The New Sudoku Players' Forum

[Yogi]

000050060402000000000001000000300204018000000000000700050060010700200400000000000

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+---+---+---+
|...|.5.|.6.|
|4.2|...|...|
|...|..1|...|
+---+---+---+
|...|3..|2.4|
|.18|...|...|
|...|...|7..|
+---+---+---+
|.5.|.6.|.1.|
|7..|2..|4..|
|...|...|...|
+---+---+---+


[Leren]

No OTP takers yet. Try an X Wing, a W Wing & BUG+1. Leren

[P.O.]

i have this one
basics:

Hidden Text: Show

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( n1r6c9   n1r4c5   n4r3c8   n1r8c3   n1r9c4   n1r2c7   n2r9c8
  n7r2c8   n1r1c1   n2r7c1   n2r6c2   n4r6c3   n4r9c2   n5r2c9
  n4r5c5   n2r3c5   n2r5c6   n7r9c5   n7r5c4   n2r1c9   n5r6c4
  n7r7c9   n7r1c6   n4r7c6   n4r1c4 )

intersections:
((((8 0) (4 8 6) (5 8 9)) ((8 0) (6 8 6) (3 8 9)))
 (((6 0) (5 7 6) (3 5 6 9)) ((6 0) (5 9 6) (3 6 9)))
 (((6 0) (4 6 5) (6 8 9)) ((6 0) (6 6 5) (6 8 9)))
 (((3 0) (5 1 4) (3 5 9)) ((3 0) (6 1 4) (3 6 9)))
 (((3 0) (2 5 2) (3 8 9)) ((3 0) (2 6 2) (3 8 9))))

PAIR COL: ((1 3 1) (3 9)) ((7 3 7) (3 9)) 
(((3 3 1) (3 5 6 7 9)) ((4 3 4) (5 6 7 9)) ((9 3 7) (3 6 9)))

( n6r9c3   n6r8c9   n6r5c7   n5r9c7   n5r8c6 )


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1      389    39     4      5      7      389    6      2               
4      689    2      689    389    389    1      7      5               
5689   36789  57     689    2      1      389    4      389             
569    679    57     3      1      689    2      589    4               
359    1      8      7      4      2      6      359    39             
369    2      4      5      89     689    7      389    1               
2      5      39     89     6      4      389    1      7               
7      389    1      2      389    5      4      39     6               
89     4      6      1      7      389    5      2      389             

8r7c4 => r6c8 <> 3,8,9
                                        |- r7c3{n9 n3} - b9n3{r7c7 r8c8}
 r7c4=8 - b9n8{r7c7 r9c9} - r9c1{n8 n9} |- b8n9{r9c6 r8c5} - r6c5{n9 n8}
                                        |- r5n9{c1 c89}
 
=> r7c4 <> 8
ste.


[yzfwsf]

Smae as P.O., but shorter.
Braid[7]: => r7c4<>8;stte
8r7c4 - 8b9{r7c7=r9c9} - r9c1{n8=n9} - 9b8{r9c6=r8c5} - r8c8{n9=n3} - r6c5{n9=n8} - r6c8{n8=n9} - 9r5{r5c8=.}

[P.O.]

Same as P.O., but shorter.

i disagree with this
the length of a forcing chain is calculated as follows: number of distinct links divided by the number of branches
this forcing chain therefore has length: 8/3 or ~ 2.6

[Cenoman]

Similar,

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 +----------------------+----------------------+--------------------+
 |  1      389     39   |  4       5     7     |  389   6     2     |
 |  4      689     2    |  689     389   389   |  1     7     5     |
 |  5689   36789   57   |  689     2     1     |  389   4     389   |
 +----------------------+----------------------+--------------------+
 |  569    679     57   |  3       1     689   |  2     589   4     |
 | f359    1       8    |  7       4     2     |  6    e359  e39    |
 |  369    2       4    |  5     dc89    689   |  7   dc389   1     |
 +----------------------+----------------------+--------------------+
 |  2      5       39   | a9-8*    6     4     |  389   1     7     |
 |  7    ga389*    1    |  2    hba389*  5     |  4    b39    6     |
 |fa89*    4       6    |  1       7    a389*  |  5     2     389   |
 +----------------------+----------------------+--------------------+

Almost S-Wing (*)
[(8)r8c5 = r8c2 - (8=9)r9c1 - r9c6 = (9)r7c4] = (93)r8c58 - (9r6c5|3r6c8) = (8,9)r6c58 - r5c89 = (98)r59c1 - r8c2 = (8)r8c5 => -8 r7c4; ste

[yzfwsf]

i disagree with this
the length of a forcing chain is calculated as follows: number of distinct links divided by the number of branches
this forcing chain therefore has length: 8/3 or ~ 2.6

My chain is as follows:
Braid[47,96] 17 Candidates,
7 Truths = {9R5 9N1 6N5 68N8 8B9 9B8}
12 Links = {8r679 9r789 3c8 9c15 7n47 9b6}
2 Eliminations --> r7c4<>8, r7c7<>9
Your chain is as follows:
P.O.'s Chain [47,96] 20 Candidates,
8 Truths = {9R5 6N58 7N3 9N1 9B8 38B9}
14 Links = {3r7 8r679 9r79 3c8 9c15 7n47 9n9 9b67}
3 Eliminations --> r7c7<>39, r7c4<>8

[P.O.]

the length of a chain is one of the variables used to assess the complexity of the reasoning that a chain represents.
a forcing chain consists of dividing a long development into short parts, thus reducing its complexity this must be taken into account when calculating its length
on the other hand, we must not forget in the assessment of the complexity the type of chain used, a braid having a higher complexity than an aic for example

[Cenoman]

My two cents.

a forcing chain consists of dividing a long development into short parts

No, a forcing chain is not a division, it is the assembly of branches on a common stem, made of three or more candidates (possibly grouped) that are in a strong link together (strong link that is native or derived from ALS, AALS, DP, Impossible Patterns,...). I can't see any division in such proccessing, just displaying as many chains as branches on the stem, for clarity.
IMHO, forcing chain is a very bad naming for these logics. A reason why I never use it (using kraken instead). But I'm not an English native speaker.

the length of a forcing chain is calculated as follows: number of distinct links divided by the number of branches

Where does this come from ? Do you have a reference ?
Never heard of that before.

To me, the complexity measuring instrument of a move, is the size of its matrix:
Matrix of ysfwsf's braid:

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8r7c7 8r9c9
      8r9c1 9r9c1
9r7c4       9r9c6 9r8c5
                  9r8c8 3r8c8
                  9r6c5       8r6c5
                        3r6c8 8r6c8 9r6c8
            9r5c1                   9r5c89

TM 7x7 (size of the matrix = size of the braid - this always true, for braids as well as whips)

Matrix of P.O.'s move:

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8r7c7 8r9c9
      8r9c1 9r9c1
            9r7c3 3r7c3
      3r9c9       3r7c7 3r8c8
9r7c4       9r9c6             9r8c5
                              9r6c5 8r6c5
            9r5c1                         9r5c89
                        3r6c8       8r6c8 9r6c8

TM 8x8 (size of the move)

EDIT: corrected typo in the matrix (above). Thanks ysfwsf for spotting.
Deleted irrelevant end of the post.

[P.O.]

the length of a forcing chain is calculated as follows: number of distinct links divided by the number of branches
this is obviously a joke but which reflects well the simplification that this type of chain achieves
i don't like the name forcing chain either, for me it's a way of reasoning that has the advantage of simplifying a long and complex development into short parts that are more accessible to understanding and mechanically counting its length without taking this objective into account seems to me to be an error
your linearly written solution would be more accessible to the understanding if its writing divided its parts according to their articulation

[yzfwsf]

Matrix of P.O.'s move:

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8r7c7 8r9c9
      8r9c1 9r9c1
            9r7c3 3r7c3
      3r9c9       3r7c7 3r8c8
9r7c4       9r9c6             9r8c5
                              9r6c5 8r6c5
            9r5c1                         9r5c89
                        3r7c4       8r7c4 9r7c4

TM 8x8

But in this matrix, row #4 and col #5 are unnecessary, as 3r7c4 is linked to 3r7c3 as well:

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You must have made a typo. r7c4 does not have 3.

[Cenoman]

You must have made a typo. r7c4 does not have 3.

Thanks, yzwsf. I have edited my post.