StrmCkr observations on puzzle reposed by eleven

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StrmCkr observations on puzzle reposed by eleven

Postby coloin » Sat Oct 04, 2008 4:18 am

Note added by Glyn. This thread is related to issues arising from a discussion of Version 3 here.
http://forum.enjoysudoku.com/viewtopic.php?p=62223#p62223

StrmCkr wrote:hey udosuk.
nice to see you have given me some proof for my theory with out reading it.

on transformation of grids A to b
(making a new puzzle using symetry of boxes)
its the same thign line of sights do not change or alter.

but can give hints at where similarties of clues are found thus restrictions must lie.

that is where i found that un marked clues can be changed in minilex grids but using the given clues rotation n boxes in unision can keep line of sights the same leaving 1 solution but altered according to the changes of line of sight.


This would be this thread.

here

so this transformation technique only works when you have a puzzle from an isomorphic grid.....

i dont doubt you can see it:)

C
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Postby coloin » Sat Oct 04, 2008 4:32 am

i can sense that braid analysis and this thread might need a revisit.

http://forum.enjoysudoku.com/viewtopic.php?t=768&start=0

Especially with reference to advanced solving techniques - ultra hard puzzles and the mellowing view on TandE.

C
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Postby eleven » Sat Oct 04, 2008 7:52 am

While the Gludo technique above is very clear and well defined, those 2 threads mainly contain cunfused stuff.
If you have in mind, that changing one number in a sudoku can lead to a puzzle with completely different properties and solution grids, it is very unprobable, that whatever is done in the first thread exactly, could lead to a new solving technique.
Concerning the other thread it seems, that this technique in most cases makes things more complicated. At the end of a long discussion there was not one sample, where it is an advantage to use it.


Note added by Glyn. Gludo is discussed here.http://forum.enjoysudoku.com/viewtopic.php?p=62152#p62152
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Postby udosuk » Sat Oct 04, 2008 8:40 am

Sudopedia has a nice article on Braid Analysis:

http://www.sudopedia.org/wiki/Braid_Analysis

You can see my proof for the "Gludo" (I think there ought to a be a descriptively better name) technique follows a similar style of analysis there. But instead of grouping the digits by the mini-rows of the leftmost block, I group them by their "mapping cycle", and hence the effects are much simpler to see. I must admit for me "braid analysis" is not an easy thing to do manually and is better left for computer programs etc.

As for StrmCkr's theories, I must also admit I never attentively read his long posts because it's very mind-exhausting. I do understand dyslexic problems and am certain he has a lot of intelligent ideas. But as a non-English background writer myself every time I make a post I spend a lot of effort to make sure it contains as few spelling/grammatical errors as possible, and still these errors creep in every now and then. I think it will also take StrmCkr a lot of effort to tidy up his writing habit but in the long term I'm sure it will be beneficial both to himself and to the readers who are interested in his ideas.:)
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Postby StrmCkr » Sat Oct 04, 2008 8:49 pm

edit
Last edited by StrmCkr on Tue Sep 03, 2013 4:44 am, edited 1 time in total.
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Postby coloin » Sun Oct 05, 2008 3:19 am

StrmCkr wrote:i belive all puzzles are formed form a automorphic grid in the first place....


Wow

i think this should read all solution grids can be "formed" from an automorphic grid.

yes although some will have many more "equivalent" clues than more distant solution grids.

Code: Select all
+---+---+---+
|123|...|...|
|456|12.|...|
|789|...|1..|
+---+---+---+
|.1.|...|...|
|...|.1.|...|
|...|...|.1.|
+---+---+---+
|..1|...|...|
|...|..1|...|
|...|...|..1|
+---+---+---+


i remember a pseudopuzzle with 2 solutions - the other solution was the MC grid......which i thought rather coincidental indeed !

i will dig it out.

Edit
having said that however..if you take a minimal puzzle from the MC grid, remove a clue, all the revealed grid solutions will share the remaing clues. It wold seem that many / all grids will approach any other grid to an extent [? 20 clues or more the same]. Boggling.

C
Last edited by coloin on Sun Oct 05, 2008 11:15 am, edited 1 time in total.
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Postby StrmCkr » Fri Oct 10, 2008 3:18 pm

edit
Last edited by StrmCkr on Tue Sep 03, 2013 4:44 am, edited 1 time in total.
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Postby Glyn » Fri Oct 10, 2008 4:57 pm

StrmCkr wrote:version 3:
Code: Select all
*-----------*
|6..|..9|.5.|
|...|.3.|..2|
|.2.|8..|9..|
|---+---+---|
|.7.|..3|.9.|
|..6|.4.|7..|
|3..|...|..1|
|---+---+---|
|2..|.1.|...|
|..7|..8|1..|
|.8.|4..|..5|
*-----------*




Code: Select all
*-----------*
|ABC|..9|.5.|
|BCA|.3.|..2|
|CAB|8..|9..|
|---+---+---|
|.7.|ABC|.9.|
|..6|BCA|7..|
|3..|CAB|..1|
|---+---+---|
|2..|.1.|ABC|
|..7|..8|BCA|
|.8.|4..|CAB|
*-----------*


An amazing observation StrmCkr.

So Set A is {2,6,?}, B is {1,5,?} and C is {3,4,?}

Incidentally could we use this observation (conjecture)
Box 3 has givens from A and B => C contains 9
Box 4 has givens from A and C => B contains 7
Box 8 has givens from B and C => A contains 8

Then it is just routine to fill the grid.
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Postby Mauricio » Fri Oct 10, 2008 5:35 pm

StrmCkr wrote:version 3:
Code: Select all
*-----------*
|6..|..9|.5.|
|...|.3.|..2|
|.2.|8..|9..|
|---+---+---|
|.7.|..3|.9.|
|..6|.4.|7..|
|3..|...|..1|
|---+---+---|
|2..|.1.|...|
|..7|..8|1..|
|.8.|4..|..5|
*-----------*



Code: Select all
*-----------*
|ABC|..9|.5.|
|BCA|.3.|..2|
|CAB|8..|9..|
|---+---+---|
|.7.|ABC|.9.|
|..6|BCA|7..|
|3..|CAB|..1|
|---+---+---|
|2..|.1.|ABC|
|..7|..8|BCA|
|.8.|4..|CAB|
*-----------*

Unfortunately this is an ad hoc observation that has nothing to do with the symmetry(automorphism) of this sudoku, otherwise it could also be applicable to boxes 2,6,7, where such observation is false.
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Postby udosuk » Fri Oct 10, 2008 6:41 pm

Mauricio wrote:Unfortunately this is an ad hoc observation that has nothing to do with the symmetry(automorphism) of this sudoku, otherwise it could also be applicable to boxes 2,6,7, where such observation is false.

I'd have to agree with Mauricio here. It's easy to observe from the solution grid for any special pattern (because it's an automorphic grid a lot of these patterns exist), and then try your luck and see if it works in the solving process. It's another matter to back up your "technique" with a sound logical proof. For me anything without the latter is not much different to blind guessing.

For example if you swap r45, then swap c56, you obtain this equivalent puzzle:
Code: Select all
6 . .|. 9 .|. 5 .
. . .|. . 3|. . 2
. 2 .|8 . .|9 . .
-----+-----+-----
. . 6|. . 4|7 . .
. 7 .|. 3 .|. 9 .
3 . .|. . .|. . 1
-----+-----+-----
2 . .|. . 1|. . .
. . 7|. 8 .|1 . .
. 8 .|4 . .|. . 5

If you observe b159 the same clue pattern applies. Yet if you try StrmCkr's trick in this puzzle you'll fail miserably.:!:

Of course we need to consider all 9 blocks for any truly logical technique. In eleven's original format there are certain patterns in the give clues (e.g. r348 all having identical layout) which are destroyed in the transformed grid above. But unless someone composes a fully logical proof to back up this "technique" I'm not prepared to use it.

As a matter of fact, if one wants to create new techniques, I think one should explore them from something like the following isomorph:
Code: Select all
2 . .|. . 8|9 . .
. . .|. 3 .|. 2 .
. 6 .|9 . .|. . 5
-----+-----+-----
7 . .|3 . .|. . 9
. 3 .|. . .|. 1 .
. . 6|. 4 .|7 . .
-----+-----+-----
. . 7|8 . .|1 . .
. 2 .|. 1 .|. . .
8 . .|. . 4|. 5 .

where b159, b267, b348 all follow the exactly same clue layout. Anything from an arbitrary irregular isomorph is too susceptible to blind luck.:idea:
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Postby StrmCkr » Sat Oct 11, 2008 1:22 pm

edit
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Postby udosuk » Sun Oct 12, 2008 12:14 am

StrmCkr,

I think your major problem is a general lack of logical sense when exploring new techniques. It seems you always invent "new techniques" from arbitrary patterns extracted from the solution grid (which is totally meanlingless, as the whole point of the game is to use the techniques to work out the solution, which you aren't supposed to know beforehand). What's worse is that you often only conveniently pick a move that only works for some random puzzles (without explaining what special properties in these random puzzles enable you to apply those moves). What's even worse is that in some cases you even choose to use just a part of your "techniques", totally ignoring the other parts of them don't work anymore.:(

It would be fine if everyone in this forum knows well about your tendencies and choose to spend the appropriate amount of attention on your "discoveries" (which IMHO shouldn't be much), otherwise people will waste a lot of time to delve into something which, frankly, doesn't have much value at all.:(

I'm sorry about the anger but as the originator of this thread I've been witnessing some very valuable and intelligent work/insights from others such as RW, eleven, Glyn and of course a lot of good references to old threads about automorphism/symmetry from experts such as Gurth & Mauricio. But your (logically unsound) "theories" have recently been taking a lot of space in this thread, and viewers might be confused that they are of equal or greater value compared to other contents, which are all based on sound logic and careful work from the authors. It'd be fine if you open your new thread about these findings of your own, but mixing your general carefree, random speculations with the great, carefully-worked posts from others doesn't look fair to me.:(

To summarise, I think for a "technique" to be valid (and useful), it must have the following characteristics:

1. It must be able to be applied to all puzzles within a certain class (e.g. with a certain symmetry/automorphism). "Only applicable in some cases" doesn't cut it.

2. It must be able to be applied to all parts of a puzzle which share a similar property. E.g., if all three of b159, b267, b348 display a certain symmetry, the technique must be applicable to all three of them. Being only able to work in one or two of them doesn't cut it.

3. The whole technique must be able to be applied fully everytime (provided you have a well-defined description of the full effect). E.g. if you have labelled the cells with {ABC} in one application, you can't just label the C-cells in another application and totally ignore the effect on the A- & B-cells.

4. The technique must be able to be applied validly even if the grid is transformed via row/column permutations and rotations etc as well as symbol remapping (provided the technique itself is not numerically-based). Of course the cells applied must be adjusted accordingly but the general pattern of the cells applied should not be dependent on a certain morphism of the grid.

5. Most important of all, you should be able to back your technique with a logically sound proof, based on the established axioms, theorems and properties. You can't count on others to do it for you, because chances are, it's all ad-hoc (as Mauricio said) and you're wasting valuable time of others. If you can prove it for yourself, then all hands to you for your great discovery. But I don't think it's very responsible if you just lay every random speculation out here and expect others to investigate/prove it for you (to put it vulgarly, "wiping your bottom"), without spending a serious amount of careful, logical work yourself.

:idea:
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Postby StrmCkr » Sun Oct 12, 2008 5:43 pm

edit
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Postby ronk » Sun Oct 12, 2008 5:53 pm

StrmCkr wrote:but it does work off and on again..

If it were a valid technique, it would work every time.
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Postby StrmCkr » Sun Oct 12, 2008 5:57 pm

edit
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