The New Sudoku Players' Forum

[Mauriès Robert]

HI all,
I suggest you solve this rather tough puzzle.
Robert
...2.43.....3...61....8..2..21...9..3.......2..8...47..5..6....29...5.....67.9...

puzzle: Show

solution: Show

Resolution detailed by the link https://www.assistant-sudoku.com/Grille_Resolue.php?RID=681&Type_Sudoku=

[denis_berthier]

SER = 9.0, W=7, gW=7

g-whips are not necessary, but for the fun of it, I activated them:

Code: Select all

***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = gW+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
singles ==> r6c2 = 6, r2c6 = 7, r3c9 = 4, r2c3 = 2, r1c1 = 6
184 candidates, 999 csp-links and 999 links. Density = 5.93%
whip[1]: r6n1{c6 .} ==> r5c6 ≠ 1, r5c4 ≠ 1, r5c5 ≠ 1
whip[1]: b3n9{r1c9 .} ==> r1c5 ≠ 9, r1c3 ≠ 9
finned-x-wing-in-columns: n9{c3 c4}{r3 r5} ==> r5c5 ≠ 9
139 g-candidates, 684 csp-glinks and 399 non-csp glinks
biv-chain-rc[4]: r3c7{n7 n5} - r2c7{n5 n8} - r2c2{n8 n4} - r5c2{n4 n7} ==> r3c2 ≠ 7
whip[4]: r1c5{n1 n5} - r1c3{n5 n7} - b7n7{r8c3 r7c1} - b7n1{r7c1 .} ==> r9c5 ≠ 1
g-whip[5]: r1c3{n5 n7} - b7n7{r8c3 r7c1} - b7n8{r7c1 r9c123} - r9c9{n8 n3} - r6c9{n3 .} ==> r1c9 ≠ 5
t-whip[6]: c3n4{r8 r5} - r5c2{n4 n7} - r5c5{n7 n5} - c4n5{r6 r3} - r3c7{n5 n7} - c1n7{r3 .} ==> r7c1 ≠ 4
t-whip[6]: c3n4{r8 r5} - r5c2{n4 n7} - r5c5{n7 n5} - r1c5{n5 n1} - r1c2{n1 n8} - r2c2{n8 .} ==> r9c2 ≠ 4
t-whip[6]: r3c6{n6 n1} - r1c5{n1 n5} - r1c3{n5 n7} - r3n7{c3 c7} - r8n7{c7 c9} - c9n6{r8 .} ==> r4c6 ≠ 6
biv-chain[3]: r4c6{n3 n8} - r5c6{n8 n6} - b6n6{r5c7 r4c9} ==> r4c9 ≠ 3
biv-chain[6]: r4c6{n3 n8} - r5c6{n8 n6} - r3c6{n6 n1} - r1n1{c5 c2} - c2n7{r1 r5} - b5n7{r5c5 r4c5} ==> r4c5 ≠ 3
whip[6]: r5c2{n4 n7} - r5c5{n7 n5} - c4n5{r6 r3} - c3n5{r3 r1} - r1n7{c3 c9} - r3c7{n7 .} ==> r5c4 ≠ 4
whip[6]: r5c2{n4 n7} - r5c5{n7 n5} - c4n5{r6 r3} - c3n5{r3 r1} - r1n7{c3 c9} - r3c7{n7 .} ==> r5c3 ≠ 4
whip[1]: c3n4{r8 .} ==> r9c1 ≠ 4
whip[6]: r8n6{c9 c7} - r8n7{c7 c3} - r1c3{n7 n5} - r5c3{n5 n9} - r6c1{n9 n5} - r6c9{n5 .} ==> r8c9 ≠ 3
t-whip[7]: b7n1{r9c2 r7c1} - r9c1{n1 n8} - r9c2{n8 n3} - r3c2{n3 n1} - c6n1{r3 r6} - r6n2{c6 c5} - r9n2{c5 .} ==> r9c7 ≠ 1
whip[6]: r8n6{c7 c9} - b6n6{r4c9 r5c7} - c7n1{r5 r7} - b9n7{r7c7 r7c9} - r7c1{n7 n8} - b8n8{r7c4 .} ==> r8c7 ≠ 8
whip[6]: r2c7{n5 n8} - r9c7{n8 n2} - c5n2{r9 r6} - c5n9{r6 r2} - r2n5{c5 c1} - b4n5{r4c1 .} ==> r5c7 ≠ 5
g-whip[6]: r5c6{n8 n6} - r3c6{n6 n1} - r1n1{c5 c2} - b1n8{r1c2 r2c123} - c7n8{r2 r789} - r8n8{c9 .} ==> r5c4 ≠ 8
z-chain[7]: b3n7{r3c7 r1c9} - r1c3{n7 n5} - r2n5{c1 c5} - c5n9{r2 r6} - c5n2{r6 r9} - r9c7{n2 n8} - r2c7{n8 .} ==> r3c7 ≠ 5
naked-single ==> r3c7 = 7
t-whip[5]: r9n1{c2 c8} - r9n4{c8 c5} - b8n2{r9c5 r7c6} - r7c7{n2 n8} - r7c4{n8 .} ==> r7c1 ≠ 1
whip[1]: b7n1{r9c2 .} ==> r9c8 ≠ 1
t-whip[3]: r8n7{c9 c3} - r7c1{n7 n8} - b8n8{r7c4 .} ==> r8c9 ≠ 8
whip[5]: r9n4{c8 c5} - r9n2{c5 c7} - r7c7{n2 n1} - r7c4{n1 n8} - b7n8{r7c1 .} ==> r9c8 ≠ 8
whip[5]: r8n8{c4 c8} - r5n8{c8 c7} - c7n6{r5 r8} - c7n1{r8 r7} - r7n2{c7 .} ==> r7c6 ≠ 8
whip[1]: b8n8{r8c4 .} ==> r4c4 ≠ 8
whip[6]: c9n6{r4 r8} - r8n7{c9 c3} - r7c1{n7 n8} - c4n8{r7 r8} - c4n4{r8 r7} - c3n4{r7 .} ==> r4c4 ≠ 6
singles ==> r4c9 = 6, r8c9 = 7, r8c7 = 6
hidden-pairs-in-a-row: r4{n3 n8}{c6 c8} ==> r4c8 ≠ 5
naked-triplets-in-a-block: b5{r4c4 r4c5 r5c5}{n4 n5 n7} ==> r6c5 ≠ 5, r6c4 ≠ 5, r5c4 ≠ 5
z-chain[3]: c1n4{r2 r4} - r4c4{n4 n5} - r3n5{c4 .} ==> r2c1 ≠ 5
biv-chain[4]: r2n5{c7 c5} - c5n9{r2 r6} - r6c1{n9 n5} - b6n5{r6c9 r5c8} ==> r1c8 ≠ 5
singles ==> r2c7 = 5, r2c5 = 9
whip[1]: r2n8{c2 .} ==> r1c2 ≠ 8
biv-chain[4]: c4n5{r4 r3} - c4n6{r3 r5} - c4n9{r5 r6} - r6c1{n9 n5} ==> r4c1 ≠ 5
whip[1]: r4n5{c5 .} ==> r5c5 ≠ 5
naked-pairs-in-a-row: r5{c2 c5}{n4 n7} ==> r5c3 ≠ 7
hidden-pairs-in-a-column: c1{n5 n9}{r3 r6} ==> r3c1 ≠ 1
hidden-single-in-a-column ==> r9c1 = 1
biv-chain[4]: c3n4{r8 r7} - r7n7{c3 c1} - r4c1{n7 n4} - r5n4{c2 c5} ==> r8c5 ≠ 4
biv-chain[4]: r9c2{n3 n8} - r2c2{n8 n4} - r5n4{c2 c5} - r9n4{c5 c8} ==> r9c8 ≠ 3
biv-chain[4]: r4c1{n4 n7} - b7n7{r7c1 r7c3} - r1c3{n7 n5} - c5n5{r1 r4} ==> r4c5 ≠ 4
biv-chain[4]: c2n8{r9 r2} - c2n4{r2 r5} - c5n4{r5 r9} - r9n2{c5 c7} ==> r9c7 ≠ 8
singles ==> r9c7 = 2, r7c6 = 2, r6c5 = 2
biv-chain[3]: r8c3{n4 n3} - c5n3{r8 r9} - r9n4{c5 c8} ==> r8c8 ≠ 4
z-chain-rc[3]: r7c7{n8 n1} - r8c8{n1 n3} - r4c8{n3 .} ==> r7c8 ≠ 8
biv-chain-cn[4]: c2n3{r9 r3} - c2n1{r3 r1} - c5n1{r1 r8} - c5n3{r8 r9} ==> r9c9 ≠ 3
biv-chain-rc[3]: r9c9{n8 n5} - r6c9{n5 n3} - r4c8{n3 n8} ==> r8c8 ≠ 8
singles ==> r8c4 = 8, r8c3 = 4
biv-chain-rc[3]: r7c7{n8 n1} - r8c8{n1 n3} - r4c8{n3 n8} ==> r5c7 ≠ 8
stte

[denis_berthier]

Hi Robert,

It seems there are few contenders for solving non pre-digested puzzles.
Was there anything special with this one?

[Mauriès Robert]

Hi Denis,

It seems there are few contenders for solving non pre-digested puzzles.
Was there anything special with this one?

No this puzzle is nothing special apart from the fact that it is not easy to solve. In terms of TDP its level is 3, i.e. 3 sets of tracks (direct or combined, which you call DFS) are necessary to find the solution and show its uniqueness.
I'm not too surprised that few people have tackled it on this forum where one obviously prefers to make "nice moves" on easier puzzles.
I awaited your resolution with interest to find out what maximum chain length was needed. Thank you very much.
Robert

[Cenoman]

Code: Select all

 +-----------------------+-------------------------+------------------------+
 |  6      178    57     |  2       15      4      |  3      589     5789   |
 |  4589   48     2      |  3       59      7      |  58     6       1      |
 |  1579   137    3579   |  1569    8       16     |  57     2       4      |
 +-----------------------+-------------------------+------------------------+
 |  457    2      1      |  4568    3457    368    |  9      358     3568   |
 |  3      47     4579   |  45689   4579    68     |  1568   158     2      |
 |  59     6      8      |  159     12359   123    |  4      7       35     |
 +-----------------------+-------------------------+------------------------+
 |  1478   5      347    |  148     6       12-38  |  1278   13489   3789   |
 |  2      9      347    |  148     134     5      |  1678   1348    3678   |
 |  148    1348   6      |  7       1234    9      |  1258   13458   358    |
 +-----------------------+-------------------------+------------------------+

1. Kraken cell (1258)r9c7
(1|8)r9c7 - (18)r9c12 = (1|8-7)r7c1 = r78c3 - (7=51)r1c35* - (1=638)r345c6
(2)r9c7 - (r7c7|r9c5) = (2)r7c6,r6c5
(5)r9c7 - r23c7 = r1c89 - (5=1)r1c5* - (1=638)r345c6
=> -38 r7c6, -1r6c5*

2. (3=58)r69c9 - ^(81)r9c12 = (1|8-7)r7c1 = r78c3-(7=51)r1c35^-(1=683)r345c6* - r4c8 = (3)r789c8 => -3 r78c9, r4c9*, -1 r9c5^

3. (1)r1c5 = (1-3)r8c5 = r9c5 - r9c9 = r6c9 - (3=12)r67c6 => -1 r3c6; 4 placements

Code: Select all

 +-----------------------+---------------------+------------------------+
 |  6      178   a57     |  2      15     4    |  3      589    b5789*  |
 | B4589*  48     2      |  3     B59*    7    |  58     6       1      |
 |  1579   137    3579   |  159    8      6    | b57*    2       4      |
 +-----------------------+---------------------+------------------------+
 |  47-5   2      1      |  456    457    3    |  9     E58     E568    |
 |  3      47    B479-5* | C4569  B4579*  8    |De156   e15      2      |
 | A59     6      8      |  159    259    12   |  4      7       3      |
 +-----------------------+---------------------+------------------------+
 |  1478   5      347    |  148    6      12   |  1278   13489   789    |
 |  2      9     b347*   |  148    134    5    |db1678*  1348   c678    |
 |  148    1348   6      |  7      234    9    |  1258   13458   58     |
 +-----------------------+---------------------+------------------------+

4. (5=7)r1c3 - [(7)r1c9 = r3c7 - r8c7 = r8c3] = (7-6)r8c9 = r8c7 - (6=15)r5c78 => -5 r5c3

5. (5=9)r6c1 - [(9)r2c1 = r2c5 - r5c5 = r5c3] = (9-6)r5c4 = r5c7 - (6=85)r4c89 => -5 r4c1; 2 placements and basics

Code: Select all

 +--------------------+--------------------+------------------------+
 |  6     178   57    |  2     15     4    |  3      589     5789   |
 |  489   48    2     |  3    c59     7    | b58     6       1      |
 |  179   137   357   |  159   8      6    | a57     2       4      |
 +--------------------+--------------------+------------------------+
 |  47    2     1     |  456   457    3    |  9      58      568    |
 |  3     47    9     |  456   457    8    | I156    15      2      |
 |  5     6     8     |  19   c29    d12   |  4      7       3      |
 +--------------------+--------------------+------------------------+
 | z178   5    y347   |  148   6     e12   |Hf128-7 x13489  w89-7   |
 |  2     9     347   | F148  F134    5    |IG168-7 G1348    678    |
 | z18   z138   6     |  7     234    9    | H1258   13458   58     |
 +--------------------+--------------------+------------------------+

6. (7=5)r3c7 - r2c7 = (5-92)r26c5 = r6c6 - r7c6 = (2)r7c7 => -7 r7c7

7. (7=5)r3c7 - r2c7 = (5-92)r26c5 = r6c6 - (2=1)r7c6 - r8c45 = r8c78 - r79c7 = (16)r58c7 => -7 r8c7: 1 placement

8. (9)r7c9 = (9-3)r7c8 = r7c3 - (3=187)b7p178 => -7 r7c9; 6 placements & basics

Code: Select all

 +--------------------+--------------------+----------------------+
 |  6     178   57    |  2     15     4    |  3      59     589   |
 |  489   48    2     |  3     59     7    |  58     6      1     |
 |  19    13    35    |  159   8      6    |  7      2      4     |
 +--------------------+--------------------+----------------------+
 | a47    2     1     |  5-4   457    3    |  9      8      6     |
 |  3     47    9     |  6     47     8    |  15     15     2     |
 |  5     6     8     |  19    29     12   |  4      7      3     |
 +--------------------+--------------------+----------------------+
 | b178   5     347   | b14    6     b12   | b128    1349   89    |
 |  2     9     34    |  8     134    5    |  6      134    7     |
 |  18    138   6     |  7     234    9    |  1258   1345   58    |
 +--------------------+--------------------+----------------------+

9. (4=7)r4c1 - (7=1284)r7c1467 => -4 r4c4; ste

Edit 1: added missing elimination -1r6c5 in step 1. (Thanks Robert for spotting!)
Edit 2,3,4 corrected typos

[Mauriès Robert]

Hi Cenoman.
Very interesting resolution that yours, especially this kraken leading to several eliminations.
One can also obtain the same result with a set of conjugated tracks from the 15r1c5 pair, like this one :
P(5r1c2) : 5r1c5->[(7r1c3->7r7c1->18r9c12) and 5r23c7]->2r9c7->2r7c6->2r6c5
P(1r1c5) : 1r1c5->(6r3c6->8r5c6)->3r4c6
=> -3r7c6 , -8r7c6, -1r6c5 and -1r9c5 which see candidates from both tracks.
In your steps 1 and 2 you do not eliminate 1r6c5, so you cannot consider 1r1c5 and 1r8c5 strongly bound in step 3. You are missing one step.
In any case thank you for the time spent on this rather long puzzle.
Cordially
Robert

[Cenoman]

Hi Cenoman.
...In your steps 1 and 2 you do not eliminate 1r6c5, so you cannot consider 1r1c5 and 1r8c5 strongly bound in step 3. You are missing one step.

You are right, I had seen it... and forgotten to write it. 1r6c5 is eliminated by kraken step 1, by subchains and a slightly modified second chain. Now fixed; I have edited my post.

In any case thank you for the time spent on this rather long puzzle.

Thank you for reading my solution so carefully !