Help for Fishy Patterns
 

Simple fishy patterns are patterns consisting of a single number appearing at the intersections of a grid of n rows and n columns. When the numbers in the rows are confined to the columns, then any extra numbers in the columns which are not in the rows can be deleted, and vice versa. With n=2, they are called X-wings, with n=3 they are swordfish, with n=4 they are jellyfish, and with n=5 squirmbags. Complex fish occur when there is one or two extra numbers in one of the rows or columns (a fin), or a missing number (sashimi), but these generally yield fewer eliminations.

In these examples, the pattern described is seen after loading puzzle and using "Clear Basics" button.

Simple X-wings must have 4 numbers, forming a square pattern. If the number in the rows only appears twice, but more than twice in either or both of the columns then the numbers in the columns not in the rows can go. This is illustrated by the left hand image below, where there are no other 2s in the rows shown.

Complex X-wings occur much more commonly than simple X-wings. In the above images, the middle is a finned X-wing, and the left a sashimi X-wing. Note that deletions of 2's are only possibe in the box with the fins. The following are some examples, many obtained from forum.enjoysudoku.com , especially the pure xwing, swordfish and jellyfish collections

1.....5694.2.....8.5...9.4....64.8.1....1....2.8.35....4.5...1.9.....4.2621.....5  Simple Xwing in rows (example from SudokuWiki.org)
..89.52......4....1.......94...7...1.7.6.1.9.9...2...37.......5....1......64.89..  Simple Xwing in rows
...1.6.....4...3...9.8.2.5.2.5...7.9.........3.8...1.6.1.4.5.2...2...5.....6.8...  Simple Xwing in columns
....2.......346.....8...5...2.....3.31.....27.9.....6...6...1.....874.......3....  Simple Xwing in columns
....6.....1.....3....952.....4...9..2.7...6.8..6...2.....581....9.....4.....2....  Simple Xwing in columns
...5.8...65.2..3......39.543..96..8..7.1.3.6..6..85..319.85......8..2.16...3.1...  Simple Xwing in columns
3.....5...6..2..7....1....4..48.5.6.....1.....7.6.43..9....3....1..7..9...3.....5  Small sashimi Xwing rows, 2r Franken swordfish
69...2..........31...........314....2.....6.....3........71..4.86....5...........  Small sashimi Xwing rows, 2r Franken swordfish
....1.8.47.4..2....5..3.2..63...5....452.836....3...58..3.2..8....7..4.34.7.5....  Big sashimi Xwing rows
..12..3...2...14..3...5...64...2...7..78..5...1...9...63..8.9.........63..29...8.  Big sashimi Xwing rows, 1c Mutant swordfish
.9..8..5...51....7.........6....9....8..5...2..14...3.8.35...4..6..2...3..2..8...  Big sashimi Xwing rows, 1r Franken swordfish
....9.87......1..5...7.642..6.4.738...........759.8.4..472.9...5..1......91.7....  Finned Xwing, sashimi Xwing, 1c Franken swordfish
.12......3.4...5..67.1.......65..8......3...9.....9.4..8.6..1.......4..3....9..7.  Finned Xwing in columns, 2c Franken swordfish
1....6..5.............3.67...784...3....59...9...6......4.7.28.7.9.......123..4..  Finned Xwing in rows, 1c Franken swordfish
...9..54.....18....6.3.....84.....569..6.5..365.....18.....9.3....24.....78..3...  Big finned Xwing rows
....42.6..1..........3..78.56......8..49.56...78......4.2..9....8.2..4...3...1..7  Sashimi Xwing in columns (AKA Skyscraper, X-cycle)
.6.7..8.......3..2..2.8..9..1....4.....3...6764.1............5.82..76.......29..4  Big sashimi Xwing columns 
.651.....4...657......9.1..8..7....2..6...4..9....1..3..3.2......851...9.....481.  Finned Xwing in columns
...6.3.5..9.8...1...8.....6.67.9...28..7.2..99...8.74.7.....6...2...8.9..8.3.4...  Big finned Xwing in columns
.7.2.......359.2....8..1.4.4......3.2...3...7.6......9.9.3..8....6.541.......9.6.  2 Big finned Xwing in columns

An interesting variant is the sashimi X wing in the next image.

This configuration is sometimes called a 'skyscraper', and can also be viewed as an alternating chain (x-cycle) of 7's of length 4.

Swordfish/Jellyfish

Things get much more complicated with higher order fish. A simple swordfish, with the number occurring at the intersections of 3 rows and 3 columns, doesn't have to have 9 occurrences, but may have 6, 7, 8 or 9. As with X wings there are finned and sashimi variants. The following examples give examples of these. The order of execution (which impacts a lot on which fish is found first) is:
x-wings
finned and sashimi x-wings.

simple swordfish
simple franken swordfish
simple mutant swordfish
finned and sashimi swordfish
simple jellyfish
.473..8......1..5..132.8......1....5..15.26..7....3......4.516..9..6......4..127.  Normal SF in rows (all 9 cells occupied!)
5..6..29832...8.....87...532....9...94.....15...8....986...75.....2...61432..5..7  Normal SF in rows (8 cells occupied)
3.1.9......68......8..5.3.41....58..8...2...6..49....75.3.8..1......27......4.5.9  Normal SF in rows (8 cells occupied)
...........91.57...539.241..61...59.....3.....94...37..162.394...58.12...........  Normal SF in rows (7 cells occupied)
...........12.34...5.4.6.1..17...36...........89...75..3.7.5.8...43.29...........  Normal SF in rows (7 cells occupied)
...7...1...8..1..52....486....9..4.8.352............21......6..6.31....7.4..9....  Normal SF in rows (6 cells occupied)
9.6.3.2.5.........3..7.1..8..1...6..2...5...4..8...9..8..9.2..7.........4.3.8.1.9  Normal SF in rows (6 cells occupied)
2....84..69..2...5...3..9..4....5..3.3..4..8.5..7....6..2..3...3...5..78..98....4  Normal SF in columns (all 9 cells occupied)
4.6..2........4....5.3..1...8.1..93........2..2.9..85..3.8..5.......7...7.1..9...  Normal SF in columns (all 9 cells occupied!)
26.9.7.4373.....89.........1..3.6..5....7....4..5.2..1.........34.....9792.4.3.16  Normal SF in columns (8 cells occupied)
..8..7.6.14....2...6..5.....3.18...6..4...8..5...73.2.....1..8...9....32.2.4..5..  Normal SF in columns (8 cells occupied)
...7..8..7..5..6......8...2.2..4.....3......7..19..5..2...5...14....3........1983  Normal SF in columns (7 cells occupied)
....1.73......4..2...8.316..4.2.681...........681.7.2..843.1...9..4......17.6....  Normal SF in columns (7 cells occupied), then jellyfish
.......63..763.48...3..8..1.3...41.5.1..8..3.5.63...7.2..7..3...74.562..65.......  Normal SF in columns (6 cells occupied)
...9..7..4..2...8..6...3..57...3........4.2...9......8.51..2..3.8.1.......6..5..9  Sashimi SF in columns
3.......1.9.4.1.6..14...89...3...4...589.437.7...3...848.6.5.37.7.8.3.2.....7....  Sashimi (big) in columns 
.4.2.........7..3..5....6..1......7....5.6......4.7...2.....1.5..3.8.........24.3  Sashimi SF in rows
6..........7...64.....92.1...4..79...3..1.42.......1.6..32....5.4.5......2.......  Sashimi SF in rows
...1...59...7..42.....64.8...9....1..21....9.7.....3...7....8..653......98..32...  Finned SF in rows
..49.5.1.5.8...3..7......56....6..9.2..5.3..1.4..2....12......5..7...1.3.6.7.19..  Finned (big) SF in rows
.1.....2.34.....56...2.6.....76285.....5.7.....69342.....4.5...56.....84.7.....1.  Finned SF in rows, then jellyfish
...........1...2..34..5..67.........15.2.3.7883.....41.........42.7.8.5671.....83  4 finned and sashimi SFs, then jellyfish
.............1.....123.456...........23...78..47.6.12...........318.764..58...23.  Sashimi SF, finned SF, or a grand 16 cell jellyfish
2.......3.8..3..5...34.21....12.54......9......93.86....25.69...9..2..7.4.......1  Jellyfish in rows, 15 cells
.............1.....123.456...........27...38..36.5.42...........682.715..74...83.  Jellyfish in columns, 16 cells  
..3..4..9....7..5.2..6..8....9.....4.4.....3.8.....7....4..3..2.2..6....7..8..6..  2 consecutive Jellyfish in rows
..1...2...2.1.3.4.5.......6.1.3.6.7...........3.4.7.2.1.......7.6.7.4.3...8...9..  3 consecutive jellyfish in rows

Franken Swordfish

A franken swordfish has a digit confined to either 3 rows / 2 columns and a box, or 3 columns / 2 rows and a box. Rather than try and explain it, I will refer you to here for a description. There are 4 types, best described at here. The following illustrate the 4 basic patterns (1r, 1c, 2r, 2c). The blue boxes define the pattern, noting that not all the blue boxes have to have a pattern digit: (purple areas = no pattern digits, Xs = possible eliminations)

        

In the following examples, copy and paste the text between the inverted commas, including the trailing comma

Type 1:
2....358.....2...1...4.56.....9.4.68..5.1.9..61.8.2.....15.8...3...4.....263....4  1r Franken swordfish 7s
...........86.59...534.718..39...87.....3.....41...32..143.925...75.14...........  1r Franken swordfish 6s, then normal SF
.1.....2.34.....56...6.4.....57862.....9.5.....74235.....3.7...96.....32.5.....1.  1r Franken swordfish 8s
.............1.....123.456...........35...78..81.2.35...........57...63..638.721.  1r Franken swordfish 4s (then sashimi SF, finned SF, jellyfish)
1....5..4..4....8..9..2.7.......7.2.2.......5.8.3.......5.1..4..6....3..3..4....1  1r Franken swordfish 9s

"S5,S8,17,3,17,9,S2,4,6,S3,127,9,12,S6,4,8,5,17,127,S4,S6,8,127,5,S9,17,3,6,1237,127,S5,8,123,137,9,S4,1278,12357,12578,S9,S4,123,1357,
S6,127,S9,35,4,S7,12,6,35,12,S8,1278,S9,1278,S4,S5,1278,6,S3,127,127,S6,3,12,S9,127,4,S8,5,S4,1257,12578,6,S3,1278,17,127,9,"  1r Franken SF 1s

"S1,S4,378,367,38,S5,S2,S9,36,379,3679,S5,367,S1,S2,367,S8,S4,S2,367,378,3678,S9,S4,367,S1,S5,378,37,S9,38,S4,S6,S1,S5,S2,36,S5,S4,S9,S2,
S1,36,S7,S8,368,S2,S1,S5,38,S7,S4,36,S9,39,S8,S6,S4,S7,39,S5,S2,S1,S5,379,S2,S1,S6,39,S8,S4,37,S4,S1,37,S2,S5,S8,S9,36,367,"  1r Franken SF 1s

Type 2:
......8.6.9...1.4...3.6.......4...1...8.2.6...5...7.......8.2...1.5...9.5.7......  1c Franken swordfish 3s
7...2......1..9.6..8.4..2....6....5.9.......1.3....7....2..6.9..4.7..8......3...6  1c Franken swordfish 5s
..1.2.3...4.5.6.1.7...1...6.8.....7.1.7...8.5.2.....6.2...5...4.5.1.2.8...9.6.5..  1c Franken swordfish 3s, then jellyfish
.....7..9....3.45...6....31....2.....5.8.16..1...6..84.7..4.9...98..2...3.5..9...  1c Franken swordfish 2s

"5,7,S1,S2,8,69,3,4,69,29,S3,289,79,1679,S4,S5,189,1269,S6,289,4,3,5,19,89,S7,129,S7,19,5,S6,3,8,19,S2,4,8,1269,3,4,1279,1279,67,5,19,129,
S4,269,79,1279,S5,67,3,S8,4,S5,269,8,2679,2679,129,19,S3,3,289,S7,S1,4,29,289,S6,5,129,1269,2689,5,269,S3,S4,89,7,"  1c Franken swordfish 8s, the 9s

"S8,S4,2567,256,256,S9,S3,57,S1,15679,35679,56,S4,S8,1356,S2,579,679,1569,3569,256,1256,S7,12356,5689,S4,689,2567,567,S1,2569,2569,S4,5789,
25789,S3,S4,S8,S3,1259,1259,S7,159,S6,29,2567,567,S9,S3,1256,S8,157,1257,S4,569,569,4568,S7,124569,1256,1689,S3,2689,S3,S1,467,S8,2469,26,679,
279,S5,5679,S2,568,1569,S3,156,S4,189,6789,"  1c Franken SF 7s

"23,S1,S5,27,S6,S9,38,278,S4,234,S6,S9,S8,47,S5,37,27,S1,S8,247,27,23,234,S1,S5,S9,S6,56,257,S3,S1,27,S4,S9,567,S8,24,S9,S8,S6,S5,237,S1,47,
37,S1,457,67,S9,378,378,S2,4567,357,56,S8,26,357,S9,37,S4,S1,257,S9,25,S1,S4,78,S6,78,S3,25,S7,S3,S4,25,S1,28,S6,58,S9,"  1c Franken swordfish 2s

Type 3:
.5.....7.2.......6...456.....7.3.4....65.12....9.7.1.....812...9.......5.1.....2.  2r Franken swordfish 8s
 
"7,S9,13,S8,6,2,S5,14,134,S6,18,5,S3,7,4,S2,9,18,S4,28,238,S5,1,9,38,S7,S6,15,7,S9,16,S2,3,146,S8,145,12,S6,4,S9,5,S8,7,S3,12,1258,S3,128,16,S4,
7,S9,126,125,S3,S5,28,24,9,S1,468,246,S7,128,1248,S6,7,38,S5,1348,124,S9,9,1248,S7,24,38,S6,1348,S5,2348," Franken swordfish 1s: Leren solution 9/6/16

"1469,149,469,S5,23,2348,148,248,S7,S3,S8,45,124,12,S7,S9,245,S6,S2,145,7,468,S9,468,1458,458,3,14789,1459,3,1268,1256,12568,4568,456789,489,
48,S6,S2,S9,7,58,458,3,S1,1789,159,59,S3,S4,1568,S2,56789,89,S5,3,S1,246,26,2469,S7,489,2489,49,S7,S8,12,1235,1235,46,469,25,469,2,469,7,S8,459,
S3,S1,459,"   2r Franken swordfish 4s

"129,1249,S6,S3,S5,19,12489,128,S7,S8,1259,1259,S4,S7,169,129,123,1369,179,S3,47,1689,S2,1689,149,S5,169,S3,S7,1259,129,S8,1259,S6,12,S4,126,
126,S8,S7,S3,S4,125,S9,15,S4,1259,1259,126,19,12569,S3,S7,S8,129,1249,34,28,S6,S7,1589,138,1359,12679,1269,37,S5,19,28,189,S4,139,S5,S8,19,19,
S4,S3,S7,S6,S2,"   2r Franken swordfish 9s

"S7,19,19,S2,3,58,4,6,58,4,S3,58,6,S9,578,78,S1,2,58,2,S6,178,17,S4,35789,79,37,S1,789,35789,3789,4,789,S6,2,357,6,S4,379,1379,S5,2,137,S8,137,
358,78,S2,1378,6,178,1357,4,S9,9,6,178,S4,17,3,S2,5,18,2,S5,4,179,S8,179,17,S3,6,38,178,1378,5,2,S6,1789,79,S4,"   2r Franken swordfish 7s

Type 4:

"4,389,589,26,368,238,S7,S1,3568,7,138,158,4,368,S9,356,S2,3568,38,S6,2,S5,S7,S1,4,38,S9,S5,19,6,27,19,27,S8,34,34,2,S7,S3,S8,59,4,56,569,1,
89,S4,189,S3,159,6,S2,59,S7,S1,S5,S4,67,S2,37,S9,368,368,36,2,S7,9,368,38,S1,45,45,3689,389,89,1,S4,S5,36,7,2,"   2c Franken SF 3s

"1249,489,149,S3,268,79,246,2478,S5,25,S7,3,1,2568,458,26,S9,48,2459,4589,S6,24,258,79,S1,2478,3,145,456,14,S9,258,458,3,1246,7,S7,S2,8,46,3,S1,
S5,46,9,3,4569,149,26,S7,45,S8,12,24,49,49,S5,S8,1,S2,7,S3,S6,S8,3,27,57,9,S6,24,245,S1,6,S1,27,57,S4,3,9,258,28,"   2c Franken SF 4s

"8,467,1345,39,49,134,37,3567,2,3457,347,1345,2,6,134,8,357,9,236,236,9,5,8,7,4,36,1,346,346,2,1,457,3468,9,378,3457,3469,5,8,369,479,346,2,1,
347,349,1,7,389,459,2,6,38,345,37,8,6,4,1,9,5,2,37,2457,2479,45,78,3,58,1,49,6,1,3479,345,67,2,56,37,49,8,"  2c Franken SF 3s

"58,S1,S2,9,4,568,3,68,7,S3,9,S4,7,268,268,S5,1268,168,S6,S7,58,S1,258,3,9,28,4,9,4,S6,S5,27,127,S8,3,12,1258,25,1578,4,S3,1268,267,156,S9,1258,
3,1578,28,268,S9,267,S4,156,4,S8,3,S6,257,257,S1,9,25,7,56,9,28,1,S4,26,568,S3,125,256,15,3,S9,58,4,S7,568,"  2c Franken SF 2s 

"89,S1,S2,689,S3,69,7,45,45,S4,39,S5,1789,19,789,S6,38,2,S6,S7,38,S2,5,4,19,19,38,1,39,S6,S4,2,38,S5,89,7,S2,4,7,189,19,S5,389,S6,38,389,5,389,69,
S7,369,4,2,S1,579,S8,19,S3,4,79,S2,15,6,359,6,1349,59,S8,2,13,S7,45,357,2,34,57,6,S1,38,3458,S9,"  2c Franken SF 9s

Mutant Swordfish

A simple (unfinned) mutant swordfish has a digit confined to a row or column and two boxes. This section is added out of interest only, since the pattern is duplicated by continuous grouped x-cycles. Also it is hard to find one where a simple swordfish doesn't give the same eliminations. The following illustrate the basic patterns, with each having a corresponding column based puzzle. The blue boxes define the pattern, noting that not all the blue boxes have to have a pattern digit: (purple areas = no pattern digits, Xs = possible eliminations)

     

The following puzzles, which occur very commonly, have the mutant pattern which is displayed if the "Mutant SF" button is clicked first. However, if the "Swordfish" button is chosen first, then a simple swordfish is found with same eliminations:

1..2......3..4.5....6..7.1.4..8...3..7..3...2..9...6...2...57....14.........6...3
12.......3..4..1....5.3..6..6..7..8...78..5.......2..1.9..4..5...86..9.......3..2
..12...3.4...3...5.6....4..2..7.1....1..2..8....5.6..2..7....6.8...5...3.4...72..

This is a column based example which doesn't have a swordfish claiming the same eliminations, but has a jellyfish which does:

1.........2.345.....5...4...6.7...3..8..1..5..1...9.4...7...5.....283.6.........8

The following example, given in the "Sudoku Snake" website, is the only example I've come accross so far which has no other swordfish/jellyfish duplicating it's eliminations:

...3.9.7.8..4.....1........2..5..6...3.....4.....1....5.....8......2.1.....7....9