimination in r3c4..
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Marty R.



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

PostPosted: Mon Jun 25, 2007 12:42 am    Post subject: Reply with quote

Quote:
It is ! Two parallel lines of different length.


We're in agreement. But Keith--my mentor whose opinion I greatly respect--indicated that my solution, which was two basically perpendicular lines, is also called a skyscraper.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Mon Jun 25, 2007 2:34 am    Post subject: Reply with quote

Marty

In logic it does not matter what you call it: you are using two conjugates which are linked (= a fork argument) however you look at it. In terms of pattern recognition it is useful to make a distinction.

I think Keith may have meant that all the structures you mentioned solved the puzzle. All four structures below are based on 9:

(a) There is a finned x-wing in rows 2 and 7. It eliminates 9 from r8c3.

(b) There is a skyscraper in rows 2 and 8. It eliminates 9 from r2c3 and r7c2.

(c) There is (what I think is now called) a two-stringed kite in column 2 and row 8. It eliminates 9 from r2c3 just as you say.

(d) Simple colouring eliminates 9 from r2c3, r3c4, r7c2, r7c6 and r8c3 in one fell swoop.

(a), (b) and (c) are all turbot fish (grouped in case (a)).

I have an idea you were flying a kite.

Steve
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Asellus



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

PostPosted: Mon Jun 25, 2007 4:32 am    Post subject: Reply with quote

I would not have recognized the W-Wing because I thought of W-Wings based on the graphic posted elsewhere showing it in a row (or column) of Boxes with "Not X" in the "third row" of the "third box" eliminating Y from the buddies of the two bivalue cells.

This example's alternate geometry reveals a more concrete notion of the logic to me. Let me give it a try:

For a matching pair of bivalue cells, XY, if there exists a strong link in a third "House" for one of these digits, X, the two ends of which "see" the two bivalue cells, then Y can be eliminated from all "buddies" of the two bivalue cells. This is a W-Wing.

In the previous graphic (alluded to above), the "Not X" is not what's essential. It is that it implies a strong link in X in the same two rows as the bivalue cells but in the third Box (a separate house). But the third house can be anywhere. In the present example, it is Row 2.

Maybe these remarks will help clarify this concept for some others. Or... maybe not.
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Asellus



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

PostPosted: Mon Jun 25, 2007 4:35 am    Post subject: Reply with quote

PS:

I too saw the finned X-Wing on 9, but only in the rows. Interesting that it is also a finned X-Wing in columns. A two-finned mutant!!!
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Mon Jun 25, 2007 5:25 am    Post subject: Reply with quote

Quote:
I have an idea you were flying a kite


A two stringed kite by any chance ? Very Happy
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keith



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

PostPosted: Mon Jun 25, 2007 11:28 pm    Post subject: Reply with quote

Quote:
I think Keith may have meant that all the structures you mentioned solved the puzzle.


What I meant was that the logic is exactly the same. Kite, fork, skyscraper, whatever. What you look for is two strong links that "line up" on their ends (in a row, column, or box).

In my view, strong links are the key idea. All these names are a little silly.

Keith
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Tue Jun 26, 2007 5:48 am    Post subject: Reply with quote

I tend to agree and I always recommend Havard's excellent explanation
of strong links which helped me a great deal in the early days.

As a development aid and a shorthand, the patterns are helpful while the fundamental understanding is still sinking in and being assimilated - especially if, like me you are more visually orientated.
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