The New Sudoku Players' Forum

[P.O.]

from the Patterns Game, SER 9.1 but an easy one;

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

..7..64...1.5...2.9...3....8...9.....4.2...6...2..1..3..5..4.9..6....7.1...8..6..

235    2358   7      19     128    6      4      1358   589             
346    1      3468   5      478    789    389    2      6789           
9      258    468    147    3      278    158    1578   5678           
8      357    136    3467   9      357    125    1457   2457           
1357   4      139    2      578    3578   1589   6      5789           
567    579    2      467    45678  1      589    4578   3               
1237   2378   5      1367   1267   4      238    9      28             
234    6      3489   39     25     2359   7      3458   1               
12347  2379   1349   8      1257   23579  6      345    245       



[Cenoman]

A krakenless solution:

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 +------------------------+-------------------------+-----------------------+
 | b235    b2358   7      |  19     128     6       |  4     a1358   589    |
 |  346     1      3468   |  5      478     789     |  89-3   2      6789   |
 |  9      b258    468    |  147    3       278     |  158    1578   5678   |
 +------------------------+-------------------------+-----------------------+
 |  8       357    136    |  3467   9       357     |  125    1457   2457   |
 |  1357    4      139    |  2      578     3578    |  1589   6      5789   |
 |  567     579    2      |  467    45678   1       |  589    4578   3      |
 +------------------------+-------------------------+-----------------------+
 |  1237   c2378   5      |  1367   1267    4       | d238    9     d28     |
 |  234     6      3489   |  39     25      2359    |  7      3458   1      |
 |  12347   2379   1349   |  8      1257    23579   |  6      345    245    |
 +------------------------+-------------------------+-----------------------+

1. (3)r1c8 = (325-8)b1p128 = r7c2 - (8=23)r7c79 => -3 r2c7; lcls, 7 placements

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 +----------------------+-----------------------+---------------------+
 |  25     258   7      |Eg19    128     6      |  4      3   Fh59    |
 |  346    1     346    |  5     478     789    |  89     2     679   |
 |  9      258 GA46     |GA47    3       28-7   | a18-5  b18-7 G567   |
 +----------------------+-----------------------+---------------------+
 |  8      357 Bd136    |Ce367   9       357    |  2     c17    4     |
 |  1357   4     139    |  2     578     3578   |  1589   6     579   |
 |  567    579   2      |  467   45678   1      |  589    78    3     |
 +----------------------+-----------------------+---------------------+
 |  127    27    5      |  167   1267    4      |  3      9     8     |
 |  234    6     8      |Df39    25      2359   |  7      45    1     |
 |  1347   379   1349   |  8     157     357    |  6      45    2     |
 +----------------------+-----------------------+---------------------+

2. (1)r3c7 = r3c8 - r4c8 = (1-6)r4c3 = (6-3)r4c4 = (3-9)r8c4 = r1c4 - (9=5)r1c9 => -5 r3c7
3. (74=6)r3c34 - r4c3 = (6-3)r4c4 = (3-9)r8c4 = r1c4 - (9=5)r1c9 - (5=467)r3c349 => -7 r3c68; lclste

[DEFISE]

No initial basics.
S2-whip[6]: r7c9{n8 n2}- r7c7{n2 n3}- c8n3{r8 r1}- b1{3r1c1 NP:25p12}- r3c2{n2 .} => -8r7c2
Single(s): 8r8c3
Box/Line: 9r8b8 => -9r9c6
Naked triplets: 346b1p469 => -3r1c1 -3r1c2
Single(s): 3r1c8, 3r7c7, 8r7c9, 2r4c7, 2r9c9, 4r4c9
Box/Line: 1r1b2 => -1r3c4
Box/Line: 5b9c8 => -5r3c8 -5r4c8 -5r6c8
whip[7]: c4n9{r1 r8}- c4n3{r8 r4}- r4n6{c4 c3}- r3n6{c3 c9}- b3n5{r3c9 r3c7}- r3n1{c7 c8}- r4n1{c8 .} => -9r1c9
STTE

[AnotherLife]

Hi P.O.,
Sorry for my belated reply. I managed to solve this puzzle manually, and this is a very rare sudoku with SER 9.1 that is solvable by ALS-chains. Actually, Cenoman's third step can be slightly optimized to finish with only singles after a simpler chain. So only one ALS-chain is needed.

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.--------------------.--------------------.------------------.
| a235   a2358  7    | 19    128    6     | 4     b1358  589 |
| 346    1      3468 | 5     478    789   | c389  2     6789 |
| 9      a258   468  | 147   3      278   | 158   1578  5678 |
:--------------------+--------------------+------------------:
| 8      357    136  | 3467  9      357   | 125   1457  2457 |
| 1357   4      139  | 2     578    3578  | 1589  6     5789 |
| 567    579    2    | 467   45678  1     | 589   4578  3    |
:--------------------+--------------------+------------------:
| 1237   237-8  5    | 1367  1267   4     | d238  9     d28  |
| 234    6      3489 | 39    25     2359  | 7     3458  1    |
| 12347  2379   1349 | 8     1257   23579 | 6     345   245  |
'-------------------'--------------------'-------------------'

1. ALS W-Wing (analogous to Cenoman's step 1; my rule works again: start a chain from an ALS of 4-5 elements)
(8=3)b1p128 - r1c8 = r2c7 - (3=8)r7c79 => -8 r7c2; lcls

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.-------------------.--------------------.--------------------.
| 25    258  7      | gF19   128    6    | 4      3     hG59  |
| 346   1    346    | 5      478    789  | 89     2     679   |
| 9     258  B46    | 47     3      278  | a18-5  b178  A67-5 |
:-------------------+--------------------+--------------------:
| 8     357  dC136  | eD367  9      357  | 2      c17   4     |
| 1357  4    139    | 2      578    3578 | 1589   6     579   |
| 567   579  2      | 467    45678  1    | 589    78    3     |
:-------------------+--------------------+--------------------:
| 127   27   5      | 167    1267   4    | 3      9     8     |
| 234   6    8      | fE39   25     2359 | 7      45    1     |
| 1347  379  1349   | 8      157    357  | 6      45    2     |
'-------------------'--------------------'--------------------'

2. (1)r3c7 = r3c8 - r4c8 = (1-6)r4c3 = (6-3)r4c4 = (3-9)r8c4 = r1c4 - (9=5)r1c9 => -5 r3c7
3. (6)r3c9 = r3c3 - r4c3 = (6-3)r4c4 = (3-9)r8c4 = r1c4 - (9=5)r1c9 => -5 r3c9; ste

Thanks for the puzzle

[P.O.]

my solution:

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3r189c8 => r8c8 <> 8
 r1c8=3 - 258b1p128 - b7n8{r7c2 r8c3}
 r8c8=3 -
 r9c8=3 - 28r7c79
 
( n8r8c3 )
intersection: ((((9 0) (8 4 8) (3 9)) ((9 0) (8 6 8) (2 3 5 9))))
TRIPLET BOX: ((2 1 1) (3 4 6)) ((2 3 1) (3 4 6)) ((3 3 1) (4 6))
(((1 1 1) (2 3 5)) ((1 2 1) (2 3 5 8)))
( n3r1c8  n3r7c7  n8r7c9  n2r9c9  n2r4c7  n4r4c9 )
intersections: ((((5 0) (8 8 9) (4 5)) ((5 0) (9 8 9) (4 5)))
               (((1 0) (3 7 3) (1 5 8)) ((1 0) (3 8 3) (1 7 8))))
 
5b3p379 => r4c4 <> 3
 r1c9=5 - r1n9{c9 c4} - r8c4{n9 n3}
 r3c7=5 - c7n1{r3 r5} - r4n1{c8 c3} - r4n6{c3 c4}
 r3c9=5 - r3n6{c9 c3} - r4n6{c3 c4}
 
ste.


thank you for your answers, hi Bogdan,
it certainly is one of the rare SER 9.1 that has a short solution with chains that are not too complex; i try lot of puzzles in that category of difficulty before finding one that meets these constraints; also ALS in chains seems a requirement at this level, not forcing chain obviously but 'forcing' is only one method, it often breaks down long developments into shorter, more easily understood pieces;

[AnotherLife]

I'm not sure if you are interested in this, but I know only one puzzle with SER 9.1 besides your one that is solvable without forcing chains.

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1....6..945.7......8.......2.7.3...4.3.9......94.2.3.1........7...8.2.1....3.4.26

It seems to have a rather long solution with ALS-chains.

[P.O.]

hi Bogdan,
indeed its solution without forcing chains is long, the one i have is 33 chains + basics but the chains only have a max length of 4;
concerning forcing chains, it is only a method of reasoning, the chains used in that reasoning can be of whatever type: simple AIC, ALS-chain etc.
the opposition between forcing chains or not is in the method of reasoning not the chains, and this method of reasoning can be simpler and more powerful than others, that is in the electronic hands of an algorithm, in the manual hands of a human it is another story i guess;

checking the puzzles from the Patterns Game, i found some solvable without forcing chains and within a reasonable time, the numbers following the ratings are the numbers of chains and the maximum length, they depend on the setting of the algorithm, and basic patterns must be added too;
from page 2 of Patterns Game Results:

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game15 "..1...2...34...15.67.....38...6.3......789......1.5...54.....69.69...32...7...4.."  9.1/2.3/2.3  (28 10)
game15 "..1...2...34...65.69.....38...6.3......789......1.5...74.....16.69...32...3...9.."  9.1/9.1/2.6  (19  7)
game17 "..1...2.....8.3...9...1...5.1.6.7.8...8...3...6.9.8.1.2...7...9...4.6.....5...7.."  9.1/9.1/2.6  (34  6)
game17 "..1...2.....3.4...5...6...7.2.6.5.8...5...9...7.9.8.2.3...8...6...4.6.....7...1.."  9.1/9.1/3.2  (45 11)
game19 "1...2...3.9.....4....5.6.....5...2..2...5...6..8...5.....8.7....3.....9.4...6...1"  9.1/9.1/8.3  (24 10)
game20 "1..8..4......1..2...7..3..96.....2...5..9..4...9.....32..6..8...7..8......1..5..7"  9.1/1.2/1.2  (25 10)
game21 "...........64.93...375.146..65...94.....4.....84...17..436.879...97.36..........."  9.1/1.2/1.2  (18  6)
game22 "...1.......1..2..3.8..4..6.7..4..8....3..1..9.5..7..3....5.......6..9..2.3..6..1."  9.1/9.1/9.0  (25  8)
game23 "12.....34..3...5..5...3...13..6.7..8..6...4..9..5.2..34...1...6..9...1..81.....45"  9.1/9.1/2.6  (27  5)
game25 "..8..59...2.....1.7..6....4..63....2.........9....74..5....9..3.1.....7...32..8.."  9.1/9.1/9/1  (31  8)
game26 "...........12.34...2.4.5.6..47...82...........62...35..8.5.6.7...37.81..........."  9.1/9.1/6.6  (44  8)
game26 "...........12.34...5.6.7.8..89...67...........12...83..7.9.2.6...84.19..........."  9.1/9.1/6.7  (48  8)
game28 ".13.....28.2......59.6.......1.43......8.1......75.4.......7.23......6.89.....57."  9.1/9.1/8.9  (34  8)
game28 ".12.....34.3......56.1.......1.72......5.4......86.9.......7.32......6.78.....59."  9.1/9.1/9.0  (35  7)


that's 14 out of 34.

[AnotherLife]

the opposition between forcing chains or not is in the method of reasoning not the chains, and this method of reasoning can be simpler and more powerful than others, that is in the electronic hands of an algorithm, in the manual hands of a human it is another story i guess;

As for me, it's hard to apply forcing chains in manual solving but I regularly apply AICs with ALS-nodes, and I consider them as a good human method.

i found some solvable without forcing chains and within a reasonable time...
........
that's 14 out of 34

I've checked all the above puzzles with YZF_Sudoku, and I found that only the last one is solvable without forcing chains.

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.12.....34.3......56.1.......1.72......5.4......86.9.......7.32......6.78.....59.

That is, it is solvable by standard patterns implemented in YZF_Sudoku and AICs with ALS-nodes. Obviously, you allow yourself to apply some more methods besides these.

[P.O.]

Obviously, you allow yourself to apply some more methods besides these.

the chains i use can form links with ALS and have what is sometimes called memorization; as an example: game15 SER 9.1/9.1/2.6 with a different setting of the algorithm, there are fewer chains but the maximum length is slightly longer;

Hidden Text: Show

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

..1...2...34...65.69.....38...6.3......789......1.5...74.....16.69...32...3...9..

intersections:
((((4 0) (4 5 5) (2 4)) ((4 0) (6 5 5) (2 4)))
 (((2 0) (4 5 5) (2 4)) ((2 0) (6 5 5) (2 4))))

TRIPLET ROW: ((7 3 7) (2 5 8)) ((7 6 8) (2 8)) ((7 7 9) (5 8))
(((7 4 8) (2 3 5 8 9)) ((7 5 8) (3 5 9)))

QUAD COL: ((1 1 1) (5 8)) ((2 1 1) (2 8)) ((8 1 7) (1 5 8)) ((9 1 7) (1 2 5 8))
(((4 1 4) (1 2 4 5 8 9)) ((5 1 4) (1 2 3 4 5)) ((6 1 4) (2 3 4 8 9)))

intersection:
((((1 0) (4 2 4) (1 2 5 7 8)) ((1 0) (5 2 4) (1 2 5))))

58      578     1       34589   35679   4678    2       479     479             
28      3       4       289     179     1278    6       5       179             
6       9       257     245     157     1247    147     3       8               
49      12578   2578    6       24      3       14578   4789    124579           
34      125     256     7       8       9       145     46      12345           
349     278     2678    1       24      5       478     46789   23479           
7       4       258     39      39      28      58      1       6               
158     6       9       458     157     1478    3       2       457             
1258    258     3       2458    1567    124678  9       478     457             


c1n2{r2 r9} - r7n2{c3 c6} => r2c6 <> 2

c3n6{r6 r5} - r5c8{n6 n4} - b9n4{r9c8 r89c9} - 79r1c89 - b1n7{r1c2 r3c3} => r6c3 <> 7

c7n7{r46 r3} - c3n7{r3 r4} => r4c89 <> 7

c5n4{r6 r4} - r4c1{n4 n9} - r4c8{n49 n8} - b9n8{r9c8 r7c7} - c3n8{r7 r6} - r6n6{c3 c8} - r5c8{n6 n4} => r6c789 <> 4

r6c7{n7 n8} - b9n8{r7c7 r9c8} - b9n7{r9c8 r89c9} => r6c9 <> 7

c3n7{r3 r4} - c2n7{r46 r1} - 49r1c89 - c7n4{r3 r45} - r5c8{n4 n6} - r6n6{c8 c3} - c3n8{r6 r7} - b9n8{r7c7 r9c8} - b9n7{r9c8 r89c9} - b3n7{r2c9 r3c7} => r3c56 <> 7

r6c7{n8 n7} - r3n7{c7 c3} - c2n7{r1 r4} - c2n1{r4 r5} - b4n5{r5c2 r45c3} - r7n5{c3 c7} => r7c7 <> 8

( n5r7c7   n8r9c8 )

intersections:
((((7 0) (8 9 9) (4 7)) ((7 0) (9 9 9) (4 7)))
 (((4 0) (8 9 9) (4 7)) ((4 0) (9 9 9) (4 7))) ( n1r2c9   n9r1c9 )
 (((7 0) (2 5 2) (7 9)) ((7 0) (2 6 2) (7 8))))

PAIR ROW: ((4 1 4) (4 9)) ((4 8 6) (4 9)) 
(((4 5 5) (2 4)) ((4 7 6) (1 4 7 8)))

( n2r4c5   n5r4c9   n4r6c5 )

c4n3{r1 r7} - c4n9{r7 r2} - r2c5{n9 n7} - r2c6{n7 n8} => r1c4 <> 8

b1n7{r1c2 r3c3} - r4c3{n7 n8} - c2n8{r46 r1} => r1c2 <> 5

c7n8{r6 r4} - r4c3{n8 n7} - r3n7{c3 c7} => r6c7 <> 7

( n8r6c7 )

X-WING ROW: n7 (1 6) (2 8)
(((4 2 4) (1 7 8)))

c3n7{r3 r4} - r6c2{n7 n2} - r6c3{n2 n6} - r5c3{n26 n5} => r3c3 <> 5

( n5r5c3   n5r1c1   n6r5c8   n6r6c3   n5r9c2 )

X-WING COL: n8 (1 4) (2 8)
(((2 6 2) (7 8)) ((8 6 8) (1 4 7 8)))

( n7r2c6   n9r2c5   n3r7c5   n6r1c5   n9r7c4   n3r1c4   n6r9c6 )

X-WING ROW: n2 (2 9) (1 4)
(((3 4 2) (2 4 5)))

c1n1{r9 r8} - r8c6{n1 n4} - r9c4{n4 n2} => r9c1 <> 2

( n1r9c1   n7r9c5   n4r9c9   n8r8c1   n7r8c9   n2r9c4   n2r2c1
  n8r2c4   n7r3c3   n4r3c7   n8r4c3   n1r5c7   n2r7c3   n8r7c6
  n8r1c2   n4r1c6   n7r1c8   n5r3c4   n1r3c5   n2r3c6   n1r4c2
  n7r4c7   n2r5c2   n3r5c9   n7r6c2   n9r6c8   n2r6c9   n4r8c4
  n5r8c5   n1r8c6   n4r4c8   n4r5c1   n3r6c1   n9r4c1 )

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



[denis_berthier]

.
All the puzzles in P.O.'s list can be solved without forcing chains.
It's always very risky to state that a puzzle needs some particular pattern: there can be alternate ways of solving it.

The first 13 need only whips (of length at most 12 - but 8 is enough for some of them).
The hardest of them (#14, the last one) can be solved in gW11:

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------------+-------------------------+-------------------------+
   ! 79      1       2       ! 4679    4589    5689    ! 478     45678   3       !
   ! 4       789     3       ! 2679    2589    5689    ! 1278    125678  15689   !
   ! 5       6       789     ! 1       23489   389     ! 2478    2478    489     !
   +-------------------------+-------------------------+-------------------------+
   ! 369     34589   1       ! 39      7       2       ! 348     4568    4568    !
   ! 23679   23789   6789    ! 5       139     4       ! 12378   12678   168     !
   ! 237     23457   457     ! 8       6       13      ! 9       12457   145     !
   +-------------------------+-------------------------+-------------------------+
   ! 169     459     4569    ! 469     14589   7       ! 148     3       2       !
   ! 1239    23459   459     ! 2349    1234589 13589   ! 6       148     7       !
   ! 8       2347    467     ! 2346    1234    136     ! 5       9       14      !
   +-------------------------+-------------------------+-------------------------+
218 candidates.
218 g-candidates, 1093 csp-glinks and 673 non-csp glinks

Code: Select all

g-whip[6]: c3n8{r5 r3} - r3n7{c3 c789} - c7n7{r2 r3} - r1c7{n7 n4} - r3c8{n4 n2} - b6n2{r5c8 .} ==> r5c7≠8
g-whip[8]: c4n3{r9 r4} - c7n3{r4 r5} - b4n3{r5c2 r6c123} - r6c6{n3 n1} - r9n1{c6 c9} - b6n1{r6c9 r5c8} - b6n7{r5c8 r6c8} - b6n2{r6c8 .} ==> r9c5≠3
whip[8]: c5n1{r9 r5} - b5n9{r5c5 r4c4} - b5n3{r4c4 r6c6} - r9c6{n3 n6} - r7c4{n6 n4} - r9c5{n4 n2} - r8c4{n2 n3} - r9c4{n3 .} ==> r8c6≠1
g-whip[8]: r4c4{n9 n3} - r6c6{n3 n1} - r5c5{n1 n9} - r1n9{c5 c1} - b4n9{r5c1 r4c2} - b4n5{r4c2 r6c123} - r6c9{n5 n4} - b4n4{r6c2 .} ==> r2c4≠9
g-whip[9]: r3n7{c8 c3} - r9n7{c3 c2} - r2n7{c2 c4} - c4n2{r2 r789} - r9n2{c5 c4} - r9n3{c4 c6} - c4n3{r8 r4} - c7n3{r4 r5} - c7n7{r5 .} ==> r1c8≠7
g-whip[9]: c6n8{r3 r8} - r7n8{c5 c7} - r1n8{c7 c8} - b3n5{r1c8 r2c789} - c6n5{r2 r1} - r1n6{c6 c4} - r2c6{n6 n9} - r2c2{n9 n7} - c4n7{r2 .} ==> r2c5≠8
g-whip[10]: c6n1{r6 r9} - r9c9{n1 n4} - r9c5{n4 n2} - b2n2{r2c5 r2c4} - c4n7{r2 r1} - c1n7{r1 r456} - r6n7{c2 c1} - r6n2{c1 c2} - c1n2{r5 r8} - r8n1{c1 .} ==> r6c8≠1
g-whip[10]: c4n3{r9 r4} - c7n3{r4 r5} - c1n3{r5 r6} - c2n3{r6 r9} - r9n7{c2 c3} - r3n7{c3 c789} - c7n7{r2 r3} - c7n2{r3 r2} - r3n2{c8 c5} - r3n3{c5 .} ==> r8c6≠3
whip[11]: r9c9{n4 n1} - r9c5{n1 n2} - b2n2{r2c5 r2c4} - c4n7{r2 r1} - c4n6{r1 r7} - r9c6{n6 n3} - c4n3{r8 r4} - c7n3{r4 r5} - c7n2{r5 r3} - c7n7{r3 r2} - c7n1{r2 .} ==> r9c4≠4
g-whip[11]: r9c9{n4 n1} - r8c8{n1 n8} - r7n8{c7 c5} - b8n1{r7c5 r8c5} - b8n5{r8c5 r8c6} - b8n9{r8c6 r789c4} - r4c4{n9 n3} - c7n3{r4 r5} - r5n1{c7 c8} - b6n7{r5c8 r6c8} - b6n2{r6c8 .} ==> r7c7≠4
whip[7]: r7c7{n8 n1} - r9c9{n1 n4} - r3c9{n4 n9} - r3c3{n9 n7} - r1c1{n7 n9} - r7c1{n9 n6} - r9c3{n6 .} ==> r3c7≠8
whip[8]: r9c9{n4 n1} - r7c7{n1 n8} - r1c7{n8 n7} - r3c7{n7 n2} - r2c7{n2 n1} - b6n1{r5c7 r5c8} - c8n2{r5 r6} - c8n7{r6 .} ==> r3c9≠4
g-whip[8]: r9n1{c6 c9} - r7c7{n1 n8} - b8n8{r7c5 r8c6} - b8n5{r8c6 r7c5} - b8n9{r7c5 r789c4} - r4c4{n9 n3} - r4c7{n3 n4} - c9n4{r4 .} ==> r8c5≠1
whip[4]: b9n4{r9c9 r8c8} - r8n1{c8 c1} - b7n2{r8c1 r8c2} - b7n3{r8c2 .} ==> r9c2≠4
g-whip[6]: r9c9{n4 n1} - b8n1{r9c6 r7c5} - r7n4{c5 c4} - r7n9{c4 c123} - r8c3{n9 n5} - b8n5{r8c5 .} ==> r9c3≠4
whip[6]: c3n8{r5 r3} - r3c9{n8 n9} - r3c6{n9 n3} - r6c6{n3 n1} - r9c6{n1 n6} - r9c3{n6 .} ==> r5c3≠7
whip[6]: r3n3{c5 c6} - r6c6{n3 n1} - r9c6{n1 n6} - r9c3{n6 n7} - r3c3{n7 n8} - r3c9{n8 .} ==> r3c5≠9
whip[6]: r3n3{c5 c6} - r6c6{n3 n1} - r9c6{n1 n6} - r9c3{n6 n7} - r3c3{n7 n9} - r3c9{n9 .} ==> r3c5≠8
whip[6]: r3c9{n8 n9} - r3c6{n9 n3} - r6c6{n3 n1} - r9c6{n1 n6} - r9c3{n6 n7} - r3c3{n7 .} ==> r3c8≠8
g-whip[5]: c7n7{r3 r5} - c7n2{r5 r123} - r3c8{n2 n4} - c7n4{r1 r4} - c7n3{r4 .} ==> r2c8≠7
g-whip[5]: c7n2{r3 r5} - c7n7{r5 r123} - r3c8{n7 n4} - c7n4{r1 r4} - c7n3{r4 .} ==> r2c8≠2
g-whip[5]: c7n4{r3 r4} - c7n3{r4 r5} - c7n7{r5 r123} - r3c8{n7 n2} - b6n2{r5c8 .} ==> r1c8≠4
whip[9]: r7c7{n1 n8} - r8c8{n8 n4} - r9n4{c9 c5} - r3n4{c5 c7} - r4c7{n4 n3} - r4c4{n3 n9} - r7c4{n9 n6} - r9c6{n6 n3} - c4n3{r8 .} ==> r9c9≠1
naked-single ==> r9c9=4
whip[1]: r9n1{c6 .} ==> r7c5≠1
whip[4]: r4c4{n9 n3} - r6c6{n3 n1} - r6c9{n1 n5} - b4n5{r6c2 .} ==> r4c2≠9
whip[6]: c3n8{r5 r3} - r3c9{n8 n9} - r3c6{n9 n3} - r6c6{n3 n1} - r6c9{n1 n5} - b4n5{r6c2 .} ==> r4c2≠8
whip[1]: r4n8{c9 .} ==> r5c8≠8, r5c9≠8
whip[4]: r6n3{c2 c6} - b5n1{r6c6 r5c5} - r5c9{n1 n6} - b4n6{r5c1 .} ==> r4c1≠3
g-whip[7]: c4n3{r9 r4} - r4n9{c4 c1} - r1n9{c1 c456} - r3c6{n9 n8} - r3c9{n8 n9} - r3c3{n9 n7} - r1c1{n7 .} ==> r9c6≠3
whip[5]: b5n9{r4c4 r5c5} - c5n1{r5 r9} - r9c6{n1 n6} - b2n6{r1c6 r2c4} - c4n7{r2 .} ==> r1c4≠9
g-whip[5]: c4n7{r1 r2} - c4n6{r2 r789} - r9c6{n6 n1} - r9c5{n1 n2} - b2n2{r2c5 .} ==> r1c4≠4
whip[1]: c4n4{r8 .} ==> r7c5≠4, r8c5≠4
whip[4]: r3n7{c8 c3} - r9c3{n7 n6} - b8n6{r9c4 r7c4} - r1c4{n6 .} ==> r1c7≠7
biv-chain[4]: r3n3{c6 c5} - c5n4{r3 r1} - r1c7{n4 n8} - r3c9{n8 n9} ==> r3c6≠9
whip[4]: c1n7{r6 r1} - r1c4{n7 n6} - b8n6{r7c4 r9c6} - r9c3{n6 .} ==> r6c3≠7
whip[5]: c1n3{r6 r8} - c1n1{r8 r7} - r7c7{n1 n8} - r4c7{n8 n4} - r1c7{n4 .} ==> r4c2≠3
naked-pairs-in-a-block: b4{r4c2 r6c3}{n4 n5} ==> r6c2≠5, r6c2≠4
whip[5]: r6c9{n5 n1} - r6c6{n1 n3} - r3c6{n3 n8} - b1n8{r3c3 r2c2} - c9n8{r2 .} ==> r4c9≠5
z-chain[4]: r4n5{c8 c2} - r4n4{c2 c7} - r1c7{n4 n8} - b9n8{r7c7 .} ==> r4c8≠8
whip[5]: c8n8{r2 r8} - b9n1{r8c8 r7c7} - r2n1{c7 c8} - b3n5{r2c8 r1c8} - b3n6{r1c8 .} ==> r2c9≠8
g-whip[5]: c4n2{r9 r2} - c4n7{r2 r1} - b2n6{r1c4 r123c6} - r9c6{n6 n1} - r9c5{n1 .} ==> r8c5≠2
whip[6]: r4c1{n9 n6} - r5c3{n6 n8} - b1n8{r3c3 r2c2} - b1n9{r2c2 r3c3} - r3c9{n9 n8} - r4c9{n8 .} ==> r5c1≠9
z-chain[4]: r9n3{c2 c4} - r4c4{n3 n9} - r5n9{c5 c3} - r5n8{c3 .} ==> r5c2≠3
whip[6]: r4c1{n6 n9} - r7c1{n9 n1} - r7c7{n1 n8} - r1c7{n8 n4} - r4c7{n4 n3} - r4c4{n3 .} ==> r5c1≠6
naked-triplets-in-a-block: b4{r5c1 r6c1 r6c2}{n2 n3 n7} ==> r5c2≠7, r5c2≠2
biv-chain[3]: r4c9{n8 n6} - b4n6{r4c1 r5c3} - c3n8{r5 r3} ==> r3c9≠8
singles ==> r3c9=9, r4c9=8
biv-chain[5]: r9c6{n6 n1} - r6c6{n1 n3} - r3c6{n3 n8} - r3c3{n8 n7} - r9c3{n7 n6} ==> r9c4≠6
biv-chain[5]: r6c3{n4 n5} - r6c9{n5 n1} - c6n1{r6 r9} - b8n6{r9c6 r7c4} - c4n4{r7 r8} ==> r8c3≠4
z-chain[3]: r8c3{n5 n9} - r7c2{n9 n4} - r4c2{n4 .} ==> r8c2≠5
whip[4]: r8c3{n9 n5} - r7c2{n5 n4} - r7c4{n4 n6} - r7c3{n6 .} ==> r7c1≠9
z-chain[3]: b5n9{r5c5 r4c4} - c1n9{r4 r8} - c6n9{r8 .} ==> r1c5≠9
biv-chain[4]: r5c9{n1 n6} - r4n6{c8 c1} - r7c1{n6 n1} - b9n1{r7c7 r8c8} ==> r5c8≠1
whip[4]: r8c3{n9 n5} - b8n5{r8c5 r7c5} - r7n9{c5 c4} - r4n9{c4 .} ==> r8c1≠9
z-chain[5]: r8n4{c4 c2} - r8n2{c2 c1} - c1n1{r8 r7} - c1n6{r7 r4} - r4n9{c1 .} ==> r8c4≠9
whip[5]: r8c3{n9 n5} - b8n5{r8c5 r7c5} - r7n9{c5 c4} - c3n9{r7 r5} - b5n9{r5c5 .} ==> r8c2≠9
biv-chain[6]: r1c7{n8 n4} - r4c7{n4 n3} - r4c4{n3 n9} - r4c1{n9 n6} - r7c1{n6 n1} - r7c7{n1 n8} ==> r2c7≠8
biv-chain[6]: r1c7{n4 n8} - r7c7{n8 n1} - r7c1{n1 n6} - r4c1{n6 n9} - r4c4{n9 n3} - r4c7{n3 n4} ==> r3c7≠4
biv-chain[4]: r3n3{c6 c5} - c5n4{r3 r1} - c7n4{r1 r4} - r4n3{c7 c4} ==> r6c6≠3
singles ==> r6c6=1, r6c9=5, r6c3=4, r4c2=5, r9c6=6, r9c3=7, r3c3=8, r3c6=3, r5c2=8, r9c5=1
whip[1]: c5n2{r3 .} ==> r2c4≠2
whip[1]: r3n7{c8 .} ==> r2c7≠7
whip[1]: r6n3{c2 .} ==> r5c1≠3the ratnaked-pairs-in-a-row: r7{c2 c4}{n4 n9} ==> r7c5≠9, r7c3≠9
hidden-triplets-in-a-column: c8{n1 n5 n8}{r8 r2 r1} ==> r2c8≠6, r1c8≠6
stte

No doubt this resolution path could be shortened, but this is not my point.
I don't like forcing-patterns in general, as it means one has to follow and combine several streams of reasoning, but this is not my point either.
As I've shown with precise stats (using my controlled-bias collection), forcing chains are rarely able to reduce the rating of a puzzle - if one has a consistent definition of their length (not the case of P.O.).

[AnotherLife]

P.O., I've analyzed your solution of this puzzle.

Code: Select all

..1...2...34...65.69.....38...6.3......789......1.5...74.....16.69...32...3...9..

I see that you apply a method called Forcing Net in HoDoKu or Dynamic Forcing Chain in YZF_Solver, and it is even more complicated than a forcing chain for a human solver.

Code: Select all

.-------------------.----------------------.---------------------.
| 58    578    1    | 34589  35679  4678   | 2      479    479   |
| 28    3      4    | 289    179    178    | 6      5      179   |
| 6     9      257  | 245    157    1247   | 147    3      8     |
:-------------------+----------------------+---------------------:
| 49    12578  2578 | 6      24     3      | 14578  489    12459 |
| 34    125    256  | 7      8      9      | 145    46     12345 |
| 349   278    268  | 1      24     5      | 478    46789  23479 |
:-------------------+----------------------+---------------------:
| 7     4      258  | 39     39     28     | 58     1      6     |
| 158   6      9    | 458    157    1478   | 3      2      457   |
| 1258  258    3    | 2458   1567   124678 | 9      478    457   |
'-------------------'----------------------'---------------------'

c5n4{r6 r4} - r4c1{n4 n9} - r4c8{n49 n8} - b9n8{r9c8 r7c7} - c3n8{r7 r6} - r6n6{c3 c8} - r5c8{n6 n4} => r6c789 <> 4

Let me try to explain your method from a human point of view.
r6c7=4 or r6c8=4 or r6c9=4 => r6c5<>4 => r4c5=4 =>
1.1 r4c8<>4
1.2 r4c1<>4 => r4c1=9 => r4c8<>9 => (because of 1.1) r4c8=8 =>
2.1 r4c4<>8
2.2 r9c8<>8 => r7c7=8 => r7c3<>8 => (because of 2.1) => r6c3=8 => r6c3<>6 => r6c8=6 => r5c8<>6 => r5c8=4 => r6c789<>4 contradiction
Consequently, r6c789<>4. You can look at this method in visual form.
Surely, this is not human logic.

[P.O.]

hi Bogdan, here is my understanding of this chain:

Code: Select all

in b5 4 is either in r6c5 or r4c5
if r6c5=4 then r6c789 <> 4
if r4c5=4 then r4c1=9     4 is eliminated by the previous link
               r4c8=8     4&9 are eliminated by the two previous links
               r7c7=8     only 8 in b9 as 8 is eliminated from r9c8 by the previous link
               r6c3=8     only 8 in c3 as 8 in r7c3 and r4c3 are eliminated by previous links
               r6c8=6     only 6 in r6 as 6 in r6c3 is eliminated by the previous link
               r5c8=4     6 is eliminated by the previous link


here the XOR relationship between n4r6c5 and n4r4c5 allows to conclude that r6c789 <> 4 for it is eliminated by both;
the chain is built linearly, each link is added in the context of all the previous links;
the visual you provided, which is very clean and precise, perfectly shows the relationship between the links and allows a linear reading of the chain; but it seems to start from the end, which is eliminated, and not from the beginning, the XOR relationship, it's confusing;

the output of the algorithm:

Code: Select all

depth: 6  candidate: 4  from cells
(((6 7 6) (4 7 8)) ((6 8 6) (4 6 7 8 9)) ((6 9 6) (2 3 4 7 9)))

((4 0)    (6 5 5) (2 4))         
((4 0)    (4 5 5) (2 4))          c5n4{r6 r4}
((9 1 9)  (4 1 4) (4 9))          r4c1{n4 n9}
((8 2 76) (4 8 6) (4 8 9))        r4c8{n49 n8}
((8 3 1)  (7 7 9) (5 8))          b9n8{r9c8 r7c7}
((8 4 1)  (6 3 4) (2 6 8))        c3n8{r7 r6}
((6 5 10) (6 8 6) (6 7 8 9))      r6n6{c3 c8}
((4 6 9)  (5 8 6) (4 6))          r5c8{n6 n4}



[eleven]

Bogdan,

already many years ago these chains were called "memory chains" (Denis and P.O. use them), because you have to remember all direct consequences of former steps. This correponds to, what you get in a simple solver, when you enter each step (e.g. place a digit). Therefore these chains are more effective than AIC's.
As you say, this is not a typically manual solving method, though you could train it to some degree.

[AnotherLife]

Eleven, it looks somewhat strange to me that firstly P.O. stated that the puzzle in question could be solved without forcing chains but then it comes to be that he used the so called 'memory chains' instead of them. Let me quote this excerpt from HoDoKu website.

Code: Select all

HoDoKu uses the following definition: In a chain every link relies only on the step immediately before it. If a link only works, if it depends on the outcome of a link further up the chain, the chain becomes a net. The same is true, if the chain forks into branches that meet again further down the chain.

So these 'memory chains' are nets in terms of HoDoKu. I've seen you use krakens (forcing chains) several times, and I consider you a manual solver. Do you think it's right to place nets before forcing chains? Maybe we've come to a great gap between computer methods and human methods.

[eleven]

I don't think, we should call "memory chains" nets, because they are very restricted nets with precise rules.
For the rest - it's a matter of taste. We both seem to have a similar one, and i saw the same from really good manual solvers.