The New Sudoku Players' Forum

[mith]

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+-------+-------+-------+
| . . . | . . . | . . . |
| . . 9 | 8 . . | . . 7 |
| . 6 . | . 5 . | . 4 . |
+-------+-------+-------+
| . 4 6 | . 3 . | . 5 . |
| . . 8 | 7 . . | . . 2 |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . 2 | . . . |
| . . 7 | 9 . . | . 2 8 |
| . 5 . | . 4 . | . 6 . |
+-------+-------+-------+
...........98....7.6..5..4..46.3..5...87....2..............2.....79...28.5..4..6.

[Leren]

Code: Select all

*----------------------------------------------------------------*
| 1234578 12378  12345 | 46    12679 134679 | 1235689 1389   56  |
| 12345   123    9     | 8     126   1346   | 12356   13     7   |
| 12378   6     b123   | 123   5     1379   | 12389   4      139 |
|----------------------+--------------------+--------------------|
| 1279    4      6     | 12    3     189    | 1789    5      19  |
|c1359   c139    8     | 7    c169   14569  | 13469  c139    2   |
| 123579  12379 b1235  | 45-6  12689 145689 | 1346789 13789  46  |
|----------------------+--------------------+--------------------|
| 134689  1389  b134   |a56    78    2      | 134579  1379  a45  |
| 1346    13     7     | 9     1-6   1356   | 1345    2      8   |
| 12389   5     b123   | 13    4     78     | 1379    6      139 |
*----------------------------------------------------------------*

(6=4) r7c49 - (4=5) r3679c3 - (5=6) r5c1258 => - 6 r6c4, r8c5; stte

Leren

[Cenoman]

Solved with fishes

Hidden Text: Show

Code: Select all

 +----------------------------+-------------------------+--------------------------+
 |  1234578   12378   12345   |  46    12679   134679   |  1235689   1389    56    |
 |  12345     123     9       |  8     126     1346     |  12356     13      7     |
 |  12378     6       123     |  123   5       1379     |  12389     4       139   |
 +----------------------------+-------------------------+--------------------------+
 |  1279      4       6       |  12    3       189      |  1789      5       19    |
 |  1359      139     8       |  7     169     14569    |  13469     139     2     |
 |  123579    12379   1235    |  456   12689   145689   |  1346789   13789   46    |
 +----------------------------+-------------------------+--------------------------+
 |  134689    1389    134     |  56    78      2        |  134579    1379    45    |
 |  1346      13      7       |  9     16      1356     |  1345      2       8     |
 |  12389     5       123     |  13    4       78       |  1379      6       139   |
 +----------------------------+-------------------------+--------------------------+

Swordfish (4)r258\c167
Swordfish (5)r258\c167
Swordfish (8)r349\c167
X-Wing (3)c49\r39; lcls

Hidden Text: Show

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 +----------------------+-----------------------+-----------------------+
 |  123    78      45   |  46    1279    139    |  1239    1389   56    |
 |  45     123     9    |  8     126     1346   |  56      13     7     |
 |  78     6       12   |  123   5       179    |  1289    4      139   |
 +----------------------+-----------------------+-----------------------+
 |  1279   4       6    |  12    3       189    |  78      5      19    |
 |  1359   139     8    |  7     169     45     |  13469   139    2     |
 |  1239   12379   35   |  45    12689   169    |  1369    78     46    |
 +----------------------+-----------------------+-----------------------+
 |  1369   1389    34   |  56    78      2      |  139     1379   45    |
 |  1346   13      7    |  9     16      1356   |  45      2      8     |
 |  1289   5       12   |  13    4       78     |  179     6      139   |
 +----------------------+-----------------------+-----------------------+

Swordfish (1)c349\r349; lcls
X-Wing (2)c25\r26; lcls
Swordfish (9)c258\r157; lcls

Hidden Text: Show

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 +--------------------+--------------------+-------------------+
 |  23     78    45   |  46   79    13     |  123    89   56   |
 |  45     23    9    |  8    126   1346   |  56     13   7    |
 |  78     6     1    |  23   5     79     |  289    4    39   |
 +--------------------+--------------------+-------------------+
 |  27     4     6    |  12   3     89     |  78     5    19   |
 |  135    139   8    |  7    169   45     |  1346   13   2    |
 |  139    27    35   |  45   28    16     |  1369   78   46   |
 +--------------------+--------------------+-------------------+
 |  136    89    34   |  56   78    2      |  13     79   45   |
 |  1346   13    7    |  9    16    1356   |  45     2    8    |
 |  89     5     2    |  13   4     78     |  79     6    13   |
 +--------------------+--------------------+-------------------+

(3)r5c8 = r2c8 - r2c2 = r1c1 => -3r5c1
Swordfish (1)r167\c167; ste

[pjb]

Can be solved with multiple fish +/- MSLSs, but:

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1234578 12378  e12345  | 46     12679  134679 | 12356891389  d56     
 12345   123     9      | 8      126    1346   | 12356  13     7     
 12378   6       123    | 123    5      1379   | 12389  4      139   
------------------------+----------------------+---------------------
 1279    4       6      | 12     3      189    | 1789   5      19     
g1359    139     8      | 7     i169   h14569  | 13469  139    2     
 123579  12379  f1235   | 45-6   12689  145689 | 134678913789 c46     
------------------------+----------------------+---------------------
 134689  1389    134    |a56     78     2      | 134579 1379  b45     
 1346    13      7      | 9      1-6    1356   | 1345   2      8     
 12389   5       123    | 13     4      78     | 1379   6      139   


(6=5)r7c4 - (5=4)r7c9 - (4=6*)r6c9 - (6=5)r1c9 - (5)r1c3 = (5)r6c3 - (5)r5c1 = (5-6)r5c6*7 = (6)r5c5 => -6 r6c4, -6 r8c5; stte

Phil

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------------+-------------------------+-------------------------+
   ! 1234578 12378   12345   ! 12346   12679   134679  ! 1235689 1389    13569   !
   ! 12345   123     9       ! 8       126     1346    ! 12356   13      7       !
   ! 12378   6       123     ! 123     5       1379    ! 12389   4       139     !
   +-------------------------+-------------------------+-------------------------+
   ! 1279    4       6       ! 12      3       189     ! 1789    5       19      !
   ! 1359    139     8       ! 7       169     14569   ! 13469   139     2       !
   ! 123579  12379   1235    ! 12456   12689   145689  ! 1346789 13789   13469   !
   +-------------------------+-------------------------+-------------------------+
   ! 134689  1389    134     ! 1356    1678    2       ! 134579  1379    13459   !
   ! 1346    13      7       ! 9       16      1356    ! 1345    2       8       !
   ! 12389   5       123     ! 13      4       1378    ! 1379    6       139     !
   +-------------------------+-------------------------+-------------------------+

1) Normal solution, using only Subsets - quite a lot of them (33):
hidden-pairs-in-a-block: b8{n7 n8}{r7c5 r9c6} ==> r9c6 ≠ 3, r9c6 ≠ 1, r7c5 ≠ 6, r7c5 ≠ 1
naked-triplets-in-a-column: c9{r3 r4 r9}{n3 n9 n1} ==> r7c9 ≠ 9, r7c9 ≠ 3, r7c9 ≠ 1, r6c9 ≠ 9, r6c9 ≠ 3, r6c9 ≠ 1, r1c9 ≠ 9, r1c9 ≠ 3, r1c9 ≠ 1
naked-triplets-in-a-column: c4{r3 r4 r9}{n3 n2 n1} ==> r7c4 ≠ 3, r7c4 ≠ 1, r6c4 ≠ 2, r6c4 ≠ 1, r1c4 ≠ 3, r1c4 ≠ 2, r1c4 ≠ 1
x-wing-in-columns: n3{c4 c9}{r3 r9} ==> r9c7 ≠ 3, r9c3 ≠ 3, r9c1 ≠ 3, r3c7 ≠ 3, r3c6 ≠ 3, r3c3 ≠ 3, r3c1 ≠ 3
naked-pairs-in-a-column: c3{r3 r9}{n1 n2} ==> r7c3 ≠ 1, r6c3 ≠ 2, r6c3 ≠ 1, r1c3 ≠ 2, r1c3 ≠ 1
swordfish-in-columns: n1{c3 c4 c9}{r9 r3 r4} ==> r9c7 ≠ 1, r9c1 ≠ 1, r4c7 ≠ 1, r4c6 ≠ 1, r4c1 ≠ 1, r3c7 ≠ 1, r3c6 ≠ 1, r3c1 ≠ 1
naked-triplets-in-a-column: c6{r3 r4 r9}{n7 n9 n8} ==> r6c6 ≠ 9, r6c6 ≠ 8, r5c6 ≠ 9, r1c6 ≠ 9, r1c6 ≠ 7
hidden-pairs-in-a-block: b2{n7 n9}{r1c5 r3c6} ==> r1c5 ≠ 6, r1c5 ≠ 2, r1c5 ≠ 1
finned-x-wing-in-columns: n2{c5 c2}{r6 r2} ==> r2c1 ≠ 2
swordfish-in-columns: n4{c3 c4 c9}{r7 r1 r6} ==> r7c7 ≠ 4, r7c1 ≠ 4, r6c7 ≠ 4, r6c6 ≠ 4, r1c6 ≠ 4, r1c1 ≠ 4
swordfish-in-columns: n7{c2 c5 c8}{r6 r1 r7} ==> r7c7 ≠ 7, r6c7 ≠ 7, r6c1 ≠ 7, r1c1 ≠ 7
swordfish-in-rows: n8{r3 r4 r9}{c1 c7 c6} ==> r7c1 ≠ 8, r6c7 ≠ 8, r1c7 ≠ 8, r1c1 ≠ 8
hidden-pairs-in-a-block: b1{n7 n8}{r1c2 r3c1} ==> r3c1 ≠ 2, r1c2 ≠ 3, r1c2 ≠ 2, r1c2 ≠ 1
hidden-pairs-in-a-block: b6{n7 n8}{r4c7 r6c8} ==> r6c8 ≠ 9, r6c8 ≠ 3, r6c8 ≠ 1, r4c7 ≠ 9
x-wing-in-columns: n2{c2 c5}{r2 r6} ==> r6c1 ≠ 2, r2c7 ≠ 2
hidden-pairs-in-a-block: b4{n2 n7}{r4c1 r6c2} ==> r6c2 ≠ 9, r6c2 ≠ 3, r6c2 ≠ 1, r4c1 ≠ 9
hidden-triplets-in-a-row: r6{n2 n7 n8}{c5 c2 c8} ==> r6c5 ≠ 9, r6c5 ≠ 6, r6c5 ≠ 1
finned-x-wing-in-rows: n9{r6 r9}{c1 c7} ==> r7c7 ≠ 9
swordfish-in-columns: n9{c2 c5 c8}{r7 r5 r1} ==> r7c1 ≠ 9, r5c7 ≠ 9, r5c1 ≠ 9, r1c7 ≠ 9
hidden-pairs-in-a-block: b7{n8 n9}{r7c2 r9c1} ==> r9c1 ≠ 2, r7c2 ≠ 3, r7c2 ≠ 1
singles ==> r9c3 = 2, r3c3 = 1
hidden-pairs-in-a-row: r9{n1 n3}{c4 c9} ==> r9c9 ≠ 9
hidden-pairs-in-a-block: b9{n7 n9}{r7c8 r9c7} ==> r7c8 ≠ 3, r7c8 ≠ 1
x-wing-in-columns: n9{c6 c9}{r3 r4} ==> r3c7 ≠ 9
hidden-triplets-in-a-row: r1{n7 n8 n9}{c5 c2 c8} ==> r1c8 ≠ 3, r1c8 ≠ 1
hidden-pairs-in-a-column: c8{n1 n3}{r2 r5} ==> r5c8 ≠ 9
swordfish-in-columns: n1{c2 c5 c8}{r5 r8 r2} ==> r8c7 ≠ 1, r8c6 ≠ 1, r8c1 ≠ 1, r5c7 ≠ 1, r5c6 ≠ 1, r5c1 ≠ 1, r2c7 ≠ 1, r2c6 ≠ 1
naked-pairs-in-a-block: b4{r5c1 r6c3}{n3 n5} ==> r6c1 ≠ 5, r6c1 ≠ 3, r5c2 ≠ 3
swordfish-in-rows: n5{r2 r5 r8}{c7 c1 c6} ==> r7c7 ≠ 5, r6c6 ≠ 5, r1c7 ≠ 5, r1c1 ≠ 5
naked-pairs-in-a-block: b1{r1c1 r2c2}{n2 n3} ==> r2c1 ≠ 3, r1c3 ≠ 3
naked-pairs-in-a-block: b9{r7c7 r9c9}{n1 n3} ==> r8c7 ≠ 3
hidden-pairs-in-a-block: b5{n4 n5}{r5c6 r6c4} ==> r6c4 ≠ 6, r5c6 ≠ 6
naked-triplets-in-a-row: r1{c3 c4 c9}{n5 n4 n6} ==> r1c7 ≠ 6, r1c6 ≠ 6
hidden-pairs-in-a-block: b3{n5 n6}{r1c9 r2c7} ==> r2c7 ≠ 3
PUZZLE 0 IS NOT SOLVED. 58 VALUES MISSING.

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Resolution state:
   23        78        45        46        79        13        123       89        56       
   45        23        9         8         126       346       56        13        7         
   78        6         1         23        5         79        28        4         39       
   27        4         6         12        3         89        78        5         19       
   35        19        8         7         169       45        346       13        2         
   19        27        35        45        28        16        1369      78        46       
   136       89        34        56        78        2         13        79        45       
   346       13        7         9         16        356       45        2         8         
   89        5         2         13        4         78        79        6         13

Subsets are not enough but a single bivalue-chain[2] will give the solution:
biv-chain[2]: c8n3{r5 r2} - b1n3{r2c2 r1c1} ==> r5c1 ≠ 3
stte


2) Is there any 1-step solution?
Starting from the resolution state after Singles and whips[1], there are 27 W1-anti-backdoors:
n7r1c2 n4r1c3 n8r1c8 n5r1c9 n5r2c1 n4r2c6 n8r3c1 n7r3c6 n7r4c1 n2r4c4 n8r4c7 n5r5c6 n4r5c7 n5r6c3 n4r6c4 n8r6c5 n7r6c8 n6r6c9 n6r7c1 n8r7c2 n5r7c4 n7r7c5 n4r7c9 n4r8c1 n5r8c7 n8r9c6 n7r9c7
but none of them leads to a 1-step solution whith whips of reasonable length.

Now, cheating by starting with the resolution state after Pairs:

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   +-------------------------+-------------------------+-------------------------+
   ! 1234578 12378   12345   ! 12346   12679   134679  ! 1235689 1389    13569   !
   ! 12345   123     9       ! 8       126     1346    ! 12356   13      7       !
   ! 12378   6       123     ! 123     5       1379    ! 12389   4       139     !
   +-------------------------+-------------------------+-------------------------+
   ! 1279    4       6       ! 12      3       189     ! 1789    5       19      !
   ! 1359    139     8       ! 7       169     14569   ! 13469   139     2       !
   ! 123579  12379   1235    ! 12456   12689   145689  ! 1346789 13789   13469   !
   +-------------------------+-------------------------+-------------------------+
   ! 134689  1389    134     ! 1356    78      2       ! 134579  1379    13459   !
   ! 1346    13      7       ! 9       16      1356    ! 1345    2       8       !
   ! 12389   5       123     ! 13      4       78      ! 1379    6       139     !
   +-------------------------+-------------------------+-------------------------+

There are 39 S2-anti-backdoors:
n7r1c2 n4r1c3 n6r1c4 n8r1c8 n5r1c9 n5r2c1 n2r2c5 n4r2c6 n6r2c7 n8r3c1 n3r3c4 n7r3c6 n7r4c1 n2r4c4 n8r4c7 n1r4c9 n9r5c2 n6r5c5 n5r5c6 n4r5c7 n5r6c3 n4r6c4 n8r6c5 n7r6c8 n6r6c9 n6r7c1 n8r7c2 n5r7c4 n7r7c5 n4r7c9 n4r8c1 n1r8c2 n6r8c5 n3r8c6 n5r8c7 n1r9c4 n8r9c6 n7r9c7 n3r9c9

and one can indeed find two absurdly long whips (for a puzzle solvable by patterns of size ≤ 3) leading to 1-step solutions (modulo Pairs):

Code: Select all

whip-rn[7]: r8n5{c6 c7} - r2n5{c7 c1} - r5n5{c1 c6} - r5n4{c6 c7} - r8n4{c7 c1} - r8n6{c1 c5} - r5n6{c5 .} ==> r8c6 ≠ 3
btte

Code: Select all

whip[8]: c6n3{r3 r8} - r8n5{c6 c7} - r2n5{c7 c1} - r5n5{c1 c6} - c4n5{r6 r7} - b8n6{r7c4 r8c5} - r5n6{c5 c7} - r5n4{c7 .} ==> r3c4 ≠ 3
btte

Not only are these solutions not really one-step (they need Pairs before and after the whip) but, needless to say, there's no chance any human solver can find these manually.

[DEFISE]

By only using patterns of size <= 3 and trying to limit their quantity.
It seems that Leren did very well in this sense, although I am not competent enough to understand his final AIC:
(6=4) r7c49 - (4=5) r3679c3 - (5=6) r5c1258 => - 6 r6c4, r8c5

My solution:
Hidden pair: 78b8p29 => -1r7c5 -6r7c5 -1r9c6 -3r9c6
Naked triplet: 123c4r349 => -1r1c4 -2r1c4 -3r1c4 -1r6c4 -2r6c4 -1r7c4 -3r7c4
Naked triplet: 139c9r349 => -1r1c9 -3r1c9 -9r1c9 -1r6c9 -3r6c9 -9r6c9 -1r7c9 -3r7c9 -9r7c9
Swordfish 4r258c167 => -4r17c1 -4r16c6 -4r67c7
Swordfish 5r258c167 => -5r16c1 -5r6c6 -5r17c7
Hidden pair 45b5p67 => -169r5c6 -6r6c4
whip[3]: r5n6{c5 c7}- r2n6{c7 c6}- c4n6{r1 .} => -6r8c5
STTE

[DEFISE]

Even better, we can start directly with the swordfish:

Swordfish 4r258c167 => -4r17c1 -4r16c6 -4r67c7
Swordfish 5r258c167 => -5r16c1 -5r6c6 -5r17c7
Hidden pair 45b5p67 => -169r5c6 -126r6c4
whip[3]: r5n6{c5 c7}- r2n6{c7 c6}- c4n6{r1 .} => -6r8c5
Singles and 2 pairs to the end.

[denis_berthier]

It seems that Leren did very well in this sense, although I am not competent enough to understand his final AIC:
(6=4) r7c49 - (4=5) r3679c3 - (5=6) r5c1258 => - 6 r6c4, r8c5

I have no idea what it means; it doesn't correspond to anything visible on the grid. But it is certainly not of length 3 (there are inner "somethings").

Even better, we can start directly with the swordfish:
Swordfish 4r258c167 => -4r17c1 -4r16c6 -4r67c7
Swordfish 5r258c167 => -5r16c1 -5r6c6 -5r17c7
Hidden pair 45b5p67 => -169r5c6 -126r6c4
whip[3]: r5n6{c5 c7}- r2n6{c7 c6}- c4n6{r1 .} => -6r8c5
Singles and 2 pairs to the end.

Usually, with Mith's puzzles, I try to get as many Subsets as possible (by de-activating all the other rules). But that's a good way of finding as few as possible.

[ghfick]

YZF_Sudoku gives an ALS XY Wing :
Almost Locked Set XY-Wing: A=r5c1258{13569}, B=r7c49{456}, C=r3679c3{12345}, X,Y=5, 4, Z=6 => r6c4,r8c5<>6 that gives stte
This is Leren's chain.
There is a Death Blossom too [which may be mith's hint?]

[denis_berthier]

YZF_Sudoku gives an ALS XY Wing :
Almost Locked Set XY-Wing: A=r5c1258{13569}, B=r7c49{456}, C=r3679c3{12345}, X,Y=5, 4, Z=6 => r6c4,r8c5<>6 that gives stte
This Leren's chain.
There is a Death Blossom too [which may be mith's hint?]

Therefore, size is 10 (4+2+4).

[mith]

Title isn't so much a hint at a specific technique, but I did find the one-step solutions (and how they simplify as more fish are used) interesting. You can lob fish at this puzzle until it reduces to a short basic chain, you can take a few fish and find something like DEFISE found, or you can find the ALS exhaust port and blow the thing to pieces.

[eleven]

It seems that Leren did very well in this sense, although I am not competent enough to understand his final AIC:
(6=4) r7c49 - (4=5) r3679c3 - (5=6) r5c1258 => - 6 r6c4, r8c5

I have no idea what it means; it doesn't correspond to anything visible on the grid. But it is certainly not of length 3 (there are inner "somethings").

fyi:
if there is no 6 in r7c49, there must be (5 and) 4r7c9
then no 4 is in r3679c3, there must be (123 and) 5r6c3
then no 5 is in r5c1258, there must be (139 and) 6r5c5
=> either 6r7c4 or 6r5c5 (or both)
Though hard, this can be found manually (but probably you would check a lot of ALS's before in vain).

[denis_berthier]

It seems that Leren did very well in this sense, although I am not competent enough to understand his final AIC:
(6=4) r7c49 - (4=5) r3679c3 - (5=6) r5c1258 => - 6 r6c4, r8c5

I have no idea what it means; it doesn't correspond to anything visible on the grid. But it is certainly not of length 3 (there are inner "somethings").

fyi:
if there is no 6 in r7c49, there must be (5 and) 4r7c9
then no 4 is in r3679c3, there must be (123 and) 5r6c3
then no 5 is in r5c1258, there must be (139 and) 6r5c5
=> either 6r7c4 or 6r5c5 (or both)
Though hard, this can be found manually (but probably you would check a lot of ALS's before in vain).

Hi eleven
I didn't question the validity of the inferences. I had no doubt Leren was correct about them. As for finding this manually, Leren is clear that he uses a solver.
My problem was with the size of the pattern (in his and other solutions). This is a general problem with 1-step solutions. They often require so large patterns that any claim to have found them manually is hardly credible, because they represent an infinitesimal percentage of similar patterns of same size. It is a clear conclusion of my systematic analysis of 1- or 2- step solutions.

[DEFISE]

(6=4) r7c49 - (4=5) r3679c3 - (5=6) r5c1258 => - 6 r6c4, r8c5

Thanks to ghfick and especially to eleven because I have a low level in AIC.
All I can say is Leren's AIC is presented in a very condensed fashion. This hides a fairly long pattern (size 10 according to Denis Berthier's calibration).
However, I basically know the argument of the AIC followers: AIC is not a "memory chain"

[denis_berthier]

However, I basically know the argument of the AIC followers: AIC is not a "memory chain"

Except the AIC notation is also used to code "memory chains" and pretend they are something new.

if there is no 6 in r7c49, there must be (5 and) 4r7c9
then no 4 is in r3679c3, there must be (123 and) 5r6c3
then no 5 is in r5c1258, there must be (139 and) 6r5c5
=> either 6r7c4 or 6r5c5 (or both)

I don't know if there is memory or not, but to me this sounds more like T&E (moreover, with branching) than anything else.