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[yzfwsf]

Code: Select all

 *-----------*
 |.2.|..8|6..|
 |1..|..4|.3.|
 |..5|.9.|..8|
 |---+---+---|
 |...|41.|..2|
 |..6|...|1..|
 |8..|.23|...|
 |---+---+---|
 |4..|.8.|5..|
 |.5.|1..|..6|
 |..2|5..|.9.|
 *-----------*
.2...86..1....4.3...5.9...8...41...2..6...1..8...23...4...8.5...5.1....6..25...9.

[denis_berthier]

SER 7.2

After the initial singles and whips[1], it can be solved

- either by bivalue-chains[4] and z-chains (all reversible patterns):

Hidden Text: Show

(solve ".2...86..1....4.3...5.9...8...41...2..6...1..8...23...4...8.5...5.1....6..25...9.")
hidden-pairs-in-a-row: r6{n1 n4}{c2 c3} ==> r6c3 ≠ 9, r6c3 ≠ 7, r6c2 ≠ 9, r6c2 ≠ 7
whip[1]: r6n7{c9 .} ==> r4c7 ≠ 7, r4c8 ≠ 7
finned-x-wing-in-columns: n6{c5 c1}{r9 r2} ==> r2c2 ≠ 6
whip[1]: r2n6{c5 .} ==> r3c4 ≠ 6
finned-x-wing-in-rows: n9{r5 r1}{c9 c2} ==> r2c2 ≠ 9
biv-chain[3]: c3n8{r8 r2} - r2c2{n8 n7} - b4n7{r4c2 r4c3} ==> r8c3 ≠ 7
z-chain[3]: r6c7{n7 n9} - r2c7{n9 n2} - r3c8{n2 .} ==> r3c7 ≠ 7
biv-chain[4]: r3c8{n7 n2} - b2n2{r3c4 r2c4} - r2n6{c4 c5} - r2n5{c5 c9} ==> r2c9 ≠ 7
z-chain[3]: r2c9{n9 n5} - r6c9{n5 n7} - r6c7{n7 .} ==> r5c9 ≠ 9
naked-single ==> r5c9 = 3
naked-single ==> r5c2 = 9
biv-chain[3]: r7c9{n7 n1} - r9n1{c9 c2} - r9n8{c2 c7} ==> r9c7 ≠ 7
z-chain[3]: r7c9{n7 n1} - r7c8{n1 n2} - r3c8{n2 .} ==> r8c8 ≠ 7
z-chain[3]: r4n3{c3 c2} - r7n3{c2 c4} - r3n3{c4 .} ==> r1c3 ≠ 3
biv-chain[4]: r4n9{c6 c7} - r4n8{c7 c8} - r8c8{n8 n2} - b8n2{r8c6 r7c6} ==> r7c6 ≠ 9
biv-chain[4]: r2c2{n7 n8} - b7n8{r9c2 r8c3} - r8c8{n8 n2} - r3c8{n2 n7} ==> r3c1 ≠ 7, r3c2 ≠ 7, r2c7 ≠ 7
biv-chain[3]: r3c8{n7 n2} - r2c7{n2 n9} - r6c7{n9 n7} ==> r6c8 ≠ 7
biv-chain[4]: r9c6{n7 n6} - r4c6{n6 n9} - r4c7{n9 n8} - r9n8{c7 c2} ==> r9c2 ≠ 7
biv-chain[4]: r7c9{n7 n1} - c3n1{r7 r6} - c3n4{r6 r1} - c9n4{r1 r9} ==> r9c9 ≠ 7
biv-chain[4]: r7c9{n7 n1} - r9n1{c9 c2} - r9n8{c2 c7} - b9n3{r9c7 r8c7} ==> r8c7 ≠ 7
hidden-single-in-a-column ==> r6c7 = 7
whip[1]: b9n7{r7c9 .} ==> r7c2 ≠ 7, r7c3 ≠ 7, r7c6 ≠ 7
whip[1]: b7n7{r9c1 .} ==> r1c1 ≠ 7
naked-pairs-in-a-column: c9{r2 r6}{n5 n9} ==> r1c9 ≠ 9, r1c9 ≠ 5
whip[1]: b3n9{r2c9 .} ==> r2c3 ≠ 9
naked-pairs-in-a-block: b1{r2c2 r2c3}{n7 n8} ==> r1c3 ≠ 7
whip[1]: b1n7{r2c3 .} ==> r2c4 ≠ 7
z-chain[3]: r8n7{c1 c6} - b8n9{r8c6 r7c4} - r7n3{c4 .} ==> r8c1 ≠ 3
biv-chain[4]: c5n6{r9 r2} - r2n5{c5 c9} - r6c9{n5 n9} - c4n9{r6 r7} ==> r7c4 ≠ 6
biv-chain[4]: r7n6{c2 c6} - b8n2{r7c6 r8c6} - r8c8{n2 n8} - b7n8{r8c3 r9c2} ==> r9c2 ≠ 6
biv-chain[4]: c2n6{r7 r3} - b1n4{r3c2 r1c3} - c9n4{r1 r9} - r9n1{c9 c2} ==> r7c2 ≠ 1
z-chain[3]: b7n1{r9c2 r7c3} - r7n9{c3 c4} - r7n3{c4 .} ==> r9c2 ≠ 3
biv-chain[4]: r1c3{n9 n4} - r6c3{n4 n1} - b7n1{r7c3 r9c2} - b7n8{r9c2 r8c3} ==> r8c3 ≠ 9
stte

or by typed-whips[5], i.e. using only 2D-chains:

Hidden Text: Show

hidden-pairs-in-a-row: r6{n1 n4}{c2 c3} ==> r6c3 ≠ 9, r6c3 ≠ 7, r6c2 ≠ 9, r6c2 ≠ 7
whip[1]: r6n7{c9 .} ==> r4c7 ≠ 7, r4c8 ≠ 7
finned-x-wing-in-columns: n6{c5 c1}{r9 r2} ==> r2c2 ≠ 6
whip[1]: r2n6{c5 .} ==> r3c4 ≠ 6
finned-x-wing-in-rows: n9{r5 r1}{c9 c2} ==> r2c2 ≠ 9
whip-rc[3]: r6c7{n7 n9} - r2c7{n9 n2} - r3c8{n2 .} ==> r3c7 ≠ 7
biv-chain-rn[4]: r2n5{c9 c5} - r2n6{c5 c4} - r6n6{c4 c8} - r6n5{c8 c9} ==> r1c9 ≠ 5
biv-chain-rn[4]: r6n6{c4 c8} - r6n5{c8 c9} - r2n5{c9 c5} - r2n6{c5 c4} ==> r7c4 ≠ 6
biv-chain-rn[4]: r7n6{c2 c6} - r4n6{c6 c8} - r4n8{c8 c7} - r9n8{c7 c2} ==> r9c2 ≠ 6
biv-chain-rn[4]: r6n6{c8 c4} - r2n6{c4 c5} - r2n5{c5 c9} - r6n5{c9 c8} ==> r6c8 ≠ 7
t-whip-cn[4]: c9n4{r9 r1} - c3n4{r1 r6} - c3n1{r6 r7} - c9n1{r7 .} ==> r9c9 ≠ 3, r9c9 ≠ 7
t-whip-bn[4]: b7n6{r7c2 r9c1} - b8n6{r9c6 r7c6} - b8n2{r7c6 r8c6} - b8n9{r8c6 .} ==> r7c2 ≠ 9
whip[1]: c2n9{r5 .} ==> r4c3 ≠ 9
whip-rc[4]: r1c4{n7 n3} - r1c1{n3 n9} - r2c3{n9 n8} - r2c2{n8 .} ==> r1c3 ≠ 7
whip-rc[4]: r2c2{n7 n8} - r2c3{n8 n9} - r2c7{n9 n2} - r3c8{n2 .} ==> r2c9 ≠ 7
whip-rc[3]: r2c9{n9 n5} - r6c9{n5 n7} - r6c7{n7 .} ==> r5c9 ≠ 9
naked-single ==> r5c9 = 3
naked-single ==> r5c2 = 9
whip-rn[3]: r3n3{c2 c4} - r7n3{c4 c2} - r4n3{c2 .} ==> r1c3 ≠ 3
whip-rc[3]: r7c9{n7 n1} - r7c8{n1 n2} - r3c8{n2 .} ==> r8c8 ≠ 7
whip-rc[5]: r4c6{n9 n6} - r4c8{n6 n8} - r8c8{n8 n2} - r8c6{n2 n7} - r9c6{n7 .} ==> r7c6 ≠ 9
whip-cn[5]: c8n1{r7 r1} - c9n1{r1 r9} - c9n4{r9 r1} - c3n4{r1 r6} - c3n1{r6 .} ==> r7c2 ≠ 1
t-whip-rn[4]: r9n1{c2 c9} - r7n1{c9 c3} - r7n9{c3 c4} - r7n3{c4 .} ==> r9c2 ≠ 3
whip-bn[5]: b7n8{r8c3 r9c2} - b7n1{r9c2 r7c3} - b9n1{r7c8 r9c9} - b9n4{r9c9 r9c7} - b9n3{r9c7 .} ==> r8c7 ≠ 8
whip-bn[5]: b7n1{r7c3 r9c2} - b7n8{r9c2 r8c3} - b9n8{r8c8 r9c7} - b9n7{r9c7 r8c7} - b9n3{r8c7 .} ==> r7c3 ≠ 7
whip-rc[5]: r4c2{n3 n7} - r2c2{n7 n8} - r9c2{n8 n1} - r7c3{n1 n9} - r7c4{n9 .} ==> r7c2 ≠ 3
hidden-pairs-in-a-row: r7{n3 n9}{c3 c4} ==> r7c3 ≠ 1
stte

- or by typed-bivalue-chains[9], with the simplest reversible chains in 2D-spaces:

Hidden Text: Show

hidden-pairs-in-a-row: r6{n1 n4}{c2 c3} ==> r6c3 ≠ 9, r6c3 ≠ 7, r6c2 ≠ 9, r6c2 ≠ 7
whip[1]: r6n7{c9 .} ==> r4c7 ≠ 7, r4c8 ≠ 7
finned-x-wing-in-columns: n6{c5 c1}{r9 r2} ==> r2c2 ≠ 6
whip[1]: r2n6{c5 .} ==> r3c4 ≠ 6
finned-x-wing-in-rows: n9{r5 r1}{c9 c2} ==> r2c2 ≠ 9
biv-chain-rn[4]: r2n5{c9 c5} - r2n6{c5 c4} - r6n6{c4 c8} - r6n5{c8 c9} ==> r1c9 ≠ 5
biv-chain-rn[4]: r6n6{c4 c8} - r6n5{c8 c9} - r2n5{c9 c5} - r2n6{c5 c4} ==> r7c4 ≠ 6
biv-chain-rn[4]: r7n6{c2 c6} - r4n6{c6 c8} - r4n8{c8 c7} - r9n8{c7 c2} ==> r9c2 ≠ 6
biv-chain-rn[4]: r6n6{c8 c4} - r2n6{c4 c5} - r2n5{c5 c9} - r6n5{c9 c8} ==> r6c8 ≠ 7
biv-chain-cn[5]: c4n9{r7 r6} - c4n6{r6 r2} - c5n6{r2 r9} - c1n6{r9 r3} - c2n6{r3 r7} ==> r7c2 ≠ 9
whip[1]: c2n9{r5 .} ==> r4c3 ≠ 9
biv-chain-rn[9]: r1n1{c8 c9} - r9n1{c9 c2} - r9n8{c2 c7} - r4n8{c7 c8} - r4n6{c8 c6} - r6n6{c4 c8} - r6n5{c8 c9} - r2n5{c9 c5} - r1n5{c5 c8} ==> r1c8 ≠ 7
biv-chain-rn[9]: r9n1{c2 c9} - r1n1{c9 c8} - r1n5{c8 c5} - r2n5{c5 c9} - r6n5{c9 c8} - r6n6{c8 c4} - r4n6{c6 c8} - r4n8{c8 c7} - r9n8{c7 c2} ==> r9c2 ≠ 3, r9c2 ≠ 7
biv-chain-rn[9]: r1n1{c9 c8} - r1n5{c8 c5} - r2n5{c5 c9} - r6n5{c9 c8} - r6n6{c8 c4} - r4n6{c6 c8} - r4n8{c8 c7} - r9n8{c7 c2} - r9n1{c2 c9} ==> r7c9 ≠ 1
hidden-pairs-in-a-column: c9{n1 n4}{r1 r9} ==> r9c9 ≠ 7, r9c9 ≠ 3, r1c9 ≠ 9, r1c9 ≠ 7
whip[1]: b3n9{r2c9 .} ==> r2c3 ≠ 9
naked-pairs-in-a-block: b1{r2c2 r2c3}{n7 n8} ==> r3c2 ≠ 7, r3c1 ≠ 7, r1c3 ≠ 7, r1c1 ≠ 7
hidden-single-in-a-row ==> r1c4 = 7
whip[1]: r3n7{c8 .} ==> r2c7 ≠ 7, r2c9 ≠ 7
whip[1]: c1n7{r9 .} ==> r7c2 ≠ 7, r7c3 ≠ 7, r8c3 ≠ 7
biv-chain-rc[3]: r7c9{n7 n3} - r5c9{n3 n9} - r6c7{n9 n7} ==> r8c7 ≠ 7, r9c7 ≠ 7, r6c9 ≠ 7
singles ==> r6c7 = 7, r3c8 = 7, r7c9 = 7, r5c9 = 3, r5c2 = 9
whip[1]: c8n2{r8 .} ==> r8c7 ≠ 2
biv-chain-cn[5]: c3n1{r7 r6} - c3n4{r6 r1} - c9n4{r1 r9} - c9n1{r9 r1} - c8n1{r1 r7} ==> r7c2 ≠ 1
biv-chain-cn[5]: c4n3{r3 r7} - c4n9{r7 r6} - c4n6{r6 r2} - c5n6{r2 r9} - c1n6{r9 r3} ==> r3c1 ≠ 3
singles ==> r3c1 = 6, r7c2 = 6
finned-x-wing-in-rows: n3{r7 r3}{c4 c3} ==> r1c3 ≠ 3
swordfish-in-columns: n3{c1 c5 c7}{r8 r1 r9} ==> r8c3 ≠ 3
biv-chain-cn[4]: c2n1{r9 r6} - c2n4{r6 r3} - c2n3{r3 r4} - c3n3{r4 r7} ==> r7c3 ≠ 1
stte

This makes me realise I haven't coded typed z-chains and I should do it.
[Edit] I've done it and it gives the following solution with max length 8, when we allow only elementary reversible 2D chains (typed bivalue-chains and typed z-chains)

Hidden Text: Show

hidden-pairs-in-a-row: r6{n1 n4}{c2 c3} ==> r6c3 ≠ 9, r6c3 ≠ 7, r6c2 ≠ 9, r6c2 ≠ 7
whip[1]: r6n7{c9 .} ==> r4c7 ≠ 7, r4c8 ≠ 7
finned-x-wing-in-columns: n6{c5 c1}{r9 r2} ==> r2c2 ≠ 6
whip[1]: r2n6{c5 .} ==> r3c4 ≠ 6
finned-x-wing-in-rows: n9{r5 r1}{c9 c2} ==> r2c2 ≠ 9
z-chain-rc[3]: r6c7{n7 n9} - r2c7{n9 n2} - r3c8{n2 .} ==> r3c7 ≠ 7
biv-chain-rn[4]: r2n5{c9 c5} - r2n6{c5 c4} - r6n6{c4 c8} - r6n5{c8 c9} ==> r1c9 ≠ 5
biv-chain-rn[4]: r6n6{c4 c8} - r6n5{c8 c9} - r2n5{c9 c5} - r2n6{c5 c4} ==> r7c4 ≠ 6
biv-chain-rn[4]: r7n6{c2 c6} - r4n6{c6 c8} - r4n8{c8 c7} - r9n8{c7 c2} ==> r9c2 ≠ 6
biv-chain-rn[4]: r6n6{c8 c4} - r2n6{c4 c5} - r2n5{c5 c9} - r6n5{c9 c8} ==> r6c8 ≠ 7
z-chain-rc[4]: r1c4{n7 n3} - r1c1{n3 n9} - r2c3{n9 n8} - r2c2{n8 .} ==> r1c3 ≠ 7
z-chain-rc[4]: r2c2{n7 n8} - r2c3{n8 n9} - r2c7{n9 n2} - r3c8{n2 .} ==> r2c9 ≠ 7
z-chain-rc[3]: r2c9{n9 n5} - r6c9{n5 n7} - r6c7{n7 .} ==> r5c9 ≠ 9
singles ==> r5c9 = 3, r5c2 = 9
z-chain-rc[3]: r7c9{n7 n1} - r7c8{n1 n2} - r3c8{n2 .} ==> r8c8 ≠ 7
z-chain-rn[3]: r4n3{c3 c2} - r7n3{c2 c4} - r3n3{c4 .} ==> r1c3 ≠ 3
z-chain-cn[5]: c8n1{r7 r1} - c9n1{r1 r9} - c9n4{r9 r1} - c3n4{r1 r6} - c3n1{r6 .} ==> r7c2 ≠ 1
z-chain-cn[6]: c7n3{r8 r9} - c7n4{r9 r3} - c2n4{r3 r6} - c2n1{r6 r9} - c2n8{r9 r2} - c3n8{r2 .} ==> r8c7 ≠ 8
z-chain-cn[7]: c2n1{r9 r6} - c2n4{r6 r3} - c2n6{r3 r7} - c1n6{r9 r3} - c1n3{r3 r1} - c5n3{r1 r8} - c7n3{r8 .} ==> r9c2 ≠ 3
biv-chain-cn[8]: c8n1{r7 r1} - c8n5{r1 r6} - c8n6{r6 r4} - c8n8{r4 r8} - c3n8{r8 r2} - c2n8{r2 r9} - c2n1{r9 r6} - c3n1{r6 r7} ==> r7c9 ≠ 1
singles ==> r7c9 = 7, r6c7 = 7
naked-pairs-in-a-column: c9{r2 r6}{n5 n9} ==> r1c9 ≠ 9
whip[1]: b3n9{r2c9 .} ==> r2c3 ≠ 9
naked-pairs-in-a-block: b1{r2c2 r2c3}{n7 n8} ==> r3c2 ≠ 7, r3c1 ≠ 7, r1c1 ≠ 7
whip[1]: c1n7{r9 .} ==> r8c3 ≠ 7, r9c2 ≠ 7
whip[1]: b1n7{r2c3 .} ==> r2c4 ≠ 7
z-chain-rc[5]: r7c4{n3 n9} - r7c3{n9 n1} - r9c2{n1 n8} - r2c2{n8 n7} - r4c2{n7 .} ==> r7c2 ≠ 3
singles ==> r7c2 = 6, r3c1 = 6
swordfish-in-columns: n3{c1 c5 c7}{r8 r1 r9} ==> r8c3 ≠ 3, r1c4 ≠ 3
naked-single ==> r1c4 = 7
hidden-single-in-a-block ==> r3c8 = 7
whip[1]: c8n2{r8 .} ==> r8c7 ≠ 2
naked-pairs-in-a-row: r8{c5 c7}{n3 n4} ==> r8c1 ≠ 3
biv-chain-cn[4]: c2n1{r9 r6} - c2n4{r6 r3} - c2n3{r3 r4} - c3n3{r4 r7} ==> r7c3 ≠ 1
stte

This is a puzzle where the elementary reversible 3D chains allow much shorter chains than only the 2D ones.
It is also a rare case where whips (or more generally the t-extensions) don't allow a solution with shorter chains than in the first solution above.

[Cenoman]

In case a one-step solution would be expected...

Code: Select all

 +-----------------------+----------------------+------------------------+
 |  379   2       3479   |  37     35    8      |  6       157   14579   |
 |  1     6789    789    |  267    56    4      |  279     3     579     |
 |  367   3467    5      |  2367   9     1      |  247     27    8       |
 +-----------------------+----------------------+------------------------+
 |  5     379     379    |  4      1     69     |  39-8    68    2       |
 |  2     39      6      |  8      7     5      |  1       4     39      |
 |  8     14      14     |  69     2     3      |  79      567   579     |
 +-----------------------+----------------------+------------------------+
 |  4     13679   1379   |  369    8     2679   |  5       127   137     |
 |  379   5       3789   |  1      34    279    |  23478   278   6       |
 |  367   13678   2      |  5      346   67     |  3478    9     1347    |
 +-----------------------+----------------------+------------------------+

Triple kraken (3)r7c2349, cell (379)r4c2, cell (6789)r2c2, as a net

Code: Select all

          (3)r7c9 - r5c9 = (3)r4c7 *
           ||
          (3-9)r7c4 = r6c4 - (9=6)r4c6 - (6=8)r4c8 *
           ||
          (3-1)r7c3 = (1-4)r6c3 = r1c3 - r1c9 = (4-1)r9c9 = (1-8)r9c2 = (8)r9c7 *
           ||
(3)r4c2 - (3)r7c2
 ||
(9)r4c2 - (9=6)r4c6 - (6=8)r4c8 *
 ||
(7)r4c2 - (7)r2c2
           ||
          (6)r2c2 - r3c12 = r3c4 - r6c4 = r4c6 - (6=8)r4c8 *
           ||
          (8)r2c2 - r9c2 = (8)r9c7 *
           ||
          (9)r2c2 - r45c2 = r4c3 - (9=6)r4c6 - (6=8)r4c8 *
--------------------------------------------------------
=> -8 r4c7; ste