The New Sudoku Players' Forum

[rjamil]

Hi again.

I am stuck in another Sudoku solving technique that was also discovered by Pritt Galford and mentioned as Rule 15B.

Maybe this one either also known by some other strategy name or completely overlap with some other strategy.

What I understand till now is shown in below exemplar:

Code: Select all

-----------------------
 a . . | . . . | . a .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------|-------|-------
 . d d | . . . | d . d
 b p p | n n n | p b p
 . d d | . . . | d . d
-----------------------

Assuming that the above exemplar is reflecting the Rule 15B strategy correctly or one may correct the same as well.

Where:
a = primary corner cells
b = secondary corner cells
d = dead zone
p = pzone
n = nzone

Will some one please identify e = elimination cells from where primary corner candidate digit can be removed?

R. Jamil

[eleven]

Oh, this is really hard to read. I guess he is describing an empty rectangle (or grouped kite).
However the empty rectangle is listed as rule Rule 44 - and the description is wrong (no resolved cells, no pair needed).

I mark cells, which do not contain a 1 with "/".
The "dead zone" is the empty rectangle. The elimination can also be made, if the "nzone" contains a 1.

Code: Select all

    -----------------------
     1 / / | / / / | / 1 /
     . . . | . . . | . . .
     . . . | . . . | . . .
    -------|-------|-------
    -1 . . | . . . | . . .
     . . . | . . . | / . /
     . . . | . . . | / . /
    -------|-------|-------


[Added:] To speak it out:
Either r1c1=1 or r1c8=1 -> r456c8<>1 -> r4c79=1.
In both cases r4c1 cannot be 1.

[StrmCkr]

I'm pretty sure that is a reference to kites and grouped kite

Code: Select all

kite
//X|///|/x/
./.|...|...
.x.|...|...
------------
./.|...|... 
.X.|...|.-x.
./.|...|...
------------
./.|...|...
./.|...|...
./.|...|...


where:
/ = no candidate
x = potential candidate
-x = potential elimination

Code: Select all

grouped kite
X/X|///|/x/
.x.|...|...
.x.|...|...
-------------
./.|...|...
.X.|...|.-x.
./.|...|...
------------
./.|...|...
./.|...|...
./.|...|...


[StrmCkr]

On second reading, since it's an extension of a finned x wing

It could be a skyscraper.

Code: Select all

 
 X//|///|/x/ 
..-X|...|...
..-X|...|...
-------------
 //X|///|/x/
-X..|...|...
-X..|...|...
 ...|...|...
-------------
 ...|...|...
 ...|...|...
 ...|...|...


where:
/ = no candidate
x= potential candidate
-x= potential elimination

[StrmCkr]

since i like over analyzing stuff and slightly stumped to what they are depicting ill map it out my self...
following the directions of the rules as outlined you get this layout:

Code: Select all

...|...|...
/x/|///|/x/
...|...|...
-------------
/./|...|/./
PSP|NNN|PSP
/./|...|/./
-------------
...|...|...
...|...|...
...|...|...

s= secondary corners
x= primary corners
/= dEad zone {no candidates}
N = n zone {no candidates}

S being the elimination zone if at least one P exists.

which is a really badly written description of a Dual linked Empty rectangle, and misses most of its potential eliminations.

on that note:
here is what a dual linked empty rectangle { aka fraken Sword Fish} looks like with it's eliminations

Code: Select all

 .-x.|. . . |.-x.
  /x/|/ / / |/x/
 .-x.|. . . |.-x.
----------------
  /x/|. . . |/x/
  x*x|-x-x-x|x*x
  /x/|. . . |/x/
----------------
 .-x.|. . . |.-x.
 .-x.|. . . |.-x.
 .-x.|. . . |.-x.

where:
/= no candidate
*= potential elimination and may contain a candidate
x= potential candidate
-x = potential elimination

[eleven]

That's nice, but obviously not what is described in the rule.
It only speaks of a single deadzone under consideration, and a single elimination (as it can be made with an empty rectangle(grouped kite).

[StrmCkr]

Rule 15B: Finned X-Wing Hybrid -- Discovered by Pritt Galford, a Finned X-Wing Hybrid begins with finding the only two occurrences in a puzzle row of a candidate digit existing in different boxes. Call these the primary corners. Then find occurrences of the same candidate digit in the same columns of a row in different boxes from the primary corners. Call these newfound cells the secondary corners. When the secondary corners are identified, further analysis proceeds to determine whether a Finned X-Wing Hybrid actually exists as follows: 1) cells of a secondary corner's box that are not in the same column and not in the same row as the secondary corner are noted to be in the deadzone, 2) cells of a secondary corner's box that are not in the same column and but are in the same row as the secondary corner are called the pzone, and 3) the cells in the same row as the secondary corners but in neither of the secondary corners' boxes are designated to the nzone. The three zones analyzed to finally determine the presence, or not, of a Finned X-Wing Hybrid formation as follows. 1) The deadzone must not contain any occurrences of the candidate digit from the basis of the primary corners. 2) The pzone must contain at least one occurrence of the candidate digit from the basis of the primary corners. 3) The nzone must not contain any occurrences of the candidate digit of the primary corners. Having reached this point with these three conditions met, a Finned X-Wing Hybrid is found and this action can be taken: the primary corner candidate digit can be eliminated from the opposite secondary corner that was analyzed.

you sure?

cell's of a secondary corner box's that are not in the same column and not in the same row as the secondary corner are to be in the dead zone.

for the eliminations it describes sight checking one of the secondary boxes at a time for an existing P if true eliminate the opposite S

[eleven]

Maybe i misread it, it is really hard to understand, what is meant. I am not a native English speaker, and i guess, neither the author.
It is not clear, if the dead/p-zone is meant to be the empty rectangle cells of one or both boxes. I thought of one, because at the end it says:
"the primary corner candidate digit can be eliminated from the opposite secondary corner that was analyzed."
The nzone obviously only contributed to the confusion. It says, there shouldn't be this candidate there, but in the one case it is irrelevant, in the other it could be eliminated, if it was there.

However, nice to remember the double linked empty rectangle (unfortunately i never spotted one in a puzzle - must be rare).

[StrmCkr]

really hard to understand,

agreed: hence the three stab's at it.

yeah, its pretty rare find manually for that bad boy but harder yet is this:

for giggles Siamese Empty rectangles to bad my Empty rectangle "pattern" thread died with the old forum I had every possible extended Rectangle listed and named lol.
for reference im pretty sure Ive only seen this once when I was documenting er's back in the day.

Code: Select all

/X/|./.|...
XXX|.X.|...
/X/|./.|...
-------------
/x/|///|/X/
...|./.|...
...|./.|...
-------------
...|./.|/x/
...|.X.|xxx
...|./.|/x/

[rjamil]

Hi eleven,

[Added:] To speak it out:
Either r1c1=1 or r1c8=1 -> r456c8<>1 -> r4c79=1.
In both cases r4c1 cannot be 1.

Code: Select all

-------+-------+-------
 1 / / | / / / | / 1 /
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+-------
-1 / / | / / / | p 1 p
 . . . | . . . | / . /
 . . . | . . . | / . /
-------+-------+-------

I think above mentioned exemplar is reflecting correct scenario.

Actually, the original site Rule 15B does not tell about r56c8 cells' condition.

If r56c8 also not contain primary corner digit then it is simply Pointing pair/triple intersection removal strategy. Otherwise, it is confusing to place the primary corner digit in box 4.

I will go through StrmCkr valuable posts and will comment if necessary.

R. Jamil