The New Sudoku Players' Forum

[wapati]

Here is an odd one. After simple stuff you come to 2 distinct swordfish patterns on the same digit and they don't affect each other at all, except that either one triggers eliminations that solve the puzzle.

Code: Select all

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


[udosuk]

Each swordfish's dual is a jellyfish which happens to totally include another swordfish...

[wapati]

Each swordfish's dual is a jellyfish which happens to totally include another swordfish...

Funny you mentioned that! I just generated a puzzle with both a sword and a jelly pattern, both required, before forcing chains, that is.

Code: Select all

...3.7...
19..8..34
..3.6.5..
...7.8...
41.....78
.2..4..5.
.........
.74.9.38.
...1.3...


[udosuk]

Can't find the jellyfish... I do suck at fishing jellys...

Code: Select all

After SSTS (basic moves, swordfish on 5s, 2 turbot-fish on 2s):
 *--------------------------------------------------------------------*
 | 256    4      256    | 3      1      7      | 8      269    269    |
 | 1      9      67     | 25     8      25     |*67     3      4      |
 | 27     8      3      | 4      6      9      | 5      1     *27     |
 |----------------------+----------------------+----------------------|
 | 369    356    69     | 7      25     8      | 1      4     -269    |
 | 4      1      569    | 2569   3      256    |*269    7      8      |
 | 78     2      78     | 69     4      1      |*69     5      3      |
 |----------------------+----------------------+----------------------|
 | 2369   356    1      | 8      57     4      | 2679   269    25679  |
 | 25     7      4      | 256    9      256    | 3      8      1      |
 | 2689   56     2689   | 1      257    3      | 4      269    5679   |
 *--------------------------------------------------------------------*

Generalised xy-wing:
r4c9=2 => r3c9=7 => r2c7=6 => r6c7=9 => r5c7=2, two 2s in b6!
Therefore r4c9<>2, and the rest of the puzzle is solved with singles.

Interestingly, you don't even need those swordfish/turbot-fish moves if you apply this generalised xy-wing move...

16 singles + 1 naked pair + 1 generalised xy-wing + 1 single + 1 naked pair + 38 singles

Edit: wrong term corrected

[daj95376]

Here is an odd one. After simple stuff you come to 2 distinct swordfish patterns on the same digit and they don't affect each other at all, except that either one triggers eliminations that solve the puzzle.

Code: Select all

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


I didn't follow udosuk's explanation for the first puzzle, so please forgive me if this is a re-hash. After udosuk's comment, I examined the puzzle for Jellyfish and found:

1) Swordfish in [r239] is included in Jellyfish [r2359] for <9>
2) Swordfish in [c159] is included in Jellyfish [c1359] for <9>

They have [r5c3] in common.

===== ===== =====

In the second puzzle, I couldn't follow udosuk's XYZ-Wing logic. I thought an XYZ-Wing involved three cells, that form a bent triple, and involves eliminations to cells common to all three.

Code: Select all

r2      -  25    Naked  Pair
r6      -  69    Naked  Pair
    b8  -  6     Locked Candidate (1)
  c259  -  5     Swordfish
r2568   -  6     Jellyfish
    b6  -  9     Locked Candidate (1)
r1c9    <> 6     XY-Wing  on [r3c9]
r5c7    <> 6     XY-Wing  on [r3c9]
r6c7    <> 6     XY-Wing  on [r3c9]


[ronk]

Each swordfish's dual is a jellyfish which happens to totally include another swordfish...

Which is another way of saying the jellyfish is "degenerate" -- meaning there is only one candidate in either a row or a column. For this puzzle and for either jellyfish, that directly implies the placement r5c3=9.

Not particularly useful, but I wonder how often that happens.

[daj95376]

Thanks ronk for the explanation!!! I noticed that upgrading each Swordfish to a Jellyfish added a cell that didn't overlap any of the cells in the original Swordfish. This matches your use of degenerate perfectly. Thanks for pointing out that [r5c3]=9 is forced. I suspected that and had planned to investigate. You saved me the trouble.

In the second puzzle, the column Swordfish has a companion row Jellyfish. This could give a person a headache!

I wonder how many puzzles would have their solutions changed if the solver hierarchy was: Jellyfish, Swordfish, and then X-Wing.

[udosuk]

Thanks for showing me the jellyfish! I just missed it inexcusably...

In the second puzzle, I couldn't follow udosuk's XYZ-Wing logic. I thought an XYZ-Wing involved three cells, that form a bent triple, and involves eliminations to cells common to all three.

Sorry! Wrong term used... Should have said "generalised xy-wing" instead... Basically, r4c9=2 would force r3c9=7 and r56c7={69}, leaving no valid candidate in r2c7, so r4c9 must not be 2.

Alternatively, it's just a simple ALS-xz:
A: r256c7={2679}
B: r3c9={27}
x=7
z=2

If r4c9=2, r256c7={679} and r3c9=7, and we'll have two 7s in b3.
Therefore r4c9<>2...

[daj95376]

Udosuk, thanks for the clarification! I will add the generalized version of XY-Wing to my list of topics to research.

[daj95376]

Which is another way of saying the jellyfish is "degenerate" -- meaning there is only one candidate in either a row or a column. For this puzzle and for either jellyfish, that directly implies the placement r5c3=9.

Not particularly useful, but I wonder how often that happens.

I can't help with the frequency of overlapping Jellyfish for the same value, but I do have some results on degenerates. I scanned, using reverse hierarchy on fish, the 94 puzzles in ab's Superior Plus collection. Here's the results.

Code: Select all

Jellyfish degenerate to Swordfish

Puzzle 17:  ............1.23..45.....61.4.....1....2.7....6.....8.91.....46..73.8............
Puzzle 29:  9.38...6....6...8.......9.5..23...5.4...6...1.5...78..3.5.......7...3....6...12.9
Puzzle 34:  .........9..3.2..464.1.8.7971.....28..5...7..42.....9515.9.4.622..5.6..1.........
Puzzle 57:  ..6.5........2785..2.9....78..6.9.7.6...4...3.5.2.8..17....2.4..6519........7.1..
Puzzle 60:  17...34...4...73....6.9..1.2..8.91.6....6....8.73.1..4.9..1.7....37...9...19...42
Puzzle 65:  8..3..71.......4.57..6.4.3..5.7.....4...5...7.....1.8..4.5.6..22.3.......76..8..4
Puzzle 67:  ..5...3..9...2..87.....1...25..1.79.4...7...2.83.9..51...7.....39..4...8..4...2..
Puzzle 68:  .328..69...9.5...1.8...9....5.2..7..9...6...2..7..3.5....5...3.8...2.5...25..716.
Puzzle 85:  .75.24...2.......4.86....1...8..2....4.571.6....8..5...9....45.5.......7...76.89.


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Swordfish degenerate to X-Wing

Puzzle 71:  .37.6.91............57.82...9.2.6...5...8...4...1.4.3...68.94............29.1.86.
Puzzle 74:  ..5...3..9...2...7...3..92..564...93....7....78...645..68..2...3...4...8..4...2..


Interestingly enough, reversing the hierarchy often resulted in shorter solutions as well!

[udosuk]

Interestingly enough, reversing the hierarchy often resulted in shorter solutions as well!

Not too surprising, because larger fish means more eliminations each time...

[wapati]

Or not, larger fish own more turf, not much left to eliminate!