The New Sudoku Players' Forum

[denis_berthier]

.

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+-------+-------+-------+
! 2 . . ! . 8 . ! . . 3 !
! . 4 . ! . 6 . ! . 2 . !
! . . 1 ! . 5 . ! 6 . . !
+-------+-------+-------+
! . . . ! 5 . 8 ! . . . !
! 5 8 7 ! . . . ! 1 9 4 !
! . . . ! 4 . 9 ! . . . !
+-------+-------+-------+
! . . 3 ! . 2 . ! 7 . . !
! . 1 . ! . 4 . ! . 8 . !
! 4 . . ! . 9 . ! . . 6 !
+-------+-------+-------+

2...8...3.4..6..2...1.5.6.....5.8...587...194...4.9.....3.2.7...1..4..8.4...9...6 #  1809 FNBWY C28.M/S8.f
SER = 7.2, non-minimal

I thought it could be useful to give the state everyone will find - which is the real starting point. Tell me what you think of make this systematic.

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Starting point: resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 2    5679 569  ! 179  8    17   ! 4    15   3    !
   ! 789  4    589  ! 1379 6    137  ! 589  2    1589 !
   ! 389  39   1    ! 2    5    4    ! 6    7    89   !
   +----------------+----------------+----------------+
   ! 1369 2369 4    ! 5    17   8    ! 23   36   27   !
   ! 5    8    7    ! 6    3    2    ! 1    9    4    !
   ! 136  236  26   ! 4    17   9    ! 2358 356  2578 !
   +----------------+----------------+----------------+
   ! 689  569  3    ! 18   2    156  ! 7    4    159  !
   ! 679  1    2569 ! 37   4    3567 ! 2359 8    259  !
   ! 4    257  258  ! 1378 9    1357 ! 235  135  6    !
   +----------------+----------------+----------------+
132 candidates

[RSW]

Three steps:

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 +-----------------+--------------+---------------+
 | 2     5679 569  | 179  8  17   | 4    15  3    |
 | 78-9  4    589  | 1379 6  137  | 589  2   158-9|
 |#389  #39   1    | 2    5  4    | 6    7  #89   |
 +-----------------+--------------+---------------+
 |#1369 #2369 4    | 5    17 8    | 23   36 #27   |
 | 5     8    7    | 6    3  2    | 1    9   4    |
 | 136   236  26   | 4    17 9    | 2358 356 2578 |
 +-----------------+--------------+---------------+
 |#689  #569  3    | 18   2  156  | 7    4  #159  |
 | 67-9  1    2569 | 37   4  3567 | 2359 8   25-9 |
 | 4     257  258  | 1378 9  1357 | 235  135 6    |
 +-----------------+--------------+---------------+


Swordfish: In rows 3 4 7, digit 9 in columns 1 2 9 => -9r28c19 -9r1c2

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 +----------------+--------------+---------------+
 | 2   b567 b569  | 179  8  17   | 4   c15   3    |
 | 78   4   a59-8 | 1379 6  137  | 589  2   d158  |
 |f389  39   1    | 2    5  4    | 6    7  de89   |
 +----------------+--------------+---------------+
 | 1369 2369 4    | 5    17 8    | 23   36  d27   |
 | 5    8    7    | 6    3  2    | 1    9    4    |
 | 136  236  26   | 4    17 9    | 2358 356 d2578 |
 +----------------+--------------+---------------+
 | 689  569  3    | 18   2  156  | 7    4    159  |
 | 67   1    2569 | 37   4  3567 | 2359 8   d25   |
 | 4    257  258  | 1378 9  1357 | 235  135  6    |
 +----------------+--------------+---------------+


(5)r2c3=(5)r1c23-(5=1)r1c8-(1=25789)r23468c9-(8)r3c9=(8)r3c1 => -8r2c3

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 +----------------+--------------+---------------+
 | 2    567  569  | 179  8  17   | 4    15  3    |
 | 78   4    59   |F1379 6 #137  | 589  2  #158  |
 | 389  39   1    | 2    5  4    | 6    7   89   |
 +----------------+--------------+---------------+
 | 1369 2369 4    | 5    17 8    | 23   36  27   |
 | 5    8    7    | 6    3  2    | 1    9   4    |
 | 136  236  26   | 4    17 9    | 2358 356 2578 |
 +----------------+--------------+---------------+
 | 69   569  3    | 8    2 #156  | 7    4  #159  |
 | 67   1    2569 | 37   4  3567 | 2359 8   25   |
 | 4    257  8    | 137  9  1357 | 235  135 6    |
 +----------------+--------------+---------------+


Finned-X-Wing: Digit 1 in rows 2 7 columns (4) 6 9, Fin: r2c4 => -1r1c6; stte

[P.O.]

Code: Select all

after singles and intersection:

   2       h56-79     569    179   8    g1+7    4     c1+5   3             
   789      4        d+589   1379  6     137   d-589   2    d1-589           
   389      39        1      2     5     4      6      7     89             
   1369     2369      4      5     17    8      23     36    27             
   5        8         7      6     3     2      1      9     4             
   136      236       26     4     17    9      2358   356   2578           
ifa(6)8±9 fa(56)±9    3      18    2    f(156)  7      4    a15+9           
  i(69)7    1         256×9  37    4     3567   2359   8     259           
   4       h25+7     e25+8   1378  9     1357   235   b+135  6           

r7n9{c1c2 c9} - b9n1{r7c9 r9c8} - r1c8{n1 n5} - r2n5{c7c9 c3} - c3n8{r2 r9} - r7{c1c2c6}{n1n5n6} - r1c6{n1 n7} - c2n7{r1 r9} - c1{r7r8}{n6n9} => r8c3 <> 9
intersection: c3n9{r1r2}
ste.


[denis_berthier]

.
The puzzle in in W4, more precisely in BC4:

Simplest-first solution in BC4: Show

finned-x-wing-in-columns: n9{c7 c3}{r8 r2} ==> r2c1≠9
swordfish-in-columns: n9{c3 c4 c7}{r8 r1 r2} ==> r8c9≠9, r8c1≠9, r2c9≠9, r1c2≠9
biv-chain[3]: r1n6{c3 c2} - b1n7{r1c2 r2c1} - r8c1{n7 n6} ==> r8c3≠6
biv-chain[3]: r2n3{c6 c4} - r8c4{n3 n7} - c1n7{r8 r2} ==> r2c6≠7
finned-x-wing-in-columns: n7{c2 c6}{r1 r9} ==> r9c4≠7
biv-chain[4]: r1c6{n1 n7} - b1n7{r1c2 r2c1} - r8c1{n7 n6} - b8n6{r8c6 r7c6} ==> r7c6≠1
finned-x-wing-in-columns: n1{c8 c6}{r9 r1} ==> r1c4≠1
biv-chain[4]: r3n8{c1 c9} - c9n9{r3 r7} - r7n1{c9 c4} - r7n8{c4 c1} ==> r2c1≠8
singles ==> r2c1=7, r8c1=6, r7c6=6, r9c2=7
whip[1]: b7n2{r9c3 .} ==> r6c3≠2
singles ==> r6c3=6, r1c2=6, r7c2=5, r4c8=6
biv-chain[3]: r9n2{c7 c3} - c3n8{r9 r2} - c7n8{r2 r6} ==> r6c7≠2
biv-chain[4]: b9n9{r8c7 r7c9} - b9n1{r7c9 r9c8} - c8n3{r9 r6} - r4c7{n3 n2} ==> r8c7≠2
biv-chain[4]: r4n9{c2 c1} - b7n9{r7c1 r8c3} - r8n2{c3 c9} - r6n2{c9 c2} ==> r4c2≠2
hidden-single-in-a-block ==> r6c2=2
biv-chain[4]: b9n1{r9c8 r7c9} - b9n9{r7c9 r8c7} - r8c3{n9 n2} - r8c9{n2 n5} ==> r9c8≠5
biv-chain[3]: r9c8{n3 n1} - c9n1{r7 r2} - r2c6{n1 n3} ==> r9c6≠3
biv-chain[3]: r9c8{n3 n1} - r7n1{c9 c4} - b8n8{r7c4 r9c4} ==> r9c4≠3
whip[1]: r9n3{c8 .} ==> r8c7≠3
naked-pairs-in-a-block: b8{r7c4 r9c4}{n1 n8} ==> r9c6≠1
naked-single ==> r9c6=5
whip[1]: c6n1{r2 .} ==> r2c4≠1
naked-pairs-in-a-column: c7{r4 r9}{n2 n3} ==> r6c7≠3
biv-chain[3]: r8n5{c9 c7} - b9n9{r8c7 r7c9} - c9n1{r7 r2} ==> r2c9≠5
naked-triplets-in-a-column: c9{r2 r3 r7}{n1 n8 n9} ==> r6c9≠8
hidden-single-in-a-block ==> r6c7=8
biv-chain[3]: b3n8{r2c9 r3c9} - b3n9{r3c9 r2c7} - r2n5{c7 c3} ==> r2c3≠8
stte

It has no 1-step whip solution of reasonable length. One must go up to length 8 to find one:

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whip[8]: c9n1{r7 r2} - b3n9{r2c9 r2c7} - c4n9{r2 r1} - r1n1{c4 c6} - r7n1{c6 c4} - r7n8{c4 c1} - c3n8{r9 r2} - r2n5{c3 .} ==> r7c9≠9
w1-tte

There are many 2-step solutions in W5, e.g.

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whip[5]: r9n1{c6 c8} - r1c8{n1 n5} - r2n5{c9 c3} - c3n8{r2 r9} - c4n8{r9 .} ==> r7c4≠1
singles ==> r7c4=8, r9c3=8
whip[3]: r1c6{n7 n1} - r2n1{c6 c9} - r7n1{c9 .} ==> r1c2≠7
stte

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whip[5]: r7c4{n8 n1} - r9n1{c6 c8} - r1c8{n1 n5} - r2n5{c9 c3} - c3n8{r2 .} ==> r9c4≠8
singles ==> r7c4=8, r9c3=8
biv-chain[5]: r3c9{n9 n8} - b1n8{r3c1 r2c1} - b1n7{r2c1 r1c2} - r1c6{n7 n1} - r7n1{c6 c9} ==> r7c9≠9
stte

P.O.: the elimination in your 1-step solution (length 12) can be done by a shorter whip:

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whip[9]: r7n9{c2 c9} - c9n1{r7 r2} - b3n9{r2c9 r2c7} - c4n9{r2 r1} - r1n1{c4 c6} - r7n1{c6 c4} - r7n8{c4 c1} - c3n8{r9 r2} - r2n5{c3 .} ==> r8c3≠9

[P.O.]

hi Denis, i know that whips are more powerful than the chains i do, they find eliminations that i don't and often are shorter than mine for the same eliminations;
from your book PBCS2:
"A target of a whip is required to be linked to its first candidate, not necessarily to its last; the condition on the last variable is changed so that the final contradiction can occur with previous right-linking candidates."
I guess that's what's happening here as with the whip[8]: the building of the whip runs into a contradiction, no more 5 in r2.
I have so far eliminated this possibility.

i wrote the chain i posted with 9 links, for you it has length 12, it was found at deph 8:

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depth: 8  candidate: 9  from cell
(((8 3 7) (2 5 6 9)))

((9 0 1 0) ((7 1 7) (6 8 9)) ((7 2 7) (5 6 9)))
((9 0) (7 9 9) (1 5 9))
((1 1 10) (9 8 9) (1 3 5))
((5 2 9) (1 8 3) (1 5))
((5 3 3) (2 3 1) (5 8 9))
((8 4 10) (9 3 7) (2 5 8))
((1 5 111) (7 6 8) (1 5 6))
((7 6 9) (1 6 2) (1 7))
((7 7 1) (9 2 7) (2 5 7))
((9 8 22) (8 1 7) (6 7 9))


[denis_berthier]

i wrote the chain i posted with 9 links, for you it has length 12, it was found at deph 8:

In any consistent notion of length based on the number of CSP-Variables, as mine, an inner Pair/Triplet/Quad must be counted as adding lengths resp. 2/3/4.
This corresponds to adding the same values to your depths.

[StrmCkr]

you can skip some of the early singles & blr:

and start from here:

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+-------------------+-----------------+---------------------+
| 2     5679  569   | 179    8   147  | 459    (15)  3      |
| 3789  4     9(58) | 1379   6   137  | 89(5)  2     89(15) |
| 389   39    1     | 239    5   234  | 6      7     89     |
+-------------------+-----------------+---------------------+
| 1369  2369  2469  | 5      17  8    | 23     36    27     |
| 5     8     7     | 6      3   2    | 1      9     4      |
| 136   236   26    | 4      17  9    | 2358   356   2578   |
+-------------------+-----------------+---------------------+
| 69-8  569   3     | (18)   2   156  | 7      4     59(1)  |
| 679   1     2569  | 37     4   3567 | 2359   8     259    |
| 4     257   25(8) | 137-8  9   1357 | 235    135   6      |
+-------------------+-----------------+---------------------+

instead of this starting point

Code: Select all

+-------------------+-----------------+---------------------+
| 2     5679  569   | 179    8   17   | 4      (15)  3      |
| 789   4     9(58) | 1379   6   137  | 89(5)  2     89(15) |
| 389   39    1     | 2      5   4    | 6      7     89     |
+-------------------+-----------------+---------------------+
| 1369  2369  4     | 5      17  8    | 23     36    27     |
| 5     8     7     | 6      3   2    | 1      9     4      |
| 136   236   26    | 4      17  9    | 2358   356   2578   |
+-------------------+-----------------+---------------------+
| 69-8  569   3     | (18)   2   156  | 7      4     59(1)  |
| 679   1     2569  | 37     4   3567 | 2359   8     259    |
| 4     257   25(8) | 137-8  9   1357 | 235    135   6      |
+-------------------+-----------------+---------------------+

and find the finishing move
Grouped Discontinuous Nice Loop: r7c4<>1
(1-8)r7c4 = r7c1 - r9c3 = (8-5)r2c3 = r2c79 - (5=1)r1c8 - r2c9 = r7c9 - 1r7c4

simple Sudoku should be able to solve it from here:
but if it cant then this

Code: Select all

2-String Kite: 1 in r1c8,r7c6 connected by b9p38 => r1c6 <> 1

and its all singles