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sept 19
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Wed Sep 19, 2007 6:12 am    Post subject: sept 19 Reply with quote

This is where I got with basic moves:
Code:

+--------------------------+--------------------------+--------------------------+
| 2       7       5        | 19      19      6        | 4       8       3        |
| 6       8       9        | 5       4       3        | 2       1       7        |
| 1       3       4        | 2       8       7        | 6       9       5        |
+--------------------------+--------------------------+--------------------------+
| 48      29      3        | 7       69      45       | 58      26      1        |
| 5       1       6        | 3       2       8        | 9       7       4        |
| 7       249     28       | 49      569     1        | 3       256     268      |
+--------------------------+--------------------------+--------------------------+
| 9       45      7        | 48      35      2        | 1       3456    68       |
| 348     245     128      | 6       135     9        | 7       2345    28       |
| 348     6       128      | 148     7       45       | 58      2345    9        |
+--------------------------+--------------------------+--------------------------+


The short skyscraper/kitelike chain in '2':
-(r6c9)=(r8c9)-(r9c8)=(r9c3)-
leaves 8 in r6c3 and the puzzle is solved.

Took me a while to spot, I had hoped for x,xy,xyz,w or other wings but no such luck (or just plain shortsighted who knows Wink )
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tippwell



Joined: 19 Sep 2007
Posts: 9

PostPosted: Wed Sep 19, 2007 10:03 am    Post subject: Reply with quote

45 in r9c6 along with r7c4 and r9c7 eliminates some 8s in boxes 8 and 9
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TKiel



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

PostPosted: Wed Sep 19, 2007 10:55 am    Post subject: Reply with quote

I made the same exclusion as nataraj but saw it as a finned X-wing.
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sdq_pete



Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL

PostPosted: Wed Sep 19, 2007 12:43 pm    Post subject: Reply with quote

There's an XY wing with pivot at R9C6 which eliminates 8 from R9C4 - however it doesn't open the puzzle.
I reached the following position:
Code:

+-------------+-----------+------------+
| 2   7   5   | 19 19  6  | 4  8    3  |
| 6   8   9   | 5  4   3  | 2  1    7  |
| 1   3   4   | 2  8   7  | 6  9    5  |
+-------------+-----------+------------+
| 48  29  3   | 7  69  45 | 58 26   1  |
| 5   1   6   | 3  2   8  | 9  7    4  |
| 7   49  28  | 49 56  1  | 3  56   28 |
+-------------+-----------+------------+
| 9   45  7   | 8  35  2  | 1  345  6  |
| 348 245 128 | 6  135 9  | 7  2345 28 |
| 348 6   128 | 14 7   45 | 58 2345 9  |
+-------------+-----------+------------+

Play this puzzle online at the Daily Sudoku site
The "almost square" of 28, with 128 at R8C3 enabled the elimination of 8's at R8C1 and R9C3. Then there was still an XY wing with pivot at R7C2 eliminating 3 in R8C5, an X-wing on 5's in C's 6 & 7 eliminating 5 in R9C8 and finally an XY wing with pivot at R9C8.
Seems all over-complicated though.

Peter
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George Woods



Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK

PostPosted: Wed Sep 19, 2007 3:09 pm    Post subject: A False UR gives the clue! Reply with quote

Using Peter's position, I was intreagued by the quad of 28,28,28, and 128 and thinking that this was a potential UR, I realised it is a false one (Unfortuately if one presses ahead and puts a 1 in r8c3 - a solution emerges- but this is yet another lucky mistake)

However looking at the 28s it seems very clear that a 2 in r8c9 leads to a 2 in r6c3 and so a 2 in r8 c2 Oh dear two 2's in row 8 Hence r8c9 must be 8 and it all falls out.

Once again I haven't seen how to transpose this into a standard move!

Looking again at the pattern of 28s They almost form what I might call "Gift wrapping" with 28s tying the imaginary parcel with tails both of which uses all the available cells for 2 in the box, Hence 2 is not allowed on the same line as the "tail extension" - I find this easier to visualise than to describe!
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Wed Sep 19, 2007 3:40 pm    Post subject: Reply with quote

I also couldn't find any wings, but the skyscraper on 2 did the job.
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sdq_pete



Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL

PostPosted: Wed Sep 19, 2007 4:01 pm    Post subject: Re: A False UR gives the clue! Reply with quote

George Woods wrote:
Oh dear two 2's in row 8 Hence r8c9 must be 8 and it all falls out.

You could also turn it round and say, 2 at R8C9 eliminates other 2's on that row (including in Box 7), and the consequent 2 at R6C3 eliminates also the 2's in C3 (including box 7). But that eliminates therefore all 2's in Box 7. Hence...

Actually I also like the logic of nataraj - but is that a skyscraper??

Peter
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Wed Sep 19, 2007 4:35 pm    Post subject: Reply with quote

Quote:
Actually I also like the logic of nataraj - but is that a skyscraper??


It isn't in my terminology, but some people would call it a skyscraper. I call it strong links. In my terminology, "skyscraper" is the version of strong links where the two strong links are parallel, a pattern that allegedly looks like a brick-and-mortar skyscraper.

My skyscraper was on the 2s in rows 4 and 9.
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KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Wed Sep 19, 2007 4:51 pm    Post subject: Reply with quote

Marty

This is where I am in this puzzle. Could you possibly explain the skyscraper - I thought I understood them, but I cannot follow it in this puzzle.

Thanks so much
Kathy

Code:

+-------------+-----------+------------+
| 2   7   5   | 19 19  6  | 4  8    3  |
| 6   8   9   | 5  4   3  | 2  1    7  |
| 1   3   4   | 2  8   7  | 6  9    5  |
+-------------+-----------+------------+
| 48  29  3   | 7  69  45 | 58 26   1  |
| 5   1   6   | 3  2   8  | 9  7    4  |
| 7   49  28  | 49 56  1  | 3  56   28 |
+-------------+-----------+------------+
| 9   45  7   | 8  35  2  | 1  345  6  |
| 348 245 128 | 6  135 9  | 7  2345 28 |
| 38  6   128 | 14 7   45 | 58 235  9  |
+-------------+-----------+------------+

Play this puzzle online at the Daily Sudoku site
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isabel



Joined: 19 Sep 2007
Posts: 1

PostPosted: Wed Sep 19, 2007 5:37 pm    Post subject: Re: sept 19 Reply with quote

nataraj wrote:
This is where I got with basic moves:
Code:

+--------------------------+--------------------------+--------------------------+
| 2       7       5        | 19      19      6        | 4       8       3        |
| 6       8       9        | 5       4       3        | 2       1       7        |
| 1       3       4        | 2       8       7        | 6       9       5        |
+--------------------------+--------------------------+--------------------------+
| 48      29      3        | 7       69      45       | 58      26      1        |
| 5       1       6        | 3       2       8        | 9       7       4        |
| 7       249     28       | 49      569     1        | 3       256     268      |
+--------------------------+--------------------------+--------------------------+
| 9       45      7        | 48      35      2        | 1       3456    68       |
| 348     245     128      | 6       135     9        | 7       2345    28       |
| 348     6       128      | 148     7       45       | 58      2345    9        |
+--------------------------+--------------------------+--------------------------+


The short skyscraper/kitelike chain in '2':
-(r6c9)=(r8c9)-(r9c8)=(r9c3)-
leaves 8 in r6c3 and the puzzle is solved.

Took me a while to spot, I had hoped for x,xy,xyz,w or other wings but no such luck (or just plain shortsighted who knows Wink )


Oops, first time I try to write something here, please forgive me when I make a mistake.

From this point you can find an xy-wing with pivot in r9c6. And a x-wing on 5's in c6 and c7.
In row 6 you will then have a naked double(?correct term?), and another one follows.
To end it, you will have another xy-wing with pivot in r9c7.

Hope this helps. If I have have given away too much, please let me know.
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sdq_pete



Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL

PostPosted: Wed Sep 19, 2007 6:11 pm    Post subject: Reply with quote

KSipher wrote:
Marty

This is where I am in this puzzle. Could you possibly explain the skyscraper - I thought I understood them, but I cannot follow it in this puzzle.

Thanks so much
Kathy

Code:

+-------------+-----------+------------+
| 2   7   5   | 19 19  6  | 4  8    3  |
| 6   8   9   | 5  4   3  | 2  1    7  |
| 1   3   4   | 2  8   7  | 6  9    5  |
+-------------+-----------+------------+
| 48  29  3   | 7  69  45 | 58 26   1  |
| 5   1   6   | 3  2   8  | 9  7    4  |
| 7   49  28  | 49 56  1  | 3  56   28 |
+-------------+-----------+------------+
| 9   45  7   | 8  35  2  | 1  345  6  |
| 348 245 128 | 6  135 9  | 7  2345 28 |
| 38  6   128 | 14 7   45 | 58 235  9  |
+-------------+-----------+------------+

Play this puzzle online at the Daily Sudoku site


Well, the logic here is as follows. Both rows 4 and 9 contain just two 2's. Now, those at R4C8 and R9C8 are in the same column, so cannot both be 2. Consequence (think about it!): either R4C2 or R9C3 must be 2 and the 2 at R6C3 is eliminated. That's your skyscraper. But I didn't see it until it was pointed out!

Peter
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Wed Sep 19, 2007 6:14 pm    Post subject: Reply with quote

many thanks, isabel, for pointing out the wings!

seems like, yet again, at some crucial point there are many different ways to solve the puzzle.

And yes, I am not quite sure about the correct termnology of the logic I used.
Basically I like to call it an alternating inference chain, which it is for sure, but then again, the reasoning uses only one digit ('2') so it could also be called "coloring", couldn't it? But on the other hand, coloring usually refers to strong links only, right? I am very confused, could someone please clear things up?
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Wed Sep 19, 2007 6:34 pm    Post subject: Reply with quote

There's a fairly easy to spot Empty Rectangle (ER) using 5's.

There are only two 5's in C6. These line up with L shaped "hinges" of 5s in both Boxes 6 & 9 (only one hinge is needed for an ER). Check this out! It doesn't matter which of the two candidates in C6 are 5s - the "hinges" ensure that there cannot be a 5 in both R4C8 and R9C8.

Easy steps from there.
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dpm



Joined: 19 Sep 2007
Posts: 10

PostPosted: Wed Sep 19, 2007 8:26 pm    Post subject: Reply with quote

KSipher wrote:
Marty

This is where I am in this puzzle. Could you possibly explain the skyscraper - I thought I understood them, but I cannot follow it in this puzzle.

Thanks so much
Kathy

Code:

+-------------+-----------+------------+
| 2   7   5   | 19 19  6  | 4  8    3  |
| 6   8   9   | 5  4   3  | 2  1    7  |
| 1   3   4   | 2  8   7  | 6  9    5  |
+-------------+-----------+------------+
| 48  29  3   | 7  69  45 | 58 26   1  |
| 5   1   6   | 3  2   8  | 9  7    4  |
| 7   49  28  | 49 56  1  | 3  56   28 |
+-------------+-----------+------------+
| 9   45  7   | 8  35  2  | 1  345  6  |
| 348 245 128 | 6  135 9  | 7  2345 28 |
| 38  6   128 | 14 7   45 | 58 235  9  |
+-------------+-----------+------------+

Play this puzzle online at the Daily Sudoku site


You don't need to worry about that -- sticking with the standard methods, there's an X-wing for 5 in C6 and C7 that eliminates 5 from R9C8. With that gone, you have an XY-wing pivoting on R9C8 (the ends are R9C1 and R8C9) that eliminates 8 from R9C7. You can then solve the puzzle using basic eliminations.

It's supposed to be possible to solve all the VH puzzles using only X-wing, XY-wing, XYZ-wing, and basic eliminations, so I always try to find a solution that doesn't require URs, colouring, or things like that, since I know that the solution exists.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Wed Sep 19, 2007 8:46 pm    Post subject: Reply with quote

.../actually I redid this and found the 5 in R4C8 was taken out by a naked triple and that my ER, although correct, did not offer an easy solution - I must have erred somewhere. However, since I am into ERs there is another one on 2's that takes out the 2 in R8C2. Now it's easy to finish !!
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TKiel



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

PostPosted: Wed Sep 19, 2007 9:47 pm    Post subject: Reply with quote

nataraj wrote:
coloring usually refers to strong links only, right?


And what you are referring to is also about strong links, but in this case there are two separate chains. That would be called multi-coloring in the terminology I learned: Two or more strongly linked chains based on the same digit.
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Asellus



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

PostPosted: Wed Sep 19, 2007 10:09 pm    Post subject: Reply with quote

Regarding all the skyscraper comments... perhaps I can shed a little light from my own experience.

When I started reading this board, I saw reference to "Skyscrapers" and "Kites" and "Turbot Fish" and thought, "Oh boy! New things to learn."

When I figured out what they were, I was very disappointed because I already knew them all. They all are really the same thing: simple colorings that can be done in ones head. They differ only in their geometries

All involve three end-to-end links on a single digit in either of the following two configurations:

X-strong-X-strong-X-strong-X
X-strong-X-weak-X-strong-X

If the strong links on the ends are parallel: "Skyscraper".
If the strong links on the ends are perpendicular: "Kite".
If the strong links on the ends are at an angle: "Turbot Fish".

Or, that's at least how the words are usually applied, it seems to me. But the names aren't always used consistently.

About the logic...

If all three links are "strong" (i.e., either/or conjugate pairs), then the relationship between the pincer ends is also conjugate: either one or the other is true, but not both. (As an aside, this can be seen as simple basic coloring.)

If the middle link is "weak" (i.e., at most one is true and both can be false), then the relationship between the pincers is what is somethings called "strongly inferential": one or both can be true. (This can be seen as what is called "multi-coloring" or "color wing" involving a weak link "bridge.")

nataraj's example is of the second sort (and would often be called a "kite").

[Edit to clarify logic description.]
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KSipher



Joined: 24 Sep 2006
Posts: 38

PostPosted: Wed Sep 19, 2007 10:17 pm    Post subject: Reply with quote

Once again, thanks for the help. I was able to finish the puzzle without needing to use a skyscraper, but I would still appreciate anyone explaining how to apply this method at the point I was stuck at (above.) I would love to add this to my 'skills.' Thanks again!
Kathy
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Wed Sep 19, 2007 10:24 pm    Post subject: VH September 19 Reply with quote

A curiosity.

The skyscraper in <2's> which eliminates <2> from R6C3 is a double!
Both R4,9 or C2,9.

Earl
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Asellus



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

PostPosted: Wed Sep 19, 2007 10:47 pm    Post subject: Reply with quote

George wrote:
Once again I haven't seen how to transpose this into a standard move!

George and Peter,

The <8> eliminations you found in Box 7 are due entirely to the configuration of the <8>s in the grid. The "almost square" of {28}s is a coincidence, though it did draw your attention to the area and provided an alternate way of seeing the inferences.

The easiest way to see it is as two Finned X-Wings. Here's a simplified grid:
Code:
+-------------+-------+---------+
|   . .   .   | . . . |  . .  . |
|   . .   .   | . . . |  . .  . |
|   . .   .   | . . . |  . .  . |
+-------------+-------+---------+
|  A8 .   .   | . . . | A8 .  . |
|   . .   .   | . . . |  . .  . |
|   . .  B8   | . . . |  . . B8 |
+-------------+-------+---------+
|   . .   .   | . . . |  . .  . |
| FA8 .  B8   | . . . |  . . B8 |
|  A8 . FB8   | . . . | A8 . .  |
+-------------+-------+---------+

Finned X-Wing "A" eliminates the fin of Finned X-Wing "B" and vice-versa.

This structure of two finned fish eliminating each other's fins comes up occasionally. (Just like some real fish!!)

You can also see it as simple coloring.
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