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Numerical phenomena for each row and column

 
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pwcediting



Joined: 26 Jun 2011
Posts: 7

PostPosted: Sun Jun 26, 2011 3:26 am    Post subject: Numerical phenomena for each row and column Reply with quote

Have you ever noticed that on each finished Sudoku, that there's a certain pattern of numbers in each set of 3 rows across and each set of 3 rows down? There's always two numbers that repeat in each cube row, and the one number that doesn't repeat add up to a certain number that repeats each of 3 times going across in that row of cubes. Am I making any sense to anyone out there? I often use it to check to make sure I've solved a puzzle correctly, although it doesn't always help.
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Sun Jun 26, 2011 4:05 pm    Post subject: Reply with quote

nope, i have not looked at finished puzzles much. Interesting idea. it may suggest a solving method? Bigger brains may provide insight. I suspect it is already covered.
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pwcediting



Joined: 26 Jun 2011
Posts: 7

PostPosted: Mon Jun 27, 2011 1:13 am    Post subject: Numerical phenomena for each row and column Reply with quote

This may already be covered somewhere, but I've never seen it. If any of you have ever seen it, well you'll understand how mathematical it makes all sudoku puzzles, not just because of their unique answers (and I copied one from a Quick Magazine, and got two other solutions than it did for 6/23/11), but because of the mathematical patterns noticed by few if any. It causes me (outside of online sudokus) to put the unique number outside of each set of 3 rows and columns, to see if there's any further patterning effect. Usually not. (But thanks Wapati, for replying to my first-ever post.)
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Mon Jun 27, 2011 6:00 am    Post subject: Reply with quote

I'm still lost.

Can you post an example and make your case with it?
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Asellus



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

PostPosted: Mon Jun 27, 2011 9:50 am    Post subject: Reply with quote

Sounds like it might be what is referred to as Braid Analysis, also perhaps called "moving pairs" or something like that. I can't recall the details other than it had to do with certain patterns that occur within the floors/towers of completed puzzles. Some people used it to help solve puzzles but it never seemed to catch on. My own casual impression long ago was that it didn't seem that helpful and was rather tedious to employ so I didn't pursue it, hence my vague recollection.
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Pat



Joined: 23 Feb 2010
Posts: 165

PostPosted: Mon Jun 27, 2011 1:42 pm    Post subject: re: Quick Magazine Reply with quote

pwcediting wrote:

    I copied one from a Quick Magazine,
    and got two other solutions than it did for 6/23/11
    never seen that magazine --
    could you please post an example?
      esp. an example such as you cite --
      "two other solutions than it did"
    thanks!
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pwcediting



Joined: 26 Jun 2011
Posts: 7

PostPosted: Mon Jun 27, 2011 1:57 pm    Post subject: Numerical phenomena for each row and column Reply with quote

I like what you said, Asellus, about "moving pairs" since that's what it mostly resembles. Luke451, I'd like to post an example, but I'm not sure how. I can email you a Word document in which I embed a puzzle, and then show the pairings outside each of the sides, floors/towers of such a puzzle, since I don't know if I can add an image to this post. I'm very new at this, so give me some clues or a way to reach you on FB so we can touch base via email in some discreet way. TY Smile
I have an idea. I will give the first 3 rows of a solution of the Quick puzzle, below, and then show you the pairs:
9 8 5 3 7 6 1 4 2
2 3 6 5 1 4 9 7 8
1 7 4 9 8 2 5 6 3
You see the "985," the "982," and "978"? Each has a "98" in common, and the different numbers, 5, 2, and 7 add up to 14. Now, take, 236, 376, and 563; the common pair is "36"; the other numbers (same as before) add up to 14. Finally, take 174, 514, and 142, and the common pair is "14" and 7, 5 & 2 add to 14. You will see different pairings in each set of 3 rows or columns, where the other numbers in each set always add up to the same sum. Now, do you follow me, Luke451 and others? Do you also see where this could be helpful, in that the same "other" numbers are used in a set? Now, you'll have to realize that in a partially completed puzzle, you can hypothesize more than one set of common pairs for a given set of numbers: you'll just have to try it on completed puzzles and then incomplete puzzles, to see what I mean. Thanks for listening. --PWC[/b]
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Pat



Joined: 23 Feb 2010
Posts: 165

PostPosted: Mon Jun 27, 2011 2:08 pm    Post subject: Reply with quote

pwcediting wrote:

I will give the first 3 rows of a solution of the Quick puzzle, below, and then show you the pairs:
Code:

  9 8 5 3 7 6 1 4 2
  2 3 6 5 1 4 9 7 8
  1 7 4 9 8 2 5 6 3


thanks
i'd still like to see the original puzzle (before looking at the answer)
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pwcediting



Joined: 26 Jun 2011
Posts: 7

PostPosted: Mon Jun 27, 2011 2:42 pm    Post subject: Numerical phenomena for each row and column Reply with quote

Neither the puzzle nor the answer(s) was the subject of these posts. Since I recopied the puzzle from Quick Magazine (Dallas, TX) into Daily Sudoku, the solutions have long since gone by the wayside. But since the solution it showed wasn't unique, I'd be interested in other people doing the puzzle to see whether they get the same results as Quick did.
What's the best way to do that? I'll use dots instead of blanks below:
. . 53 . . . 4 .
. . . . 1 . . 7 .
. 7498 . . . .
. . 9 . . . . 3 1
3 . . . . . . . 4
42 . . . . 6 . .
. . . . 6529 .
. 6. . 9 . . . .
. 9. . . 83 . .
If you take these numbers and fill them into a blank Daily Sudoku form, you can solve the puzzle. Then, when you repost, I can post the solution, and then show the "Braid Analysis" or "moving pairs" for each set of 3 rows or columns.
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Tue Jun 28, 2011 1:02 am    Post subject: Reply with quote

Here ya go.

Code:
 *-----------*
 |..5|3..|.4.|
 |...|.1.|.7.|
 |.74|98.|...|
 |---+---+---|
 |..9|...|.31|
 |3..|...|..4|
 |42.|...|6..|
 |---+---+---|
 |...|.65|29.|
 |.6.|.9.|...|
 |.9.|..8|3..|
 *-----------*


 *-----------*
 |985|376|142|
 |236|514|978|
 |174|982|563|
 |---+---+---|
 |659|427|831|
 |318|659|724|
 |427|831|659|
 |---+---+---|
 |843|165|297|
 |761|293|485|
 |592|748|316|
 *-----------*
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pwcediting



Joined: 26 Jun 2011
Posts: 7

PostPosted: Tue Jun 28, 2011 2:51 am    Post subject: Numerical phenomena for each row and column Reply with quote

OK, Luke 451, here are the sums on the top caps from left to right: 17, 19, 17; and the sums on the sides going from top to bottom: 14, 0, 15. From there, you can tell me the pairs of numbers (e.g., 985, 982, 978 yields 98 (or 89), corresponding to the 14). And, these relate directly to your posts.
17 19 17
*--------------*
|985|376|142|
|236|514|978| 14 (98, 36, 14)
|174|982|563|
|----+---+----|
|659|427|831|
|318|659|724| 0 (no pairs; all 3 numbers repeat each time)
|427|831|659|
|----+---+----|
|843|165|297|
|761|293|485| 15 (48, 16, 29)
|592|748|316|
*--------------*
And remember, these "moving pairs" and correspondences are true for any Sudoku that you've ever done or ever will do, unless it's got more than 9 boxes. I've seen the Monster Sudokus with 16 boxes, and have never tried to solve one, let alone look for mathematical relationships.

Blest regards.
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Pat



Joined: 23 Feb 2010
Posts: 165

PostPosted: Tue Jun 28, 2011 10:23 am    Post subject: Reply with quote

pwcediting wrote:

Neither the puzzle nor the answer(s) was the subject of these posts.

Since I recopied the puzzle from Quick Magazine (Dallas, TX) into Daily Sudoku,
the solutions have long since gone by the wayside.

But since the solution it showed wasn't unique,
I'd be interested in other people doing the puzzle
to see whether they get the same results as Quick did.

Code:

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


i'm sorry that you consider my question off-topic

the fact is that you've accused the magazine of publishing a flawed puzzle ( a puzzle with more than one answer )

so i'm glad i got you to post the puzzle

as we can all see, it has exactly one answer
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pwcediting



Joined: 26 Jun 2011
Posts: 7

PostPosted: Tue Jun 28, 2011 3:54 pm    Post subject: Numerical phenomena for each row and column Reply with quote

Thanks, Pat.
Actually, I wasn't accusing the magazine of a flawed puzzle. I didn't know that a puzzle had to have only one answer. Why isn't it possible for one puzzle out of ... to have more than one answer? I don't know how I came up with 2 other answers, unless I miscopied a number. I'll recopy the numbers again, and see what happens.
Did you get the point of the numerical phenomena?
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jun 28, 2011 4:48 pm    Post subject: Reply with quote

http://sudopedia.org/wiki/Traveling_Pairs circa Nov 2006. Without using the full power of Braid Analysis, I use traveling pairs and traveling triples as an alternate POV to ... to ... gee, I'm not sure what they're alternate to.
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pwcediting



Joined: 26 Jun 2011
Posts: 7

PostPosted: Tue Jun 28, 2011 7:12 pm    Post subject: Numerical phenomena for each row and column Reply with quote

Hi, Ronk,
I'll check out the site you posted, and get back with you later.
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Tue Jun 28, 2011 9:44 pm    Post subject: Reply with quote

The posted puzzle has a single solution and does not require advanced moves.

If you want advice on posting puzzles or images, scroll down to the "Site Help" thread.

Since this methods seems to have no dependence on starting values, how does it exclude deadly patterns in any reliable way?

Keith
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