The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . 9 | . 8 7 | 6 . . |
| 5 4 . | . . . | . . 7 |
| . . . | . . . | . . 3 |
+-------+-------+-------+
| . 7 . | . . . | . . . |
| . . 8 | . 2 9 | . . . |
| . . 5 | . . 6 | 2 . . |
+-------+-------+-------+
| . . . | . 9 2 | 8 . . |
| . 9 . | . . 8 | . 7 . |
| . . . | 7 . . | . 1 . |
+-------+-------+-------+
..9.876..54......7........3.7.........8.29.....5..62......928...9...8.7....7...1.

an extreme puzzle with lots of... >_>

[denis_berthier]

.
I don't know a lot of what you meant (I found only two jellyfish), but it also has a lot of g-candidates and g-whips, leading to a solution in gW9.

The puzzle is in T&E(1) and could therefore be solved by braids. However, SER 9.4 means it will be on the hard side of a solution with whips/braids (e.g. it has no solution in W14), so I preferred trying with g-whips.

Resolution state after Singles:

Code: Select all

   +----------------------+----------------------+----------------------+
   ! 123    123    9      ! 12345  8      7      ! 6      245    1245   !
   ! 5      4      1236   ! 12369  136    13     ! 19     8      7      !
   ! 12678  1268   1267   ! 124569 1456   145    ! 1459   2459   3      !
   +----------------------+----------------------+----------------------+
   ! 123469 7      12346  ! 13458  1345   1345   ! 13459  34569  145689 !
   ! 1346   136    8      ! 1345   2      9      ! 7      3456   1456   !
   ! 1349   13     5      ! 1348   7      6      ! 2      349    1489   !
   +----------------------+----------------------+----------------------+
   ! 13467  1356   13467  ! 13456  9      2      ! 8      3456   456    !
   ! 12346  9      12346  ! 13456  13456  8      ! 345    7      2456   !
   ! 23468  23568  2346   ! 7      3456   345    ! 3459   1      24569  !
   +----------------------+----------------------+----------------------+

230 candidates, 1649 csp-links and 1649 links. Density = 6.26%

whip[1]: c8n2{r3 .} ==> r1c9 ≠ 2
234 g-candidates, 1359 csp-glinks and 792 non-csp glinks
z-chain[3]: c4n9{r3 r2} - r2n2{c4 c3} - r2n6{c3 .} ==> r3c4 ≠ 6
finned-jellyfish-in-rows: n4{r1 r6 r5 r7}{c8 c9 c4 c1} ==> r9c1 ≠ 4, r8c1 ≠ 4
biv-chain[4]: r2n2{c3 c4} - r2n9{c4 c7} - b9n9{r9c7 r9c9} - b9n2{r9c9 r8c9} ==> r8c3 ≠ 2
t-whip[4]: r9n9{c9 c7} - r2n9{c7 c4} - r2n2{c4 c3} - c2n2{r3 .} ==> r9c9 ≠ 2
hidden-single-in-a-block ==> r8c9 = 2
biv-chain[5]: r9n9{c9 c7} - r2n9{c7 c4} - r2n2{c4 c3} - b4n2{r4c3 r4c1} - b4n9{r4c1 r6c1} ==> r6c9 ≠ 9
g-whip[5]: r7n1{c3 c4} - b5n1{r6c4 r4c456} - c7n1{r4 r123} - r1n1{c9 c2} - b4n1{r5c2 .} ==> r8c1 ≠ 1
t-whip[6]: b9n6{r7c9 r9c9} - r9n9{c9 c7} - r2n9{c7 c4} - r2n2{c4 c3} - c2n2{r3 r9} - c2n5{r9 .} ==> r7c2 ≠ 6
whip[7]: r9n8{c1 c2} - b7n2{r9c2 r9c3} - r2n2{c3 c4} - r2n9{c4 c7} - r9n9{c7 c9} - r9n6{c9 c5} - b2n6{r2c5 .} ==> r9c1 ≠ 3
whip[7]: r9n8{c2 c1} - b7n2{r9c1 r9c3} - r2n2{c3 c4} - r2n9{c4 c7} - r9n9{c7 c9} - r9n6{c9 c5} - b2n6{r2c5 .} ==> r9c2 ≠ 3
whip[7]: r9n8{c2 c1} - b7n2{r9c1 r9c3} - r2n2{c3 c4} - r2n9{c4 c7} - r9n9{c7 c9} - r9n6{c9 c5} - b2n6{r2c5 .} ==> r9c2 ≠ 5
hidden-single-in-a-block ==> r7c2 = 5
t-whip[5]: b9n5{r9c7 r9c9} - r9n9{c9 c7} - b3n9{r3c7 r3c8} - c8n2{r3 r1} - b3n5{r1c8 .} ==> r4c7 ≠ 5
g-whip[7]: r2n9{c4 c7} - r9n9{c7 c9} - b9n6{r9c9 r7c789} - c4n6{r7 r8} - r8c1{n6 n3} - c3n3{r9 r4} - b5n3{r4c4 .} ==> r2c4 ≠ 3
g-whip[7]: r4n2{c1 c3} - r2n2{c3 c4} - r2n9{c4 c7} - r9n9{c7 c9} - b9n6{r9c9 r7c789} - c4n6{r7 r8} - r8c1{n6 .} ==> r4c1 ≠ 3
g-whip[7]: r7c9{n6 n4} - r7c8{n4 n3} - b6n3{r4c8 r4c7} - b5n3{r4c5 r456c4} - b2n3{r1c4 r2c456} - c3n3{r2 r789} - r8c1{n3 .} ==> r7c1 ≠ 6
g-whip[7]: r7c9{n6 n4} - r7c8{n4 n3} - b6n3{r4c8 r4c7} - b5n3{r4c5 r456c4} - b2n3{r1c4 r2c456} - c3n3{r2 r789} - r8c1{n3 .} ==> r7c3 ≠ 6
g-whip[8]: r9n9{c9 c7} - r2n9{c7 c4} - c4n6{r2 r789} - r9n6{c5 c123} - r8c1{n6 n3} - c7n3{r8 r4} - c3n3{r4 r2} - r2n2{c3 .} ==> r9c9 ≠ 5
whip[1]: b9n5{r9c7 .} ==> r3c7 ≠ 5
g-whip[8]: r9n9{c9 c7} - r2n9{c7 c4} - c4n6{r2 r789} - r9n6{c5 c123} - r8c1{n6 n3} - c7n3{r8 r4} - c3n3{r4 r2} - r2n2{c3 .} ==> r9c9 ≠ 4
whip[8]: r4n2{c3 c1} - c1n4{r4 r7} - r7c9{n4 n6} - r4n6{c9 c8} - r7c8{n6 n3} - b6n3{r4c8 r4c7} - r4n9{c7 c9} - r9c9{n9 .} ==> r4c3 ≠ 4
whip[1]: c3n4{r9 .} ==> r7c1 ≠ 4
g-whip[8]: b5n4{r4c6 r456c4} - r1n4{c4 c9} - r7c9{n4 n6} - r7c8{n6 n3} - r6c8{n3 n9} - r4n9{c9 c1} - r4n6{c1 c3} - r4n2{c3 .} ==> r4c8 ≠ 4
g-whip[8]: c1n9{r6 r4} - r4n2{c1 c3} - r2n2{c3 c4} - r2n9{c4 c7} - r9n9{c7 c9} - b9n6{r9c9 r7c789} - c4n6{r7 r8} - r8c1{n6 .} ==> r6c1 ≠ 3
g-whip[9]: r2n2{c3 c4} - r2n9{c4 c7} - r9n9{c7 c9} - b9n6{r9c9 r7c789} - c4n6{r7 r8} - r8c1{n6 n3} - r1c1{n3 n1} - r7c1{n1 n7} - r3n7{c1 .} ==> r3c3 ≠ 2
g-whip[9]: r2n2{c3 c4} - r2n9{c4 c7} - r9n9{c7 c9} - b9n6{r9c9 r7c789} - c4n6{r7 r8} - r8c1{n6 n3} - c3n3{r9 r4} - r4n2{c3 c1} - r1c1{n2 .} ==> r2c3 ≠ 1
whip[5]: r2n1{c6 c7} - r2n9{c7 c4} - r2n2{c4 c3} - r1c2{n2 n3} - r1c1{n3 .} ==> r1c4 ≠ 1
g-whip[9]: r3n8{c2 c1} - r9n8{c1 c2} - c2n2{r9 r1} - r2c3{n2 n3} - b2n3{r2c5 r1c4} - b5n3{r5c4 r4c456} - b6n3{r4c7 r456c8} - r7n3{c8 c1} - c1n7{r7 .} ==> r3c2 ≠ 6
t-whip[4]: c2n6{r5 r9} - r9n8{c2 c1} - b7n2{r9c1 r9c3} - r4n2{c3 .} ==> r4c1 ≠ 6
whip[5]: c2n6{r5 r9} - r8c1{n6 n3} - r1n3{c1 c4} - r7n3{c4 c8} - r6n3{c8 .} ==> r5c2 ≠ 3
t-whip[6]: c2n6{r5 r9} - r9n8{c2 c1} - b7n2{r9c1 r9c3} - r4n2{c3 c1} - c1n9{r4 r6} - c1n4{r6 .} ==> r5c1 ≠ 6
t-whip[6]: r4n6{c9 c3} - b1n6{r3c3 r3c1} - r8c1{n6 n3} - b4n3{r5c1 r6c2} - r1n3{c2 c4} - r5n3{c4 .} ==> r5c8 ≠ 6
whip[6]: b1n6{r3c3 r3c1} - r8c1{n6 n3} - c3n3{r7 r2} - b2n3{r2c5 r1c4} - r7n3{c4 c8} - c8n6{r7 .} ==> r4c3 ≠ 6
hidden-single-in-a-block ==> r5c2 = 6
whip[7]: r7n7{c3 c1} - r7n1{c1 c4} - b7n1{r7c3 r8c3} - r4c3{n1 n2} - r2c3{n2 n6} - c4n6{r2 r8} - r8c1{n6 .} ==> r7c3 ≠ 3
jellyfish-in-columns: n3{c3 c7 c5 c6}{r2 r4 r8 r9} ==> r8c4 ≠ 3, r8c1 ≠ 3, r4c8 ≠ 3, r4c4 ≠ 3
naked-single ==> r8c1 = 6
naked-pairs-in-a-block: b7{r9c1 r9c2}{n2 n8} ==> r9c3 ≠ 2
biv-chain[4]: r2c7{n1 n9} - b9n9{r9c7 r9c9} - r9n6{c9 c5} - c4n6{r7 r2} ==> r2c4 ≠ 1
biv-chain[4]: r2n9{c4 c7} - b9n9{r9c7 r9c9} - r9n6{c9 c5} - c4n6{r7 r2} ==> r2c4 ≠ 2
singles ==> r2c3 = 2, r9c2 = 2, r9c1 = 8, r3c2 = 8, r4c1 = 2, r6c1 = 9, r5c1 = 4, r3c3 = 6, r3c1 = 7, r7c3 = 7
whip[1]: b1n1{r1c2 .} ==> r1c9 ≠ 1
whip[1]: c9n1{r6 .} ==> r4c7 ≠ 1
whip[1]: r2n3{c6 .} ==> r1c4 ≠ 3
biv-chain[2]: r7n1{c4 c1} - c3n1{r8 r4} ==> r4c4 ≠ 1
whip[2]: c3n1{r8 r4} - b5n1{r4c5 .} ==> r8c4 ≠ 1
swordfish-in-rows: n4{r1 r6 r7}{c9 c8 c4} ==> r8c4 ≠ 4, r4c9 ≠ 4, r4c4 ≠ 4, r3c8 ≠ 4, r3c4 ≠ 4
stte

[urhegyi]

Chironex fleckeri

Geographic Range. Chironex fleckeri, also known as box jellyfish, lives in and around the waters of Australia.

[mith]

.
I don't know a lot of what you meant (I found only two jellyfish), but it also has a lot of g-candidates and g-whips, leading to a solution in gW9.

There are multiple finned jellyfish, but your resolution path ends up bypassing them I guess?

[edit]Yeah, you're getting the elimination for the finned jelly on 1 with a g-whip[5], and a couple eliminations for the finned jelly on 3 with whip[7]s.

There is a path using the three finned jellys, some basic AICs/bivalue-chains, and then the three basic jellys (once the fin is removed) - though there are other options that bypass the basic fish.[/edit]

[denis_berthier]

.
I don't know a lot of what you meant (I found only two jellyfish), but it also has a lot of g-candidates and g-whips, leading to a solution in gW9.

There are multiple finned jellyfish, but your resolution path ends up bypassing them I guess?
[edit]Yeah, you're getting the elimination for the finned jelly on 1 with a g-whip[5].[/edit]

Actually, it would mean I don't detect this finned jelly. Otherwise, it would be applied before any g-whip[5]. No time now, but I'lI have to check if it's a standard finned jelly.

[RSW]

My solver found three finned jellyfish:
Finned Jellyfish: Digit 1 in rows 1 5 6 7 columns 1 2 (3) 4 9, Fin: r7c3 => -1r8c1
Finned Jellyfish: Digit 3 in rows 1 5 6 7 columns 1 2 (3) 4 8, Fin: r7c3 => -3r8c1 -3r9c12
Finned Jellyfish: Digit 4 in rows 1 5 6 7 columns 1 (3) 4 8 9, Fin: r7c3 => -4r89c1
but couldn't proceed beyond that point without resorting to dubious (T&E) techniques.

[Cenoman]

Code: Select all

 +---------------------------+--------------------------+---------------------------+
 |  123*^   b123*^   9       |  12345*^& 8       7      |  6       245^&   145*&    |
 |  5        4      c1236    | d12369    136     13     | e19      8       7        |
 |  12678   b1268    1267    |  124569   1456    145    |  1459    2459    3        |
 +---------------------------+--------------------------+---------------------------+
 |  123469   7       12346   |  13458    1345    1345   |  13459   34569   145689   |
 |  1346*^&  136*^   8       |  1345*^&  2       9      |  7       3456^&  1456*&   |
 |  1349*^&  13*^    5       |  1348*^&  7       6      |  2       349^&   1489*&   |
 +---------------------------+--------------------------+---------------------------+
 |  13467*^& 1356*^  13467*^&|  13456*^& 9       2      |  8       3456^&  456&     |
 |  6-1342   9       1346-2  |  13456    13456   8      |  345     7       2456     |
 |  268-34  a2568-3  2346    |  7        3456    345    | f3459    1      g4569-2   |
 +---------------------------+--------------------------+---------------------------+

1. (2)r9c2 = r13c2 - r2c3 = (2-9)r2c4 = r2c7 - r9c7 = (9)r9c9 => -2 r9c9; +2r8c9
2. (1)r7c3 = JF(1)r1567\c1249 => -1 r8c1
3. (3)r7c3 = JF(3)r1567\c1248 => -3 r89c1, r9c2
4. (4)r7c3 = JF(4)r1567\c1489 => -4 r89c1; +6 r8c1 & basics

Code: Select all

 +-------------------------+---------------------------+---------------------------+
 |  123     123    9       |    12345    8      7      |  6       245     145      |
 |  5       4     b1236    | EAb69-123  a136    13     | F19      8       7        |
 |  1278    1268   1267    |   c12459-6  1456   145    |  145-9   2459    3        |
 +-------------------------+---------------------------+---------------------------+
 |  12349   7      12346   |    13458    1345   1345   |  1345-9  34569   145689   |
 |  134     136    8       |    1345     2      9      |  7       3456    1456     |
 |  1349    13     5       |    1348     7      6      |  2       349     1489     |
 +-------------------------+---------------------------+---------------------------+
 |  1347    135    1347    |   D13456    9      2      |  8       3456    456      |
 |  6       9      134     |    1345     1345   8      |  345     7       2        |
 |  28      258    234     |    7       C3456   345    | A3459    1      B69-45    |
 +-------------------------+---------------------------+---------------------------+

5. (6)r2c5 = (6-29)r2c34 = (9)r3c4 => -6 r3c4
6. (9)r9c7 = (9-6)r9c9 = r9c5 - r7c4 = (6-9)r2c4 = (9)r2c7 loop => -123 r2c4, -9r34c7, -45 r9c9; lclste

[mith]

Yeah, that loop is what I had in mind when I mentioned bypassing the basic fish.

There's an alternate solution path which follows more directly from the finned jellyfish eliminations:

SET version: r145678c567 and r239c123489 contain the same 18 digits. There are five empty cells in the first group. The second group contains one each of 1345 which must occupy four of those empty cells.

However, we can deduce that there is at least one more digit from 345 in the second group, in r9c23 - if neither cell was from 345, we would have 268 in four cells, which is a problem. So there is one more 345, taking the last empty cell from the first group, and we can eliminate any 26789 from the first group cells, any 1345 from the second group cells other than in b7, and 268 from r7c123+r8c3.

MSLS version: 13 Cells r239c57+r9c1236,r23c6,r8c1,13 Links 13r2,145r3,345r9,6c5,9c7,268b7
24 Eliminations: r3c1234,r2c34<>1, r8c3<>2, r2c34,r1c4<>3, r3c48,r9c9<>4, r3c48,r9c9<>5, r7c123,r8c35<>6, r4c7<>9, r3c5<>6, r3c7<>9

A bunch of basics from there, and then a short chain or ALS technique to finish off (there are a couple options in the cells from Cenoman's step 5).

[denis_berthier]

.
I don't know a lot of what you meant (I found only two jellyfish), but it also has a lot of g-candidates and g-whips, leading to a solution in gW9

There are multiple finned jellyfish, but your resolution path ends up bypassing them I guess?
[edit]Yeah, you're getting the elimination for the finned jelly on 1 with a g-whip[5].[/edit]

Actually, it would mean I don't detect this finned jelly. Otherwise, it would be applied before any g-whip[5]. No time now, but I'lI have to check if it's a standard finned jelly.

There was indeed an unjustified restriction in my rules for finned jellyfish. (It was inadvertently inherited from the rules for normal Jellyfish, where it was introduced for efficiency reasons and where it had no restrictive impact.)
After correction, I find 5 of them and the resolution path is much simpler (in SFin+W4). Starting from the same resolution state as before (after Singles):

whip[1]: c8n2{r3 .} ==> r1c9 ≠ 2
z-chain[3]: c4n9{r3 r2} - r2n2{c4 c3} - r2n6{c3 .} ==> r3c4 ≠ 6
finned-jellyfish-in-rows: n3{r5 r6 r1 r7}{c4 c8 c2 c1} ==> r9c1 ≠ 3, r8c1 ≠ 3, r9c2 ≠ 3
finned-jellyfish-in-rows: n1{r5 r6 r1 r7}{c4 c9 c2 c1} ==> r8c1 ≠ 1
finned-jellyfish-in-rows: n4{r1 r6 r5 r7}{c8 c9 c4 c1} ==> r9c1 ≠ 4, r8c1 ≠ 4
biv-chain[4]: r2n2{c3 c4} - r2n9{c4 c7} - b9n9{r9c7 r9c9} - b9n2{r9c9 r8c9} ==> r8c3 ≠ 2
z-chain[4]: r8c1{n6 n2} - r4n2{c1 c3} - r2n2{c3 c4} - c4n6{r2 .} ==> r8c5 ≠ 6
t-whip[4]: r9n9{c9 c7} - r2n9{c7 c4} - r2n2{c4 c3} - c2n2{r3 .} ==> r9c9 ≠ 2
singles ==> r8c9 = 2, r8c1 = 6
biv-chain[4]: r9n9{c9 c7} - r2n9{c7 c4} - c4n6{r2 r7} - r9n6{c5 c9} ==> r9c9 ≠ 4, r9c9 ≠ 5
biv-chain[4]: r2c7{n1 n9} - b9n9{r9c7 r9c9} - r9n6{c9 c5} - c4n6{r7 r2} ==> r2c4 ≠ 1
biv-chain[4]: r2n9{c4 c7} - b9n9{r9c7 r9c9} - r9n6{c9 c5} - c4n6{r7 r2} ==> r2c4 ≠ 2, r2c4 ≠ 3
singles ==> r2c3 = 2, r9c2 = 2, r9c1 = 8, r3c2 = 8, r3c3 = 6, r3c1 = 7, r7c3 = 7, r5c2 = 6, r4c1 = 2, r6c1 = 9, r7c2 = 5
whip[1]: b9n5{r9c7 .} ==> r3c7 ≠ 5, r4c7 ≠ 5
whip[1]: b1n1{r1c2 .} ==> r1c4 ≠ 1, r1c9 ≠ 1
whip[1]: c9n1{r6 .} ==> r4c7 ≠ 1
whip[1]: r2n3{c6 .} ==> r1c4 ≠ 3
biv-chain[2]: r7n1{c4 c1} - c3n1{r8 r4} ==> r4c4 ≠ 1
whip[2]: c3n1{r8 r4} - b5n1{r4c5 .} ==> r8c4 ≠ 1
z-chain[3]: b8n1{r7c4 r8c5} - c3n1{r8 r4} - c6n1{r4 .} ==> r3c4 ≠ 1
whip[3]: c3n1{r4 r8} - b8n1{r8c5 r7c4} - b5n1{r5c4 .} ==> r4c9 ≠ 1
biv-chain[3]: c9n1{r5 r6} - r6c2{n1 n3} - r6c8{n3 n4} ==> r5c9 ≠ 4
jellyfish-in-columns: n3{c3 c5 c6 c7}{r4 r8 r2 r9} ==> r8c4 ≠ 3, r4c8 ≠ 3, r4c4 ≠ 3
z-chain[3]: r8c4{n4 n5} - r9c6{n5 n3} - r9c3{n3 .} ==> r9c5 ≠ 4
jellyfish-in-columns: n4{c3 c5 c6 c7}{r4 r8 r3 r9} ==> r8c4 ≠ 4, r4c9 ≠ 4, r4c8 ≠ 4, r4c4 ≠ 4, r3c8 ≠ 4, r3c4 ≠ 4
stte

[mith]

Nice, thanks Denis

[denis_berthier]

Hi Mith,
I'm the one who should thank you. I hadn't checked my Finned-Fish rules since their first version some 10-15 years ago. Your puzzle has been the occasion to spot unnecessarily restrictive conditions on Finned-Jellyfish and Finned-Swordfish. While they couldn't lead to unjustified eliminations and false results, they missed a few legitimate eliminations.
I checked my corrections on a collection 1200+ puzzles and I found no problem. Soon, after still more checking, I'll publish them on GitHub.