Distributed Disjointed subset * Chains *

Advanced methods and approaches for solving Sudoku puzzles

Distributed Disjointed subset * Chains *

Postby StrmCkr » Mon Jan 16, 2017 10:48 am

I need some help formulating a rules set or an implementation method for programing
Code: Select all
.---------------.---------------.-------------.
| 5   8    2679 | 267  1    279 | 679  3    4 |
| 3   4    679  | 5    79   8   | 679  1    2 |
| 29  27   1    | 267  3    4   | 5    679  8 |
:---------------+---------------+-------------:
| 4   29   29   | 1    8    6   | 3    5    7 |
| 7   1    8    | 3    4    5   | 26   26   9 |
| 6   5    3    | 27   279  279 | 8    4    1 |
:---------------+---------------+-------------:
| 8   3    27   | 9    6    1   | 4    27   5 |
| 29  6    4    | 8    5    27  | 1    279  3 |
| 1   279  5    | 4    27   3   | 279  8    6 |
'---------------'---------------'-------------'


while looking at this puzzle over in the xyz-hybrid thread I noticed something interesting, that i would like to definitely program I need help on this one

i do not know if its covered under DDS {subset counting}

locked dds and/or almost locked dds (adds) can be bridged / chained together to apply eliminations.

Example 1a: DDS + ADDS
Code: Select all
:---------------+---------------+-------------:
| 8   3    27@  | 9    6    1   | 4   27@*  5 |
| 29* 6    4    | 8    5    27  | 1    279? 3 |
| 1   279  5    | 4    27   3   | 79-2  8   6 |
'---------------'---------------'-------------'


A : 27 @ R7C38 z = 2,7
B : 279 @ R8C19,R7C8 z = 2

all cells that see "pivot" "?" and @* cells may exclude common z from A&B

Example 1b:
Code: Select all
:---------------+---------------+-------------:
| 8   3    27   | 9    6    1   | 4    27   5 |
| 29@ 6    4    | 8    5    27* | 1    279  3 |
| 1  279@? 5    | 4    27@*  3  | 279  8    6 |
'---------------'---------------'-------------'

A: 27 @ R8C6,R9C5 z = 2,7
B: 279 @ R8C1,R9C25 Z= 2

all cells that see "pivot" "?" and @* cells may exclude common z in A&B


example 2a: ADDS + ADDS
Code: Select all
:---------------+---------------+-------------:
| 8   3    27@  | 9    6    1   | 4   27*   5 |
| 29*@ 6    4   | 8    5    27  | 1   279*? 3 |
| 1  279@?  5   | 4    27   3   | 79-2 8    6 |
'---------------'---------------'-------------'


A: 279 @ R7C3,R8C1,R9C2 Z = 2
B: 279 @ R7C8,R8C19, Z = 2

all cells that see all "pivot" ? cells may exclude common z in A&B

example 2b: adds + adds
Code: Select all
:---------------+---------------+-------------:
| 8   3    27 | 9    6    1   | 4   27   5 |
| 29@* 6   4  | 8   5  27*    | 1  279*? 3 |
| 1  279@? 5  | 4   27@  3    | 79-2  8  6 |
'---------------'---------------'-------------'

A: 279 @ R8C168 z= 2
B: 279 @ R8C1,R9C25 Z= 2

all cells that see all "pivot" ? cells may exclude common z in A&B


example 3: ADDS +ADDS +ADDS + adds
Code: Select all
:---------------+---------------+-------------:
| 8   3    27   | 9    6    1   | 4    27   5 |
| 29  6    4    | 8    5    27  | 1    279? 3 |
| 1   279? 5    | 4    27   3   | 79-2  8   6 |
'---------------'---------------'-------------'


A: 279 @ R7C3,R8C1,R9C2 Z = 2
C: 279 @ R8C168 z= 2
B: 279 @ R7C8,R8C19 Z = 2
D: 279 @ R8C1,R9C25 Z= 2

all cells that see all "pivot" ? cells may exclude common z in A,B,C,D
Some do, some teach, the rest look it up.
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StrmCkr
 
Posts: 647
Joined: 05 September 2006

Re: Distributed Disjointed subset * Chains *

Postby rjamil » Mon Jan 16, 2017 2:46 pm

Hi StrmCkr,

StrmCkr wrote:
Code: Select all
.---------------.---------------.-------------.
| 5   8    2679 | 267  1    279 | 679  3    4 |
| 3   4    679  | 5    79   8   | 679  1    2 |
| 29  27   1    | 267  3    4   | 5    679  8 |
:---------------+---------------+-------------:
| 4   29   29   | 1    8    6   | 3    5    7 |
| 7   1    8    | 3    4    5   | 26   26   9 |
| 6   5    3    | 27   279  279 | 8    4    1 |
:---------------+---------------+-------------:
| 8   3    27   | 9    6    1   | 4    27   5 |
| 29  6    4    | 8    5    27  | 1    279  3 |
| 1   279  5    | 4    27   3   | 279  8    6 |
'---------------'---------------'-------------'

I believe that you have collected pm from where XYZ-Wings Hybrid Type 2 elimination occurred, for that I have already completed programming.

Find Below steps to be taken for programming/understanding in my own way (however, credit goes to Prett Galford, who discovered; eleven and blue, who showed exemplars):

1) XYZ-Wing Hybrid strategy is based on four cells, i.e., one pivot cell (or hinge or apex), two pincer cells (or wings) and one hybrid cell (or finned), that contain exactly three values (or candidates or digits) and align within a chute;
2) Pivot cell contains all three values; and pincer cells and hybrid cell contain two values each;
3) First pincer cell align with pivot cell's line;
4) Second pincer cell contains only one common value with first pincer cell and align with pivot cell's box but not first pincer cell's line;

For Type 1:-
Code: Select all
-----------+----------+----------
  . abc  . |  .  . bc | -c -c -c
  .  .   . |  .  .  . |  .  .  .
  .  .  ac |  . bc  . |  .  .  .
-----------+----------+----------
5) Hybrid cell contains same values as first pincer cell (i.e., naked pair within box) and align with both first pincer cell's box and second pincer cell's line;
6) First and second pincers' common value may be eliminated from cells align with pivot cell and first pincer cell common line but not boxes.
Code: Select all
.3.....2.....4.9..7..6......8.3.2.........4.1.........4.9.6.......5...3.1........ Column
................12....34...............1..56..23.....7......2.8..9.....35.4..9... Row
................12....345.....1.6..7..8.......53....4....9.......4.5....1.......6 Column

For Type 2:-
Code: Select all
-----------+----------+----------
  . abc  . |  .  . bc |  .  .  .
 -c -c  -c |  .  .  . |  .  .  .
  .  .  ac |  . ac  . |  .  .  .
-----------+----------+----------
5) Hybrid cell contains same values as second pincer cell (i.e., naked pair within line) and align with both first pincer cell's box and second pincer cell's line;
6) First and second pincers' common value may be eliminated from cells align with pivot cell and second pincer cell common box but not first pincer cell and hybrid cell lines.
Code: Select all
................12....345.....1.6..7..8.......53....4....9.......4.5....1.......6 Row, Column

Hope the above steps cover both types and easy to understand/program.

R. Jamil

Edit: Exemplars added.
rjamil
 
Posts: 132
Joined: 15 October 2014
Location: Karachi, Pakistan

Re: Distributed Disjointed subset * Chains *

Postby StrmCkr » Tue Jan 17, 2017 9:36 am

more examples:
Code: Select all
 .  14  .  | .  . . |  .  .  . |
 . 1234  . | . 24 34| -4 -4 -4 |
 .  .  45  | .  . . |  .  . 45 |


Code: Select all
.  14  .  | .  . . |  .  .  . |
 . 1234  . | . 24 34|  -4 -4 -4|
 .  .  45  | .  . . |  47 .475 |
Some do, some teach, the rest look it up.
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StrmCkr
 
Posts: 647
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Re: Distributed Disjointed subset * Chains *

Postby rjamil » Tue Jan 17, 2017 1:53 pm

Hi StrmCkr,

It looks to me that WXYZ-Wing with naked tuple combination align within a chute.

Maybe, its (called WXYZ-Wings Hybrid) also work like XYZ-Wing Hybrid, i.e., XYZ-Wing with naked double combination align within a chute.

R. Jamil

Exemplars added:
Code: Select all
 ---------------+-------------+-----------
    .  wz    .  | wz   .   .  |  .  .   .
    . wxyz   .  |  .  xz  yz  |  .  .   .
   -Z  -Z   -Z  |  .   .   .  |  .  .   .
 ---------------+-------------+-----------
 ---------------+-------------+-----------
    .  wz    .  | xyz  .   .  |  .  .   .
    . wxyz   .  |  .  xz  yz  | -Z -Z  -Z
    .   .    .  |  .   .   .  |  .  .   .
 ---------------+-------------+-----------
rjamil
 
Posts: 132
Joined: 15 October 2014
Location: Karachi, Pakistan

Re: Distributed Disjointed subset * Chains *

Postby rjamil » Wed Feb 01, 2017 6:58 pm

Hi StrmCkr,

StrmCkr wrote:more examples:
Code: Select all
 . 14  .  | .  . . |  .  .  . |
 . 1234 . | . 24 34| -4 -4 -4 |
 .  .  45 | .  . . |  .  . 45 |


Code: Select all
 .  14  . | .  . . |  .  .  . |
 . 1234 . | . 24 34|  -4 -4 -4|
 .  .  45 | .  . . |  47 .475 |


Did you mean Irregular WXYZ-Wings?

I accidently found this site describing ER Winks (i.e. Empty Rectangle Weak Links and suggest name as Irregular WXYZ-Wings).

R. Jamil
rjamil
 
Posts: 132
Joined: 15 October 2014
Location: Karachi, Pakistan

Re: Distributed Disjointed subset * Chains *

Postby StrmCkr » Fri Feb 03, 2017 2:15 am

No, weak links require strong links with in sector to function. Ie limited placement.
Weaklinks can expand alot of techniques by a singular digit chain.


This idea here in uses an almost locked set of digits in a space as a strong link between groups to perform extra eliminations.

The difference being outside the sets could be other same candidates not removed yet which would render a single digit chain fruitless.
Some do, some teach, the rest look it up.
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