Bent Almost Restricted N(aked)-Set {Barn}

Advanced methods and approaches for solving Sudoku puzzles

Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby StrmCkr » Tue Feb 07, 2017 8:10 am

fine, that's now an official wzyz-wing :)


:P the good news is i finally solved my overlapping als-xz code problem and it correctly finds these now woot woot.
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Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby rjamil » Sun Sep 24, 2017 10:15 am

Hi,

Having come to know through StrmCkr recent pm conversations that some more WXYZ-Wings exemplars, not covered in my previous posts, are as follows:
Code: Select all
  --------------+-------------+-----------  --------------+-------------+-----------
01) .  wz    .  |  .   .   .  |  .  .   . 02) .  xyz   .  |  .   .   .  |  .  .   .
   -Z wxyz wxyz |  .  xyz  .  |  .  .   .    -Z wxyz wxyz |  .  wz   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

  --------------+-------------+-----------  --------------+-------------+-----------
03) .   wz   .  | -Z  -Z  -Z  |  .  .   . 04) .   wz   .  | -Z  -Z  -Z  |  .  .   .
   -Z  wxy  wxy |  .  xyz  .  |  .  .   .    -Z  wxy  wxy |  .  xyz  .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

a) First and second apex share mini-line;
b) First and second apex contain 3 or 4 values in total;
c) First wing contains 2 or 3 values and shares apex line but not box;
d) Second wing contains 2 or 3 values and shares apex box but not mini-line;
e) First and second wings contain all 4 values in total and only one common value;
f) First and second apex total values; and first and second wings common value contain all 4 values in total;
g) First and second wings common value may be eliminated from cell in apex mini-line;
h) If first and second apex contain 3 values in total then first and second wings common value may also be eliminated from intersection cells of first wing box and second wing line.

R. Jamil

Correction in points d and e.
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Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby StrmCkr » Mon Sep 25, 2017 5:19 am

ab . . | ab . .
--------------
ac . . | abc . .


works pretty much like my earlier examples
Code: Select all
    +----------+-----------+----------+
    | abc -c -c|  bc -c  -c| -c -c -c |
    |  .  .  . |  .   .  . |  .  .  . |
    |  .  . ac |  .   bc . |  .  .  . |


but the inner-workings gets harder to build if i look at
Code: Select all
. 124  .  |  .  .  .  | 13  .  .
  .  .    . |  .  .  .  |  .  .  .
  24 -24 -24|  .  .  .  |  . 234 .


which all function as an als-xy wing easier then trying to figure out a method of identifying Almost almos als-xz rule
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Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby rjamil » Mon Sep 25, 2017 3:12 pm

Hi StrmCkr,

StrmCkr wrote:works pretty much like my earlier examples
Code: Select all
+----------+-----------+----------+
| abc -c -c|  bc -c  -c| -c -c -c |
|  .  .  . |  .   .  . |  .  .  . |
|  .  . ac |  .   bc . |  .  .  . |

Please note that, I have already discussed XYZ-Wings Hybrid strategies, implemented both types of the same and shared source code accordingly.

Code: Select all
  --------------+-------------+-----------  --------------+-------------+-----------
   abc -c   -c  | bc  -c  -c  | -c -c  -c    abc -c   -c  | ad   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .    -c  -c   -c  |  .   .   .  |  .  .   .
    .   .   ad  |  .  bd   .  |  .  .   .    -c  -c   bc  |  .  bd   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

Please also note that the above mentioned cases might also be considered as WXYZ-Wings strategies (that contain 4 cells with 4 clues in total), as blue mentioned in XYZ-Wings Hybrid post.

StrmCkr wrote:but the inner-workings gets harder to build if i look at
Code: Select all
. 124  .  |  .  .  .  | 13  .  .
  .  .    . |  .  .  .  |  .  .  .
  24 -24 -24|  .  .  .  |  . 234 .

I will go through rest of the cases and will let share outcome here as and when needed.

Added: (Corrected as per below given StrmCkr guidelines).
Code: Select all
WXYZ-Wings Box-Box wise:-
  --------------+-------------+-----------  --------------+-------------+-----------
01)-Z  xyz  -Z  | -XZ -XZ xz  | -Z -Z  -Z 02)-Z  xyz  -Z  |  .   .  wy  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .    -Z  -Z   -Z  |  .   .   .  |  .  .   .
    .   .   wy  |  .  wx   .  |  .  .   .    -XZ -XZ  xz  |  .  wx   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

  --------------+-------------+-----------  --------------+-------------+-----------
03) .  xyz   .  | -XZ -XZ xz  |  .  .   . 04) .  xyz   .  |  .   .  wy  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .   .   wy  |  .  wxz  .  |  .  .   .    -XZ -XZ  xz  |  .  wxz  .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

01)
a) Apex contains three values;
b) First wing shares apex line but not box; and contains two values;
c) First wing contains two apex values;
d) Second wing shares apex box but not first wing line; and contains two values;
e) Second wing contains one apex value not in first wing values;
f) Third wing shares first and second wings intersection mini-line;
g) Third wing contains two values; one value from first wing values; and one value from second wing values not in apex values;
h) Apex value not in second and third wings values may be eliminated from cells in apex and first wing line;
i) First and third wings common value may also be eliminated from cells in first wing mini-line.

02)
a) Apex contains three values;
b) First wing shares apex line but not box; and contains two values;
c) First wing contains one apex value;
d) Second wing shares apex box but not first wing line; and contains two values;
e) Second wing contains two apex values not in first wing values;
f) Third wing shares first and second wings intersection mini-line;
g) Third wing contains two values; one value from first wing values not in apex values; and one value from second wing values;
h) Apex value not in first and third wings values may be eliminated from cells in apex and second wing box;
i) Second and third wings common value may also be eliminated from cells in second wing mini-line.

03)
a) Apex contains three values;
b) First wing shares apex line but not box; and contains two values;
c) First wing contains two apex values;
d) Second wing shares apex box but not first wing line; and contains two values;
e) Second wing contains one apex value not in first wing values;
f) Third wing shares first and second wings intersection mini-line;
g) Third wing contains three values; two values from first wing values; and one value from second wing values not in apex values;
h) First wing values may be eliminated from cells in first wing mini-line.

04)
a) Apex contains three values;
b) First wing shares apex line but not box; and contains two values;
c) First wing contains one apex value;
d) Second wing shares apex box but not first wing line; and contains two values;
e) Second wing contains two apex values not in first wing values;
f) Third wing shares first and second wings intersection mini-line;
g) Third wing contains three values; one value from first wing values not in apex values; and two values from second wing values;
h) Second wing values may be eliminated from cells in second wing mini-line.

Added on 20170927:
Code: Select all
WXYZ-Wings Row-Column-Box wise:- one eimination (2 exemplars)
  --------------+-------------+-----------  --------------+-------------+-----------
01) .  xyz   .  |  .   .   .  |  . wx   . 02) .  xyz  yz  |  .   .   .  |  . -Z   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .  yz    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .  -Z    .  |  .   .   .  |  . wz   .     .  wx    .  |  .   .   .  |  . wz   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

a) Apex contains either two or three values; (added on 20170927: apex contains "x" value and either "y" or "z", or both "yz" values)
b) First wing shares apex row/column but not box; and contains two values;
c) First wing contains one value from apex values;
d) Second wing shares first wing column/row but not box; and contains two values;
e) Second wing contains one value from first wing values not in apex values; and one value from apex values not in first wing values;
f) Third wing shares apex column/row but not in second wing row/column intersection cell; and contains two values; (Updated on 20170928)
g) Third wing contains two values from apex values not in first wing values;
h) Second and third wings common value may be eliminated from cell in apex column/row and second wing row/column intersection.

R. Jamil
Last edited by rjamil on Wed Sep 27, 2017 8:34 pm, edited 5 times in total.
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Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby StrmCkr » Tue Sep 26, 2017 5:00 am

Please also note that the above mentioned cases might also be considered as WXYZ-Wings strategies (that contain 4 cells with 4 clues in total), as blue mentioned

i do agree they fit the bill as 4 cells with 4 digits: however they are bent around multiple sectors {instead of 1}, until i manage to come up with a simplistic rule that allows my code to deduce these easily as an als-xzish rule.. i'm not going to include them as a barns per-say thus stick them in with als-xy rule at this time as it already find them.

WXYZ-Wings Box-Box wise:- { i do find all of these as an als-XY rule : instead of trying decipher it as a hybrid-wing or almost almost als-xz rule }
with the following addition eliminations: {as seen in the theorized wxyz example case, and as pointed out way back then is easier to view it as an als-xy rule...}

Code: Select all
als-xy code:
  --------------+-------------+-----------  --------------+-------------+-----------
01)-Z  xyz  -Z  | -ZX -ZX xz  | -Z -Z  -Z 02)-Z  xyz  -Z  |  .   .  wy  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .    -Z  -Z   -Z  |  .   .   .  |  .  .   .
    .   .   wy  |  .  wx   .  |  .  .   .    -ZX -ZX  xz  |  .  wx   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

Code: Select all
 als-yx code
  --------------+-------------+-----------  --------------+-------------+-----------
03) .  xyz   .  | -ZX -ZX  xz |  .  .   . 04) .  xyz   .  |  .   .  wy  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .   .   wy  |  .  wxz  .  |  .  .   .     -ZX -ZX xz  |  .  wxz  .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
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Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby rjamil » Wed Sep 27, 2017 12:48 pm

Hi StrmCkr,

StrmCkr wrote:i do agree they fit the bill as 4 cells with 4 digits: however they are bent around multiple sectors {instead of 1},

If n cells contain n digits; and all cells share one sector/unit only, then its fall under naked tuples definition. What I understand the difference between naked tuples and wings is that wings cells share more than one sector/unit. Am I right?

R. Jamil
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Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby StrmCkr » Wed Sep 27, 2017 4:07 pm

rjamil wrote:Hi StrmCkr,

StrmCkr wrote:i do agree they fit the bill as 4 cells with 4 digits: however they are bent around multiple sectors {instead of 1},

If n cells contain n digits; and all cells share one sector/unit only, then its fall under naked tuples definition. What I understand the difference between naked tuples and wings is that wings cells share more than one sector/unit. Am I right?

R. Jamil


guess i need to be more careful with wording, {hopefully you can figure out what i meant }

all wings have this in in common:
    at least 1 digit common to both A & B sets that only occurs in a sector that is peer to both A & B sectors. *
    at least 1 other digit that is common to both A & B where that digit also exists in A and B but not all digits are in the intersection
    Set A has N cells with N+1 digits *
    Set B has N cells with N+1 digits *

Code: Select all
     .  xyz   .  | -ZX -ZX  xz |  .  .   .   -<----- set A using Row sector:  3 digits in 2 cells
        .   .    .  |  .   .   .  |  .  .   .   
        .   .   wy  |  .  wxz  .  |  .  .   .   <----- set B using Row sector:   4 digits in 2 cells. { not a valid  set B as defined above}



your other point on N tubules aka subset: yes a subset can also be a "wing"

N digits in N cells In 1 sector: if found remove all N digits from all peer cells of n cells.
that would eliminate abc from the "." cells in the row.

more advance elimination would also consider the location of each of the N digit and remove the peers cells to those number cell specifically.
ie: it would remove C from R23C123

Code: Select all
.   abc     ac  |  .   .   .  |  .  ab  .       
.     .      .  |  .   .   .  |    .  .   .   
.     .      .  |  .   .   .  |  .  .   .   
 


now how can the above be a "wing"
Code: Select all
.   abc     ac  |  .   .   .  |  .  ab  .       
.     .      .  |  .   .   .  |    .  .   .   
.     .      .  |  .   .   .  |  .  .   .   
 


set A: Box 1 digits ABC
set B: Col 7 digit ab
X: B
Z: A
eliminates A from the row

set A: Box 1 digits ABC
set B: Col 7 digit ab
X: a
Z: b
eliminates B from the row

set A: Box 1 digits ABC
set B: Col 3 digit ac
X: a
Z: c
eliminates c from the row and C from R23C123
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Re: Bent Almost Restricted N(aked)-Set {Barn}

Postby rjamil » Wed Sep 27, 2017 8:31 pm

Hi StrmCkr,

StrmCkr wrote:more advance elimination would also consider the location of each of the N digit and remove the peers cells to those number cell specifically.
ie: it would remove C from R23C123

Code: Select all
.   abc     ac  |  .   .   .  |  .  ab  .
.     .      .  |  .   .   .  |    .  .   .
.     .      .  |  .   .   .  |  .  .   .

Well, in above case, I will consider it in two moves, i.e,, Naked triplet in row 1; and then pointing and claiming intersection in Box 1 clue "c". (However, understand how separate three XYZ-Wings work. Thanks for providing clear picture.)

Note: please look in to WXYZ-Wings Row-Column-Box wise point "f" again (That's why I consider it as third wing instead of second apex). I have updated as per my previous post.

R. Jamil

Added on 20170929:
After further pm correspondence with StrmCkr; reading again specific portions of this site; and analyzing WXYZ-Wings patterns, got an idea of how to code all aspect of WXYZ-Wings that already SudokuWiki site detected as Bent Quads, as follows:

a) Grab four unsolved cells, not in one unit, having four clues in total;
b) Combine clues in cells that share unit separately;
c) Each unit clue(s), not present in other units, may be eliminated from unit other cells;
d) Two or more units common clue(s) may be eliminated from units' intersection cell(s).
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