The New Sudoku Players' Forum

[3FB504F3]

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*-----------*
|1..|...|.2.|
|...|9..|1.3|
|.7.|5..|84.|
|-----------|
|...|163|...|
|6..|...|..2|
|...|275|...|
|-----------|
|.29|..8|.5.|
|8.1|..9|...|
|.4.|...|..1|
*-----------*

[gurth]

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 *--------------------------------------------------------------------*
 | 1      3689   3468   | 3467   348    67     | 567    2      5679   |
 | 245    568    24568  | 9      248    267    | 1      67     3      |
 | 239    7      236    | 5      23     1      | 8      4      69     |
 |----------------------+----------------------+----------------------|
 | 24579  589    24578  | 1      6      3      | 457    79     4578   |
 | 6      135    357    | 8      9      4      | 357    13     2      |
 | 349    1389   348    | 2      7      5      | 346    1369   468    |
 |----------------------+----------------------+----------------------|
 | 37     2      9      | 3467   1      8      | 3467   5      467    |
 | 8      356    1      | 3467   345    9      | 2      36     47     |
 | 357    4      3567   | 367    235    267    | 9      8      1      |
 *--------------------------------------------------------------------*


If r3c9 is 9, then via singles, locked candidates, naked pairs and a naked triple, a
contradiction is reached, depending on the path followed.

Therefore r3c9 is 6; stte.

[eleven]

Hm, this is not exactly what we want to see as solutions, "try a number and click on solve, until you get a contradiction"
btw it is (again) not stte after this move.

Of course we would accept Sudoku Explainer's description of this move, which i copied here:

Hidden Text: Show

Chain 1:
If R1C2 contains the value 9, then R9C5 cannot contain the value 3 (View 1):
(1) If R1C2 contains the value 9, then R1C2 cannot contain the value 8 (the cell can contain only one value)
(2) If R1C2 contains the value 9 (initial assumption), then R3C1 cannot contain the value 9 (the value can occur only once in the block)
(3) If R3C1 does not contain the value 9, then R3C9 must contain the value 9 (only remaining possible position in the row)
(4) If R3C9 contains the value 9, then R3C9 cannot contain the value 6 (the cell can contain only one value)
(5) If R3C9 does not contain the value 6, then R3C3 must contain the value 6 (only remaining possible position in the row)
(6) If R3C3 contains the value 6, then R2C2 cannot contain the value 6 (the value can occur only once in the block)
(7) If R1C2 contains the value 9 (initial assumption), then R1C2 cannot contain the value 6 (the cell can contain only one value)
(8) If R1C2 does not contain the value 6 and R2C2 does not contain the value 6 (6), then R8C2 must contain the value 6 (only remaining possible position in the column)
(9) If R8C2 contains the value 6, then R8C2 cannot contain the value 5 (the cell can contain only one value)
(10) If R8C2 does not contain the value 5, then R8C5 must contain the value 5 (only remaining possible position in the row)
(11) If R8C5 contains the value 5, then R8C5 cannot contain the value 4 (the cell can contain only one value)
(12) If R8C5 does not contain the value 4, then R1C4 cannot contain the value 4 (Pointing: Cells R7C4,R8C4: 4 in block and column)
(13) If R1C4 does not contain the value 4 and R1C2 does not contain the value 8 (1), then R1C3 cannot contain the value 3 (Hidden Pair: Cells R1C3,R1C5: 4,8 in row)
(14) If R1C2 contains the value 9 (initial assumption), then R1C2 cannot contain the value 3 (the cell can contain only one value)
(15) If R3C3 contains the value 6 (5), then R3C3 cannot contain the value 3 (the cell can contain only one value)
(16) If R3C3 does not contain the value 3, R1C2 does not contain the value 3 (14) and R1C3 does not contain the value 3 (13), then R3C1 must contain the value 3 (only remaining possible position in the block)
(17) If R3C1 contains the value 3, then R3C5 cannot contain the value 3 (the value can occur only once in the row)
(18) If R1C4 does not contain the value 4 (12), then R1C5 cannot contain the value 3 (Hidden Pair: Cells R1C5,R2C5: 4,8 in block)
(19) If R8C5 contains the value 5 (10), then R8C5 cannot contain the value 3 (the cell can contain only one value)
(20) If R8C5 does not contain the value 3, R1C5 does not contain the value 3 (18) and R3C5 does not contain the value 3 (17), then R9C5 must contain the value 3 (only remaining possible position in the column)

Chain 2: If R9C5 must contain the value 3, then R9C5 cannot contain the value 3 (View 2):
(1) If R1C2 contains the value 9, then R1C2 cannot contain the value 8 (the cell can contain only one value)
(2) If R1C2 contains the value 9 (initial assumption), then R3C1 cannot contain the value 9 (the value can occur only once in the block)
(3) If R3C1 does not contain the value 9, then R3C9 must contain the value 9 (only remaining possible position in the row)
(4) If R3C9 contains the value 9, then R3C9 cannot contain the value 6 (the cell can contain only one value)
(5) If R3C9 does not contain the value 6, then R3C3 must contain the value 6 (only remaining possible position in the row)
(6) If R3C3 contains the value 6, then R2C2 cannot contain the value 6 (the value can occur only once in the block)
(7) If R1C2 contains the value 9 (initial assumption), then R1C2 cannot contain the value 6 (the cell can contain only one value)
(8) If R1C2 does not contain the value 6 and R2C2 does not contain the value 6 (6), then R8C2 must contain the value 6 (only remaining possible position in the column)
(9) If R8C2 contains the value 6, then R8C2 cannot contain the value 5 (the cell can contain only one value)
(10) If R8C2 does not contain the value 5, then R8C5 must contain the value 5 (only remaining possible position in the row)
(11) If R8C5 contains the value 5, then R8C5 cannot contain the value 4 (the cell can contain only one value)
(12) If R8C5 does not contain the value 4, then R1C4 cannot contain the value 4 (Pointing: Cells R7C4,R8C4: 4 in block and column)
(13) If R1C4 does not contain the value 4 and R1C2 does not contain the value 8 (1), then R1C3 cannot contain the value 3 (Hidden Pair: Cells R1C3,R1C5: 4,8 in row)
(14) If R3C3 contains the value 6 (5), then R3C3 cannot contain the value 3 (the cell can contain only one value)
(15) If R1C2 contains the value 9 (initial assumption), then R1C2 cannot contain the value 3 (the cell can contain only one value)
(16) If R8C2 contains the value 6 (8), then R8C2 cannot contain the value 3 (the cell can contain only one value)
(17) If R8C2 does not contain the value 3 and R1C2 does not contain the value 3 (15), then R5C3 cannot contain the value 3 (Claiming: Cells R5C2,R6C2: 3 in column and block)
(18) If R8C2 does not contain the value 3 (16) and R1C2 does not contain the value 3 (15), then R6C3 cannot contain the value 3 (Claiming: Cells R5C2,R6C2: 3 in column and block)
(19) If R6C3 does not contain the value 3, R5C3 does not contain the value 3 (17), R3C3 does not contain the value 3 (14) and R1C3 does not contain the value 3 (13), then R9C3 must contain the value 3 (only remaining possible position in the column)
(20) If R9C3 contains the value 3, then R9C5 cannot contain the value 3 (the value can occur only once in the row)

The code for my own solution is ...

[JC Van Hay]

Code: Select all

+-----------------------+--------------------+------------------+
| 1      3689   3468    | 3467  348    67    | 567   2     5679 |
| 245    58(6)  2458(6) | 9     248    (267) | 1     (67)  3    |
| 29(3)  7      2-6(3)  | 5     2(3)   1     | 8     4     69   |
+-----------------------+--------------------+------------------+
| 24579  589    24578   | 1     6      3     | 457   79    4578 |
| 6      135    357     | 8     9      4     | 357   137   2    |
| 349    1389   348     | 2     7      5     | 346   1369  468  |
+-----------------------+--------------------+------------------+
| 7(3)   2      9       | 3467  1      8     | 3467  5     467  |
| 8      (356)  1       | 3467  34(5)  9     | 2     367   467  |
| 57(3)  4      57(36)  | 367   (235)  67(2) | 9     8     1    |
+-----------------------+--------------------+------------------+


Kraken Cell (235)r9c5 :=> [6r2c23==3r3c3==6r9c3] - 6r3c3

2r9c5-2r9c6=2r2c6-HP(67)r2c68=6r2c23
||
3r9c5-3r3c5.r9c13=*[3r3c3=*r3c1-3r7c1=*(3-6)r8c2=6r9c3]
||
5r9c5-5r8c5=(5-6)r8c2=6r9c3

Code: Select all

+-----------------+-----------------+---------+
| 1     (36)  348 | 34-7  348  (67) | 5  2  9 |
| 45    56    248 | 9     248  26   | 1  7  3 |
| 9     7     23  | 5     23   1    | 8  4  6 |
+-----------------+-----------------+---------+
| 2     8     7   | 1     6    3    | 4  9  5 |
| 6     1     5   | 8     9    4    | 7  3  2 |
| 34    9     34  | 2     7    5    | 6  1  8 |
+-----------------+-----------------+---------+
| 7     2     9   | 6     1    8    | 3  5  4 |
| 8     5(3)  1   | 34    345  9    | 2  6  7 |
| 5(3)  4     6   | (37)  235  2-7  | 9  8  1 |
+-----------------+-----------------+---------+


[(7=3)r9c4-3r9c1=3r8c2-(3=6)r1c2-(6=7)r1c6] - 7r1c4.r9c6; singles to the end.

[denis_berthier]

Code: Select all

*-----------*
|1..|...|.2.|
|...|9..|1.3|
|.7.|5..|84.|
|-----------|
|...|163|...|
|6..|...|..2|
|...|275|...|
|-----------|
|.29|..8|.5.|
|8.1|..9|...|
|.4.|...|..1|
*-----------*

Just for (my own) fun, a solution with no complex nets:

Hidden Text: Show

Code: Select all

***  SudoRules 20.0.s based on CSP-Rules 2.0.s, config = W+S ***
;;; obvious singles, whips[1] and bivalue-chains:
singles: r5c6 = 4, r5c4 = 8, r5c5 = 9, r9c8 = 8, r9c7 = 9, r8c7 = 2, r7c5 = 1, r3c6 = 1
whip[1]: c8n9{r6 .} ==> r6c9 ≠ 9, r4c9 ≠ 9
whip[1]: r2n5{c3 .} ==> r1c3 ≠ 5, r1c2 ≠ 5
biv-chain[2]: r3n6{c9 c3} - b7n6{r9c3 r8c2} ==> r8c9 ≠ 6
biv-chain[3]: r4c2{n8 n5} - c9n5{r4 r1} - r1n9{c9 c2} ==> r1c2 ≠ 8

;;; the hardest part:
whip[5]: r1n8{c3 c5} - r1n4{c5 c4} - c5n4{r2 r8} - r8n5{c5 c2} - c2n6{r8 .} ==> r1c3 ≠ 6
whip[5]: r4c2{n8 n5} - c9n5{r4 r1} - c9n9{r1 r3} - r3n6{c9 c3} - r2c2{n6 .} ==> r6c2 ≠ 8
whip[6]: r9n6{c6 c3} - r3n6{c3 c9} - c8n6{r2 r6} - r6n1{c8 c2} - r6n9{c2 c1} - r3n9{c1 .} ==> r8c4 ≠ 6
whip[6]: r8c9{n7 n4} - r8c4{n4 n3} - r8c5{n3 n5} - r9c5{n5 n2} - b2n2{r2c5 r2c6} - r2n7{c6 .} ==> r8c8 ≠ 7
biv-chain[6]: r8c8{n3 n6} - b7n6{r8c2 r9c3} - r3n6{c3 c9} - b3n9{r3c9 r1c9} - c2n9{r1 r6} - r6n1{c2 c8} ==> r6c8 ≠ 3
whip[5]: r5n1{c2 c8} - r6n1{c8 c2} - c2n9{r6 r1} - c2n3{r1 r8} - c8n3{r8 .} ==> r5c2 ≠ 5
whip[5]: r5c2{n3 n1} - r6c2{n1 n9} - r1n9{c2 c9} - r1n5{c9 c7} - r5n5{c7 .} ==> r5c3 ≠ 3
whip[6]: c2n8{r2 r4} - c2n5{r4 r8} - c5n5{r8 r9} - r9n2{c5 c6} - r2c6{n2 n7} - r2c8{n7 .} ==> r2c2 ≠ 6

naked-pairs-in-a-column: c2{r2 r4}{n5 n8} ==> r8c2 ≠ 5
hidden-single-in-a-row ==> r8c5 = 5
whip[1]: c5n4{r2 .} ==> r1c4 ≠ 4
naked-pairs-in-a-column: c5{r3 r9}{n2 n3} ==> r2c5 ≠ 2, r1c5 ≠ 3
naked-pairs-in-a-row: r8{c2 c8}{n3 n6} ==> r8c4 ≠ 3
hidden-pairs-in-a-row: r1{n4 n8}{c3 c5} ==> r1c3 ≠ 3
biv-chain[3]: b1n9{r3c1 r1c2} - r1n3{c2 c4} - r3c5{n3 n2} ==> r3c1 ≠ 2
whip[4]: b1n9{r3c1 r1c2} - c2n6{r1 r8} - b7n3{r8c2 r9c3} - c5n3{r9 .} ==> r3c1 ≠ 3
stte

As pairs are subsumed by whips[2], disallowing Subsets in the above solution wouldn't change the rating.
Allowing g-candidates (i.e. adding g-whips) or a slight form of AND-branching (i.e. adding braids) doesn't change the resolution path and rating (i.e. W = gW = B = 6).

So this puzzle is clearly harder than those usually discussed here, but should not be a real challenge for advances solvers.
The challenge would now be to find a solution with patterns using only (in their complete descriptions) less than 6 CSP-Variables each (or 2D-cells in the Extended Sudoku Board view).

[daj95376]

Hm, this is not exactly what we want to see as solutions, "try a number and click on solve, until you get a contradiction"

I've almost certainly mentioned this previously, but I'm not above repeating myself.

Sometimes, logic can be interpreted in two ways -- one favorable and one unfavorable. Consider JC's post above. It's the "favorable" interpretation allowed for Kraken Row/Column/Box/Cell solutions. However, if you reverse his Kraken Cell logic, then you have a forcing chain where =6r3c3 has three streams that lead to a contradiction by eliminating all candidates in cell r9c5. The conclusion follows that 6r3c3 can be eliminated.

Sometimes, it's a fine line between acceptable and unacceptable. Yes, I agree with eleven's statement quoted above ... but only because gurth's solution lacks structure in reaching his conclusion. However, what would we have said if he'd provided a complex network showing all of the intermediate interactions ... similar to JC's embedded Hidden Pair logic?

_

[eleven]

However, what would we have said if he'd provided a complex network showing all of the intermediate interactions ... similar to JC's embedded Hidden Pair logic?

If someone had shown the same nice solution as JC, written from right to left as contradiction net, for me there is no quality difference, because it is logically the same. In fact for a manual solver it is often easier to spot a contradiction, than to derive something from 2 or 3 possibilities (however it is presented then).
For finding short solutions, you would look for digits, which could help much, if you can eliminate them (at least they should give you a number), and you would not go through 3 digit cells, hoping that all of them could lead to the (1) the same and (2) a useful result.

Code: Select all

+-----------------------+--------------------+------------------+
| 1      3689   3468    | 3467  348    67    | 567   2     5679 |
| 245    58(6)  2458(6) | 9     248    (267) | 1     (67)  3    |
| 29(3)  7      2-6(3)  | 5     2(3)   1     | 8     4     69   |
+-----------------------+--------------------+------------------+
| 24579  589    24578   | 1     6      3     | 457   79    4578 |
| 6      135    357     | 8     9      4     | 357   137   2    |
| 349    1389   348     | 2     7      5     | 346   1369  468  |
+-----------------------+--------------------+------------------+
| 7(3)   2      9       | 3467  1      8     | 3467  5     467  |
| 8      (356)  1       | 3467  34(5)  9     | 2     367   467  |
| 57(3)  4      57(36)  | 367   (235)  67(2) | 9     8     1    |
+-----------------------+--------------------+------------------+


Kraken Cell (235)r9c5 :=> [6r2c23==3r3c3==6r9c3] - 6r3c3

2r9c5-2r9c6=2r2c6-HP(67)r2c68=6r2c23
||
3r9c5-3r3c5.r9c13=*[3r3c3=*r3c1-3r7c1=*(3-6)r8c2=6r9c3]
||
5r9c5-5r8c5=(5-6)r8c2=6r9c3

From right to left:

Code: Select all

                  6r2c23=HP(67)r2c68-2r2c6=r9c6        -2r9c5
               /
                                     3r9c13          \     
(9-6)r3c9=6r3c3-  6r9c3 =(6-3)r8c2=    ||              -3r9c5
                                     3r7c1-r3c1=r3c5 /

               \  6r9c3 =(6-5)r8c2=r8c5                -5r9c5

contradiction (r9c5 is empty) => r3c9<>9