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| soduko
| | Joined: 10 Oct 2005 | | Posts: 50 | | : | |
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 Posted: Thu Nov 10, 2005 1:48 pm Post subject: New graphic representation of methods |
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Hello
I like to propose a new graphic representation of solving methods
The outline is as follows:
there are the following square marks
. (a dot) stands for all /any candidate (including the ones mentioned)
- (a dash) stands for all candidates except those mentioned)
1-9 A-Z a-z stands for individual candidates
+ (a plus) stands for other candidates
a method is discribed as a line thre rows or complete grid whatever is nessesary.
Boxes are not drawn if they are not nessesary.
More rules will follow as this post continues .
a couple of examples using these rules:
forced moves can be represented as:
| Code: |
. . . . A . . . .
=>
- - - - A - - - -
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(remove all A candidates from the rest of the row)
pinned squares as:
| Code: |
- - - - A+ - - - -
- - - - A - - - -
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(remove all other candidats from the A square)
X wing in blocks (to take a more complex example) as
| Code: |
- - A+ | . . . | - - A+
- - - | . . . | - - -
- A+ - | . . . | A+ - -
=>
- - A+ | - - - | - - A+
- - - | . . . | - - -
- A+ - | - - - | A+ - -
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and so on
If combinations of numbers and letters are used there must be a line wich indicates what a - means like
- = all except 1-9
- = all except A-z
- = all except 1-9 and a-z
I am not at home for the moment but i hope that the examples are clear. |
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| Lummox JR
| | Joined: 07 Sep 2005 | | Posts: 202 | | : | |
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| Posted: Thu Nov 10, 2005 9:49 pm Post subject: |
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I'm not sure this is clear enough for general use, nor strictly necessary as full explanations make more sense--particularly for advanced techniques.
Also note that "generalized X-wing", or X-wing by blocks as you called it, doesn't really exist except in the presence of a much simpler technique. Always it's possible to find a simpler form of box-line interaction. For example: If the only candidates for digit 6 in row 2 are in box 2, eliminate all other 6's in box 2. |
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| soduko
| | Joined: 10 Oct 2005 | | Posts: 50 | | : | |
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| Posted: Thu Nov 24, 2005 11:45 pm Post subject: |
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| Quote: |
Also note that "generalized X-wing", or X-wing by blocks as you called it, doesn't really exist except in the presence of a much simpler technique. Always it's possible to find a simpler form of box-line interaction. For example: If the only candidates for digit 6 in row 2 are in box 2, eliminate all other 6's in box 2.
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Sorry but I think you are wrong.
| Code: |
the Box X wing
- - A+ | . . . | - - A+
- - - | . . . | - - -
- A+ - | . . . | A+ - -
=>
- - A+ | - - - | - - A+
- - - | . . . | - - -
- A+ - | - - - | A+ - -
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is not reductable via (two) box row interchange(s) and one simple X-wing
(the two candidates in either box are not on the same collumn)
and for it to be able to reduce them by box-row interactions the A 's must be in collumns in both boxes)
an
Box row interaction is | Code: |
- - - | . . . | . . .
- - - | . . . | . . .
A+ A+ A+ | . . . | . . .
=>
- - - | . . . | . . .
- - - | . . . | . . .
A+ A+ A+ | - - - | - - -
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| Quote: | I'm not sure this is clear enough for general use, nor strictly necessary as full explanations make more sense--particularly for advanced techniques.
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I know it has its limits but it is nice for simple methods and it really shows where to look for and what the result will be.
I could even explain why you were wrong with this simple technic |
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| Lummox JR
| | Joined: 07 Sep 2005 | | Posts: 202 | | : | |
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| Posted: Fri Nov 25, 2005 4:35 am Post subject: |
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| soduko wrote: | Sorry but I think you are wrong.
the Box X wing
| Code: | - - A+ | . . . | - - A+
- - - | . . . | - - -
- A+ - | . . . | A+ - -
=>
- - A+ | - - - | - - A+
- - - | . . . | - - -
- A+ - | - - - | A+ - - |
is not reductable via (two) box row interchange(s) and one simple X-wing
(the two candidates in either box are not on the same collumn)
and for it to be able to reduce them by box-row interactions the A 's must be in collumns in both boxes) |
You misunderstand how box-line interaction works. It does not require the A's to line up, or even for there to be only two candidates per box. It does not require any interchanges, or anything to make this conform to a simple X-wing. The logic of box-line interaction is much simpler: The only possible choices for row 2 are in box 2. Therefore, all other choices in box 2 can be eliminated.
| Code: | * * *|* * *|* * *
. . .|* * *|. . .
* * *|* * *|* * * |
...becomes:
| Code: | * * *|- - -|* * *
. . .|* * *|. . .
* * *|- - -|* * * |
The so-called "box X-wing" is just a special case of this. But this is a basic technique, so there's no reason to look at anything as complex as an X-wing or variant. |
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| soduko
| | Joined: 10 Oct 2005 | | Posts: 50 | | : | |
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| Posted: Fri Nov 25, 2005 11:13 am Post subject: |
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Ahh
What you call a boxed X wing is something different than what I call a boxed X-wing.
I mean a X-wing where the collumns are replaced by a boxes
(or alternativly the rows replaced by boxes)
You mean two box-row interactions.
They are two different kind of beasts..
Ps
To go back to the original reason for posting
If you replace the . (dot) with a - (dash) , the * (star) with a . (dot)
you are almost in my way of representation.
The only difference is that I represent * (star) in box 2 with 2+ (or A+)
and that is only to show you what a - (dash) means (everything except 2 or A). |
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| Lummox JR
| | Joined: 07 Sep 2005 | | Posts: 202 | | : | |
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| Posted: Fri Nov 25, 2005 6:30 pm Post subject: |
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| soduko wrote: | Ahh
What you call a boxed X wing is something different than what I call a boxed X-wing.
I mean a X-wing where the collumns are replaced by a boxes
(or alternativly the rows replaced by boxes) |
Well yes, I got that. I was explaining why this is a useless technique because it's equivalent to a box-line intersection.
| Quote: | | You mean two box-row interactions. |
No, I mean one. A single interaction: All of row 2's choices for the digit are in box 2, so all other choices in box 2 can be eliminated.
| Quote: | | They are two different kind of beasts. |
Well, the box X-wing could be considered such if you were using a larger sudoku, like a 16x16, but in a 9x9 it always reduces to simple box-line interaction. (Standard X-wing, however, is indeed a different beast. It's a positional subset.)
Actually, my recent discovery of constraint subsets and, for large sudoku, multi-box-multi-line interaction, pretty much rules out box X-wing's usefulness in larger sudoku too--except that it may be easier to spot.
| Quote: | Ps
To go back to the original reason for posting
If you replace the . (dot) with a - (dash) , the * (star) with a . (dot)
you are almost in my way of representation.
The only difference is that I represent * (star) in box 2 with 2+ (or A+)
and that is only to show you what a - (dash) means (everything except 2 or A). |
Like I said initially, I don't see much hope for this representation. For one thing, it's simply not clear. For another, advanced techniques require more sophisticated markup. I don't think it's possible nor desirable to standardize the representation of methods. |
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| soduko
| | Joined: 10 Oct 2005 | | Posts: 50 | | : | |
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| Posted: Sun Nov 27, 2005 10:37 pm Post subject: |
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How can the example I gave is equivalent to a box-line intersection?
| Code: |
- - A+ | . . . | - - A+
- - - | . . . | - - -
- A+ - | . . . | A+ - -
=>
- - A+ | - - - | - - A+
- - - | . . . | - - -
- A+ - | - - - | A+ - -
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I just do not see it...
you need both boxes for the elimination to take place. |
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