The New Sudoku Players' Forum

[P.O.]

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9  .  2  .  .  3  7  .  .
.  .  7  5  .  6  9  4  .
.  4  .  7  9  .  .  .  1
.  .  9  .  6  .  .  1  .
.  2  .  .  .  1  .  .  5
8  .  .  3  .  .  4  .  .
.  .  4  8  .  .  5  .  .
.  9  .  6  .  4  1  7  .
6  .  .  .  3  .  .  .  4

9.2..37....75.694..4.79...1..9.6..1..2...1..58..3..4....48..5...9.6.417.6...3...4

9      1568   2      14     148    3      7      568    68             
13     138    7      5      128    6      9      4      238             
35     4      3568   7      9      28     2368   23568  1               
3457   357    9      24     6      2578   238    1      2378           
347    2      36     49     478    1      368    3689   5               
8      1567   156    3      257    2579   4      269    2679           
1237   137    4      8      127    279    5      2369   2369           
235    9      358    6      25     4      1      7      238             
6      1578   158    129    3      2579   28     289    4           


[P.O.]

my solution is an application of the strategy i talked about in this post:
http://forum.enjoysudoku.com/post333356.html#p333356
relationship OR between n9r7c9 - n9r79c8 => r1c5 <> 4 ste.
r7c9=9 context:

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((9 0) (7 9 9) (2 3 6 9))                                r7c9=9
   ((6 1 10) (7 8 9) (2 3 6 9))                            n6r7c8
   ((9 1 2 2) ((5 8 6) (3 6 8 9)) ((6 8 6) (2 6 9)))       n9r56c8
   ((9 1 1 2) ((9 4 8) (1 2 9)) ((9 6 8) (2 5 7 9)))       n9r9c46

((6 1 10) (7 8 9) (2 3 6 9))                             n6r7c8
   ((3 2 10) (8 9 9) (2 3 8))                              n3r8c9
   ((3 2 1 11) ((7 1 7) (1 2 3 7)) ((7 2 7) (1 3 7)))      n3r7c12

((9 1 1 2) ((9 4 8) (1 2 9)) ((9 6 8) (2 5 7 9)))        n9r9c46
   ((8 2 1 31) ((9 7 9) (2 8)) ((9 8 9) (2 8 9)))          n8r9c78
   ((2 2 1 31) ((9 7 9) (2 8)) ((9 8 9) (2 8 9)))          n2r9c78

((3 2 10) (8 9 9) (2 3 8))                               n3r8c9
   ((8 3 10) (8 3 7) (3 5 8))                              n8r8c3
   ((8 3 1 11) ((9 7 9) (2 8)) ((9 8 9) (2 8 9)))          n8r9c78
   ((2 3 1 11) ((9 7 9) (2 8)) ((9 8 9) (2 8 9)))          n2r9c78
   ((3 3 1 2) ((3 7 3) (2 3 6 8)) ((3 8 3) (2 3 5 6 8)))   n3r3c78
   ((3 3 1 2) ((2 1 1) (1 3)) ((2 2 1) (1 3 8)))           n3r2c12
   ((3 3 1 2) ((7 1 7) (1 2 3 7)) ((7 2 7) (1 3 7)))       n3r7c12

((8 2 1 31) ((9 7 9) (2 8)) ((9 8 9) (2 8 9)))           n8r9c78
   ((8 3 2 13) ((8 3 7) (3 5 8)) ((9 3 7) (1 5 8)))        n8r89c3
   ((8 3 2 13) ((1 2 1) (1 5 6 8)) ((2 2 1) (1 3 8)))      n8r12c2

((2 2 1 31) ((9 7 9) (2 8)) ((9 8 9) (2 8 9)))           n2r9c78
   ((2 3 12) (4 4 5) (2 4))                                n2r4c4


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9    18   2    14   148  3    7    58   68           
13   138  7    5    128  6    9    4    28           
5    4    6    7    9    28   238  238  1             
47   57   9    2    6    58   38   1    78           
47   2    3    49   48   1    68   89   5             
8    156  15   3    7    59   4    29   26           
137  137  4    8    12   27   5    6    9             
2    9    8    6    5    4    1    7    3             
6    157  15   19   3    79   28   28   4             

4r1c5 => r6c8 <> 2,9
 r1c5=4 - r5c5{n4 n8} - r5c7{n8 n6} - r6c9{n6 n2}
 r1c5=4 - c4n4{r1 r5} - b5n9{r5c4 r6c6}
=> r1c5 <> 4


r79c8=9 context:

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((9 0 2 0) ((7 8 9) (2 3 6 9)) ((9 8 9) (2 8 9)))        r79c8=9
   ((9 1 12) (5 4 5) (4 9))                                n9r5c4
   ((9 1 1 13) ((6 8 6) (2 6 9)) ((6 9 6) (2 6 7 9)))      n9r6c89

((9 1 12) (5 4 5) (4 9))                                 n9r5c4
   ((9 2 1) (6 9 6) (2 6 7 9))                             n9r6c9
   ((9 2 2 2) ((7 6 8) (2 7 9)) ((9 6 8) (2 5 7 9)))       n9r79c6

((9 2 1) (6 9 6) (2 6 7 9))                              n9r6c9
   ((7 3 10) (4 9 6) (2 3 7 8))                            n7r4c9


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9      1568   2      14     148    3      7      568    68             
13     138    7      5      128    6      9      4      238             
35     4      3568   7      9      28     2368   23568  1               
345    35     9      24     6      258    238    1      7               
347    2      36     9      478    1      368    368    5               
8      1567   156    3      257    257    4      26     9               
1237   137    4      8      127    279    5      2369   236             
235    9      358    6      25     4      1      7      238             
6      1578   158    12     3      2579   28     289    4       

4r1c5 => r129c2 <> 8
 r1c5=4 - r5n4{c5 c1} - b4n7{r5c1 r6c2} - c2n6{r6 r1}
 r1c5=4 - r5n4{c5 c1} - r5n7{c1 c5} - c5n8{r5 r2}
 r1c5=4 - r1c4{n4 n1} - r9c4{n1 n2} - r9c7{n2 n8}
=> r1c5 <> 4


[SteveG48]

Let me see if I understand what you are doing. The logic is:

Kraken 9 Box 9 => Kraken cell (2,9)r6c8 OR Kraken Column 8c2 => -4 r1c5 .

Correct?

If so, in establishing the two contexts from the possibilities of the 9s in box 9, what moves are you allowing?

[P.O.]

the reasoning is:
in the following relationship OR one of n9r7c9 or n9r79c8 must be true, the technique develops the consequences of setting alternatively each of them true reaching in each case a resolution state, then if a candidate is proven false in both of these resolution states then it can't be part of the solution and can be eliminated: if n9r7c9 is true r1c5 <> 4 and if n9r79c8 is true r1c5 <> 4 => r1c5 <> 4 is true.
the contexts are reached be developing the chains.

[SteveG48]

Yes, I think I followed and summarized the reasoning correctly. The question then is how you "developed the consequences" to arrive at the contexts. What moves do you allow in doing that?

If I assume 9 r7c9 is true and proceed allowing just singles to be taken, I don't get to the context you have for that scenario. If I allow all basic moves, I get all the way to a contradiction, allowing me to simply eliminate 9 r7c9. Either way, I don't get to your context.

Unfortunately, I don't understand the notation that you use in the hidden text. I've puzzled out some of it, but not enough. Perhaps if you'd translate a line or two it would help.

[P.O.]

here the consequences of setting r7c9=9, they follow the chain construction which is a bfs algorithm, the links that are single candidate are set and their eliminations done, the links that are group candidates do their eliminations, when all the links are done the resulting naked singles if any are set and their eliminations done

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                             at depth 1 there are 3 links
r7c9=9 - r7n6{c9 c8}         r7c8=6
       - b6n9{r6c9 r56c8}    r56c8=9
       - r9n9{c8 c46}        r9c46=9
         
                             from depth 1 to depth 2
r7c8=6 - b9n3{r7c8 r8c9}     r8c9=3
       - r7n3{c8 c12}        r7c12=3
       
                             from depth 1 to depth 2
r9c46=9 - 28r9c78            r9c78=28

                             from depth 2 to depth 3
r8c9=3 - r8n8{c9 c3}         r8c3=8
       - b9n8{r8c9 r9c78}    r9c78=8
       - b9n2{r8c9 r9c78}    r9c78=2
       - b3n3{r2c8 r3c78}    r3c78=3
       - r2n3{c9 c12}        r2c12=3
       - b7n3{r8c13 r7c12}   r7c12=3
       
                             from depth 2 to depth 3
r9c78=8 - b7n8{r9c23 r8c3}   r8c3=8
        - c2n8{r9 r12}       r12c2=8
         
                             from depth 2 to depth 3
r9c78=2 - c4n2{r9 r4}        r4c4=2


n5r3c1 is a NS it is set
n6r3c3 becomes a NS it is set
n2r8c1 becomes a NS it is set
n3r5c3 becomes a NS it is set
n5r8c5 becomes a NS it is set
n7r6c5 becomes a NS it is set

this is the resolution state that is reached and where n4r1c5 is proven contradictory, it is consistent it is not contradictory yet.

[SteveG48]

Thank you. I now understand what you did (and didn't do) in arriving at context 1.

If you would indulge me one more time, I'd like to understand the notation that you use in doing what you do. Here are the first few lines in your text for arriving at context 1:

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((9 0) (7 9 9) (2 3 6 9))                                r7c9=9
   ((6 1 10) (7 8 9) (2 3 6 9))                            n6r7c8
   ((9 1 2 2) ((5 8 6) (3 6 8 9)) ((6 8 6) (2 6 9)))       n9r56c8
   ((9 1 1 2) ((9 4 8) (1 2 9)) ((9 6 8) (2 5 7 9)))       n9r9c46


Could you translate? I can figure out things like (799) referring to row 7, column 9, box 9, and (2369) referring to the candidates there. What does the (9 0) mean there and similar in the first terms in following lines?

[P.O.]

a cell is coded ( (RCB coordinates) (candidates) )
a link is one or more cells preceded by a header ( (header) (cell) ... )

a link composed of a single cell has a header of length 2 or 3
a link composed of several cells has a header of length 4

the first digit of the header indicates the candidate that is set
the second digit of the header indicates the depth

for a link composed of several cells the third digit indicates the unit in which the cells are row=1 col=2 box=3
the last digit of the header is a code that indicates how the current link is linked to the previous one
for the first link of a chain this code is absent if the link codes a single cell or set to zero for a link of several cells

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((9 0) (7 9 9) (2 3 6 9))     : cell r7c9 forms a link on 9 at deph 0
((6 1 10) (7 8 9) (2 3 6 9))  : cell r7c8 forms a link on 6 at deph 1
                                linked to the previous one by the logic indicated by the code 10

((9 1 2 2) ((5 8 6) (3 6 8 9)) ((6 8 6) (2 6 9))) : cells r5c8 and r6c8 form a link on 9 at depth 1 in col
((9 1 1 2) ((9 4 8) (1 2 9)) ((9 6 8) (2 5 7 9))) : cells r9c4 and r9c6 form a link on 9 at depth 1 in row
these two links are linked to the previous one by the logic indicated by the code 2



[SteveG48]

Thank you!

[yzfwsf]

Hi P.O.
I modified the code for dynamic chains in my solver to support grouped nodes, but the solver can't find your elimination, is your code using a dynamic locking subset to extend the chain?

[P.O.]

hi yzfwsf,
the elimination is not found in the first resolution state but in each of the resolution state resulting from the development of the chains of the relation OR between n9r7c9 and n9r79c8 and therefore it is concluded that it is also valid in the first resolution state.

[yzfwsf]

Do you mean you used Dynamic+Dynamic Forcing Chains?

The first level of dynamics reaches the context you mentioned, while the second level of dynamics starts from 4r1c5 under the aforementioned context, which leads to conflicts?

[P.O.]

here is what i do:
starting from a resolution state
i find a relationship OR, from each term i develop its chain, from the links of the chain i set a context on the resolution state, if the context is not contradictory i build the chains i can find in it and keep their eliminations
when this is done i take the intersection of the different sets of eliminations, if it is not empty the eliminations found are necessarily valid because one of the terms is necessarily true
then i use theses eliminations to solve the puzzle
the relationship OR ensures the logic of the process

[yzfwsf]

Hi P.O.: Thanks.
Your chain is a "Dynamic+Dynamic Forcing Chain".

r7c9=9 context:

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9    18   2    14   148  3    7    58   68           
13   138  7    5    128  6    9    4    28           
5    4    6    7    9    28   238  238  1             
47   57   9    2    6    58   38   1    78           
47   2    3    49   48   1    68   89   5             
8    156  15   3    7    59   4    29   26           
137  137  4    8    12   27   5    6    9             
2    9    8    6    5    4    1    7    3             
6    157  15   19   3    79   28   28   4 


The context is the first dynamic layer.

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4r1c5 => r6c8 <> 2,9
 r1c5=4 - r5c5{n4 n8} - r5c7{n8 n6} - r6c9{n6 n2}
 r1c5=4 - c4n4{r1 r5} - b5n9{r5c4 r6c6}
=> r1c5 <> 4


The chain is the second dynamic layer.

r79c8=9 context:

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9      1568   2      14     148    3      7      568    68             
13     138    7      5      128    6      9      4      238             
35     4      3568   7      9      28     2368   23568  1               
345    35     9      24     6      258    238    1      7               
347    2      36     9      478    1      368    368    5               
8      1567   156    3      257    257    4      26     9               
1237   137    4      8      127    279    5      2369   236             
235    9      358    6      25     4      1      7      238             
6      1578   158    12     3      2579   28     289    4


The context is the first dynamic layer.

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4r1c5 => r129c2 <> 8
 r1c5=4 - r5n4{c5 c1} - b4n7{r5c1 r6c2} - c2n6{r6 r1}
 r1c5=4 - r5n4{c5 c1} - r5n7{c1 c5} - c5n8{r5 r2}
 r1c5=4 - r1c4{n4 n1} - r9c4{n1 n2} - r9c7{n2 n8}
=> r1c5 <> 4


The chain is the second dynamic layer.

[P.O.]

thanks yzfwsf, so i will use this name 'Dynamic+Dynamic Forcing Chain’ to identify this method
although the process is certainly more complex than that of an ordinary forcing-chain, the forcing-chain it gives are simpler for the same resolution
my next puzzle will illustrate this point