More Eliminations in Pattern than Solutions

Advanced methods and approaches for solving Sudoku puzzles

More Eliminations in Pattern than Solutions

Postby daj95376 » Wed Dec 20, 2006 11:07 pm

Code: Select all
7..96.1....4..26.3...3.5.2.14......2..7.2.4..9......67.7.6.3...4.62..3....1.94..6 #B026 8

Code: Select all
# ronk solution: finned franken jellyfish c147b3\r2579
# (#) fin cell: [r3c9]-8-[r5c9]
# (#) fin cell: [r6c7]-8-[r5c9]

  .  .  . |  .  .  . |  .  .  .
 *8  8  . |  .  .  . |  . *8  .
  .  .  8 |  .  .  . |  .  . #8
 ---------+----------+----------
  .  .  8 |  .  8  . |  .  8  .
 *8  .  . | *8  .  . |  .  8 -8
  .  8  8 |  .  8  . | #8  .  .
 ---------+----------+----------
 *8  .  8 |  .  8  . | *8  8  8
  .  8  . |  .  8  . |  .  8  8
 *8  8  . | *8  .  . | *8  .  .

Code: Select all
# using ronk's solution ...
# my perspective: finned Kraken Jellyfish [r2579C1478]
# (+) fin    cell: [r4c8]-8-                  [r5c9]
# (+) fin    cell: [r6c7]-8-                  [r5c9]
# (#) Kraken cell: [r8c8]-8-[r2c8]=8=[r3c9]-8-[r5c9]

  .  .  . |  .  .  . |  .  .  .
 *8  8  . |  .  .  . |  . *8  .
  .  .  8 |  .  .  . |  .  .  8
 ---------+----------+----------
  .  .  8 |  .  8  . |  . +8  .
 *8  .  . | *8  .  . |  . *8 -8
  .  8  8 |  .  8  . | +8  .  .
 ---------+----------+----------
 *8  .  8 |  .  8  . | *8 *8  8
  .  8  . |  .  8  . |  . #8  8
 *8  8  . | *8  .  . | *8  .  .

However, there's a second elimination supported by this pattern. I have a horrible solution requiring an intermediate skyscraper. Is there a more traditional fish solution? (note: if [r4c7] contains <8>, then this elimination shouldn't occur.)

Code: Select all
  .  .  . |  .  .  . |  .  .  .
  8  8  . |  .  .  . |  .  8  .
  .  .  8 |  .  .  . |  .  .  8
 ---------+----------+----------
  .  .  8 |  .  8  . |  .  8  .
  8  .  . |  8  .  . |  .  8  8
  .  8  8 |  .  8  . |  8  .  .
 ---------+----------+----------
  8  .  8 |  .  8  . |  8  8  8
  .  8  . |  .  8  . |  .  8 -8
  8  8  . |  8  .  . |  8  .  .
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Postby wapati » Thu Dec 21, 2006 1:09 am

Skyscraper is an almost X-wing.

2 locked candidates on each wing.

There is no such critter here.
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Postby daj95376 » Thu Dec 21, 2006 5:48 am

wapati wrote:Skyscraper is an almost X-wing.

2 locked candidates on each wing.

There is no such critter here.

There is if you (jokingly) construct a Kraken Leviathan! The Kraken cell creates a nightmarish chain -- including a Skyscraper.

The other option is to create a Kraken 1-Wing using the same Kraken cell, but then people might argue that it's a forcing chain/net. (If you read closely, my message didn't say that I had a fish solution with an embedded Skyscraper. I just asked if someone else had a fish solution.)

BTW: The Kraken Leviathan/1-Wing performs, in one operation, both eliminations shown above.
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re: _finned_ Franken Jellyfish - two separate fins

Postby Pat » Thu Dec 21, 2006 1:34 pm

      [ off-topic ]
daj95376 wrote:
      B026 8
      [ 31 clues ]
Code: Select all
 7 . . | 9 6 . | 1 . .
 . . 4 | . . 2 | 6 . 3
 . . . | 3 . 5 | . 2 .
-------+-------+------
 1 4 . | . . . | . . 2
 . . 7 | . 2 . | 4 . .
 9 . . | . . . | . 6 7
-------+-------+------
 . 7 . | 6 . 3 | . . .
 4 . 6 | 2 . . | 3 . .
 . . 1 | . 9 4 | . . 6




ronk's solution: finned Franken Jellyfish c147b3\r2579
fin cell: [r3c9]-8-[r5c9]
fin cell: [r6c7]-8-[r5c9]

Code: Select all
  .  .  . |  .  .  . |  .  .  .
 *8  8  . |  .  .  . |  . *8  .
  .  .  8 |  .  .  . |  .  . #8
 ---------+----------+----------
  .  .  8 |  .  8  . |  .  8  .
 *8  .  . | *8  .  . |  .  8 -8
  .  8  8 |  .  8  . | #8  .  .
 ---------+----------+----------
 *8  .  8 |  .  8  . | *8  8  8
  .  8  . |  .  8  . |  .  8  8
 *8  8  . | *8  .  . | *8  .  .




hi daj95376,

thanks for the interesting example -- could you please point me to the source?

~ Pat
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Re: re: _finned_ Franken Jellyfish - two separate fins

Postby ronk » Thu Dec 21, 2006 2:17 pm

Pat wrote:thanks for the interesting example -- could you please point me to the source?

This thread is the online source. Danny, aka daj95376, and I have been working offline via PM to try to find examples of fish that logically explain some of the eliminations made by templates.

Danny generated 240 puzzles that required templates to solve -- over and above logical techniques of his solver. After stumbling about a bit and feeling overwhelmed, we decided to concentrate on the 14 puzzles that were also not solved by logical techniques of my solver. (I suspect Mike Barker's solver could solve all of them.)

These 14 puzzles are:
Code: Select all
.3...8..4..4.7.6..6....572.....5.982.6..2..3.928.3.....756....9..6.8.3..3..5...7. #B020 1
7..96.1....4..26.3...3.5.2.14......2..7.2.4..9......67.7.6.3...4.62..3....1.94..6 #B026 8
8....3..14..7..9.8.15..8.3...93.2.4..8.....9..5.1.98...4.2..38.3.1..4..99..5....4 #B044 6
...42...1.32....6.7.59......7.3....5..4.5.1..6....9.2......13.6.6....25.9...36... #B046 8
4...5..3997..6.2.5..3...6...4.2.3.5.5...9...4.3.6.5.7...5...4..7.4.3..2636..8...7 #B049 1
......45..9..7.1.31.5.34....7...39.4.4.7.5.3.6.39...2....36.7.59.6.5..4..57...... #B074 8
6..9.4.....4.8...29...7......2..97.8.1.748.5.7.92..4......9...55...2.8.....4.5..7 #B107 3
5.7..94.......4.7......72.81......24..3...1..79......52.13......5.9.......45..7.3 #B130 6
5.7..9.3..29.....14...5..9.1.5.63.2...........9.41.3.5.7..4...93.....64..6.5..7.3 #B132 8
...85...29.....71..6..1...8..7..18..49..8..51..16..4..6...2..8..29.....48...74... #B147 3
...6.8..45......38.68.35.1...15...6...9.1.7...5...68...8.15.37.37......51..7.3... #B166 2
..367..9..97..1.3.4.........4.52...36...1...27...96.4.........6.7.4..12..2..634.. #B172 8
39.......7.1.9...8.4.17..9.56.8.......3...7.......6.53.3..89.6.1...4.5.9.......87 #B195 2
.4.6.8....1..5.8..7.8.3....4....25..2...6...8..57....4....1.3.2..7.4..8....5.3.6. #B212 9

The "Bnnn x" comment indicates puzzle #nnn in Danny's puzzle set B. The 'x' merely indicates the puzzle is void of clue digit 'x'.
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re(2): _finned_ Franken Jellyfish - two separate fins

Postby Pat » Thu Dec 21, 2006 3:26 pm

ronk wrote:
Pat wrote:thanks for the interesting example -- could you please point me to the source?

This thread is the online source.

Danny, aka daj95376, and I have been working via PM to try to find examples of fish that logically explain some of the eliminations made by templates.

.3...8..4..4.7.6..6....572.....5.982.6..2..3.928.3.....756....9..6.8.3..3..5...7. #B020 1
7..96.1....4..26.3...3.5.2.14......2..7.2.4..9......67.7.6.3...4.62..3....1.94..6 #B026 8
8....3..14..7..9.8.15..8.3...93.2.4..8.....9..5.1.98...4.2..38.3.1..4..99..5....4 #B044 6
...42...1.32....6.7.59......7.3....5..4.5.1..6....9.2......13.6.6....25.9...36... #B046 8
4...5..3997..6.2.5..3...6...4.2.3.5.5...9...4.3.6.5.7...5...4..7.4.3..2636..8...7 #B049 1
......45..9..7.1.31.5.34....7...39.4.4.7.5.3.6.39...2....36.7.59.6.5..4..57...... #B074 8
6..9.4.....4.8...29...7......2..97.8.1.748.5.7.92..4......9...55...2.8.....4.5..7 #B107 3
5.7..94.......4.7......72.81......24..3...1..79......52.13......5.9.......45..7.3 #B130 6
5.7..9.3..29.....14...5..9.1.5.63.2...........9.41.3.5.7..4...93.....64..6.5..7.3 #B132 8
...85...29.....71..6..1...8..7..18..49..8..51..16..4..6...2..8..29.....48...74... #B147 3
...6.8..45......38.68.35.1...15...6...9.1.7...5...68...8.15.37.37......51..7.3... #B166 2
..367..9..97..1.3.4.........4.52...36...1...27...96.4.........6.7.4..12..2..634.. #B172 8
39.......7.1.9...8.4.17..9.56.8.......3...7.......6.53.3..89.6.1...4.5.9.......87 #B195 2
.4.6.8....1..5.8..7.8.3....4....25..2...6...8..57....4....1.3.2..7.4..8....5.3.6. #B212 9


The "Bnnn x" comment indicates puzzle #nnn in Danny's puzzle set B;
the 'x' merely indicates the puzzle is void of clue digit 'x'.


thanks, ronk.
i liked B026 as an example of multiple fins.
~ Pat
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Postby daj95376 » Thu Dec 21, 2006 7:04 pm

Hello Pat. I'm glad that you like puzzle B026. Ron and I have only just begun examining these puzzles for fish solutions. Input from others is welcome and encouraged! Just remember, the purpose of this thread is to have fun and share puzzles/solutions that can be understood by less sophisticated Sudoku players; i.e. me!!!:D

BTW: In this thread, it's okay to extend the concept of Kraken beyond its traditional definition. Just please indicate when and how you are doing so -- like my mentioning the Skyscraper in the solution to puzzle B026. (I think Ron is closing in on a more traditional solution for the second elimination.)
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Postby StrmCkr » Sat Dec 23, 2006 12:26 pm

removed
Last edited by StrmCkr on Mon Jun 10, 2013 4:05 pm, edited 2 times in total.
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Postby daj95376 » Sat Dec 23, 2006 1:26 pm

I'm sorry StrmCkr, but I can't follow your solution to puzzle B026. Maybe you can follow mine -- sans Singles.

Code: Select all
7..96.1....4..26.3...3.5.2.14......2..7.2.4..9......67.7.6.3...4.62..3....1.94..6 #B026 8

r1  b3  -  45    Naked  Pair            row and box
  c1    -  2     Locked Candidate (2)

r7c8    <> 9     Templates (A: 2)       SSTS: Colors
r8c9    <> 9     Templates (A: 2)       SSTS: Colors
r4c8    <> 9     Templates (A: 2)       SSTS: X-Wing
r4c7    =  9     Hidden Single          critical to dual eliminations in <8>

Code: Select all
# single-digit DIC/N [r3] on <8>
#
# [r3c9]-8-[r58c9]
#
# [r3c9]=8=([r2c8],[r3c3])
#       -8-([r4c3],[r4c8])
#       =8=[r4c5]            (this won't happen until after Hidden Single above!)
#       -8-[r78c5]
#       =8=[r9c4]
#       => Skyscraper [r58]
#       -8-([r6c2],[r7c1])
#       =8=([r5c1],[r8c2])
#       -8-[r58c9]
 *--------------------------------------------------------------------*
 | 7      23     23     | 9      6      8      | 1      45     45     |
 | 58     589    4      | 1      7      2      | 6      89     3      |
 | 6      1      89     | 3      4      5      | 7      2      89     |
 |----------------------+----------------------+----------------------|
 | 1      4      358    | 7      358    6      | 9      358    2      |
 | 358    6      7      | 58     2      9      | 4      1358   15-8   |
 | 9      2358   2358   | 4      358    1      | 58     6      7      |
 |----------------------+----------------------+----------------------|
 | 258    7      589    | 6      158    3      | 258    1458   14589  |
 | 4      589    6      | 2      158    7      | 3      1589   15-8   |
 | 2358   358    1      | 58     9      4      | 258    7      6      |
 *--------------------------------------------------------------------*

Code: Select all
  c9    -  15    Naked  Pair

r5c4    <> 5     Templates (A: 4)       SSTS: Multi-Colors
r8c5    <> 5     Templates (A: 4)         "     "     "
r6c2    <> 5     Templates (A: 4)       SSTS: Swordfish
r7c1    <> 5     Templates (A: 4)         "       "

  c2    -  238   Naked  Triple
    b7  -  238   Naked  Triple

r6c5    <> 5     XY-Wing  on [r4c8]
r1c2    <> 2     XY-Wing  on [r4c3]
r6c3    <> 2     XY-Wing  on [r4c3]
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does this help Danny?

Postby StrmCkr » Sun Dec 24, 2006 10:31 am

edit
Last edited by StrmCkr on Mon Jun 10, 2013 4:05 pm, edited 1 time in total.
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Postby daj95376 » Sat Dec 30, 2006 6:25 pm

So, I guess that I'm the only one having trouble with this elimination.

Code: Select all
...85...29.....71..6..1...8..7..18..49..8..51..16..4..6...2..8..29.....48...74... #B147 3

# note: XYZ-Wing on [r2c2] => r1c2<>3, but may not be necessary for elimination
 *-----------------------------------------------------------------------------*
 | 137     1347    34      | 8       5       3679    | 369     3469    2       |
 | 9       345     8       | 234     34      236     | 7       1       356     |
 | 357     6       2       | 3479    1       379     | 359     349     8       |
 |-------------------------+-------------------------+-------------------------|
 | 235     35      7       | 24-3    349     1       | 8       2369    369     |
 | 4       9       6       | 237     8       237     | 23      5       1       |
 | 23      8       1       | 6       39      5       | 4       2379    379     |
 |-------------------------+-------------------------+-------------------------|
 | 6       1347    345     | 1359    2       39      | 1359    8       3579    |
 | 137     2       9       | 135     6       8       | 135     37      4       |
 | 8       13      35      | 1359    7       4       | 123569  2369    3569    |
 *-----------------------------------------------------------------------------*

Code: Select all
# or any of these (later) eliminations
 *--------------------------------------------------------------------*
 | 1      47     34     | 8      5      3679   | 369    69-3   2      |
 | 9      5-3    8      | 24-3   34     26-3   | 7      1      356    |
 | 357    6      2      | 379    1      379    | 359    4      8      |
 |----------------------+----------------------+----------------------|
 | 25-3   35     7      | 24     49-3   1      | 8      269-3  69-3   |
 | 4      9      6      | 237    8      237    | 23     5      1      |
 | 2-3    8      1      | 6      39     5      | 4      2379   379    |
 |----------------------+----------------------+----------------------|
 | 6      47     345    | 1359   2      39     | 159-3  8      3579   |
 | 37     2      9      | 15     6      8      | 15     37     4      |
 | 8      1      35     | 359    7      4      | 2569-3 2369   3569   |
 *--------------------------------------------------------------------*
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Postby ronk » Sat Dec 30, 2006 9:44 pm

daj95376 wrote:So, I guess that I'm the only one having trouble with this elimination.

Code: Select all
...85...29.....71..6..1...8..7..18..49..8..51..16..4..6...2..8..29.....48...74... #B147 3

I don't think you've brought attention to puzzle #B147 before. I figured out r4c4<>3 but I had a head start, so I won't post my deduction ... at least not just yet.
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Postby StrmCkr » Sun Dec 31, 2006 7:15 am

edit
Last edited by StrmCkr on Mon Jun 10, 2013 4:05 pm, edited 2 times in total.
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Postby ronk » Sun Dec 31, 2006 11:51 am

StrmCkr wrote:
Code: Select all
 23      8       1       | 6       39      5       | 4       2379    379  <- row 6


note.
the diffrence in types of "yield chains" arrises from haveing the chain spans in a row/column/quad with more then 1 bivalved cell.(connected or not)

i can apply a yeild chain type 1. on row6

heres the conjugated als

r6c5 cannot = 3 based on conjugated als [237]

R6c1 [23]
R6c8 [237]
R6c9 [37]

excelude n=3 from:
r6c5

where n is the linking number.

Based on row 6 only, the following are two valid outcomes:
Code: Select all
 2       8       1       | 6       3       5       | 4       7       9    <- row 6


 2       8       1       | 6       3       5       | 4       9       7    <- row 6

In each case, note that r6c5=3. As before, you are either 1) using undisclosed information to make a valid deduction, or 2) your deduction is invalid -- as in guessing. And as before, I'm inclined to believe the latter.
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Postby StrmCkr » Sun Dec 31, 2006 12:28 pm

edit
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