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The following Sudoku-X puzzle can be solved quickly.
(generated and displayed with Sudoku9Explainer)
+----------------------+----------------------+----------------------+
| 3 19 2 | 567 4 567 | 56 8 19 |
| 1468 489 5 | 689 2 689 | 16 7 3 |
| 68 7 69 | 35689 1 35689 | 2 4 569 |
+----------------------+----------------------+----------------------+
| 2 34589 3469 | 469 69 3489 | 134568 1356 7 |
| 7 348 1 | 346 5 2 | 9 36 468 |
| 4568 34589 3469 | 3489 7 1 | 34568 356 2 |
+----------------------+----------------------+----------------------+
| 145 1345 34 | 2 8 469 | 7 169 146 |
| 9 6 8 | 1457 3 457 | 145 2 145 |
| 14 2 7 | 14569 69 4569 | 134568 13569 468 |
+----------------------+----------------------+----------------------+ Sudoku-X
Update (Nov 15, 2025)
+----------------------+----------------------+----------------------+
| 3 1-9 2 | 567 4 567 | 56 8 19 | 9
| 1468 489 5 | 689 2 689 | 16 7 3 | 8
| 68 7 69 | 35689 1 35689 | 2 4 569 | 7
+----------------------+----------------------+----------------------+
| 2 34589 3469 | 469 69 3489 | 134568 1356 7 | 6
| 7 348 1 | 346 5 2 | 9 36 468 | 5
| 4568 34589 3469 | 3489 7 1 | 34568 356 2 | 4
+----------------------+----------------------+----------------------+
| 145 1345 34 | 2 8 469 | 7 169 146 | 3
| 9 6 8 | 1457 3 457 | 145 2 145 | 2
| 14 2 7 | 14569 69 4569 | 134568 13569 468 | 1
+----------------------+----------------------+----------------------+
a b c d e f g h i Sudoku_X
The one-stepper (pretty!) eliminates (9)b8 solving the puzzle with lclste.
Update (Nov 16, 2025)
+----------------------+----------------------+----------------------+
| 3 1-9 2 | 567 4 567 | 56 8 *19 | 9
| 1468 (489) 5 | 689 2 689 | 16 7 3 | 8
|(68) 7 (69) | 35689 1 35689 | 2 4 569 | 7
+----------------------+----------------------+----------------------+
| 2 34589 3469 |(469) (69) *3489 | 134568 1356 7 | 6
| 7 348 1 | 346 5 2 | 9 36 468 | 5
| 4568 34589 3469 |*3489 7 1 | 34568 356 2 | 4
+----------------------+----------------------+----------------------+
| 145 1345 34 | 2 8 469 | 7 169 146 | 3
| 9 6 8 | 1457 3 457 | 145 2 145 | 2
| 14 2 7 | 14569 69 4569 | 134568 13569 468 | 1
+----------------------+----------------------+----------------------+
a b c d e f g h i Sudoku_X
The move previously described is ALS-xz with transport with
ALS1:(9684)a6.b8.c6, ALS2:(469)d6.e6
I propose the following interesting (many patterns!) Sudoku-X puzzle.
(generated and displayed with Sudoku9Explainer)
+-------+-------+-------+
| . . 3 | . . . | . . . |
| . . . | . . 8 | 9 . . |
| 7 . 9 | . . . | . 5 . |
+-------+-------+-------+
| . . . | . 1 . | 6 . . |
| . . . | 8 . 3 | . . . |
| . 1 . | . 5 . | . 2 . |
+-------+-------+-------+
| . 9 . | 3 . . | . . . |
| . . 8 | . . 4 | . . . |
| . . . | . . . | . . 6 |
+-------+-------+-------+ Sudoku_X
Update (Nov 19, 2025)
After basics
+----------------------+----------------------+----------------------+
| 18 248 3 | 124579 2479 125 | 247 6 12478 |
| 124 5 126 | 1247 23467 8 | 9 147 12347 |
| 7 2468 9 | 124 2346 126 | 12348 5 1234 |
+----------------------+----------------------+----------------------+
| 2358 2378 257 | 24 1 9 | 6 478 34578 |
| 259 267 2567 | 8 24 3 | 1457 1479 14579 |
| 389 1 4 | 6 5 7 | 38 2 389 |
+----------------------+----------------------+----------------------+
| 246 9 1257 | 3 2678 1256 | 18 1478 124578 |
| 126 27 8 | 12579 2679 4 | 1257 3 12579 |
| 12345 2347 127 | 12579 2789 125 | 124578 14789 6 |
+----------------------+----------------------+----------------------+ Sudoku_X
Update (Nov 20, 2025)
The first move eliminates (8)g4, (8)g1, (8)b9 and gives 18 placements!
+----------------------+----------------------+-----------------------+
| 18 24-8 3 | 124579 2479 125 | 247 6 12478 | 9
| 124 5 126 | 1247 23467 8 | 9 147 12347 | 8
| 7 2468 9 | 124 2346 126 | 12348 5 1234 | 7
+----------------------+----------------------+-----------------------+
| 2358 2378 257 | 24 1 9 | 6 478 34578 | 6
| 259 267 2567 | 8 24 3 | 1457 1479 14579 | 5
| 389 1 4 | 6 5 7 | 3-8 2 389 | 4
+----------------------+----------------------+-----------------------+
| 246 9 1257 | 3 2678 1256 | 18 1478 124578 | 3
| 126 27 8 | 12579 2679 4 | 1257 3 12579 | 2
| 12345 2347 127 | 12579 2789 125 | 12457-8 14789 6 | 1
+----------------------+----------------------+-----------------------+
a b c d e f g h i Sudoku_X
Update (Nov 21, 2025)
After all eliminations of the previous fish on 8, we get
+-------------------+-------------------+-------------------+
| 1 24 3 | 24579 2479 25 | 247 6 8 | 9
| 24 5 6 | 1247 2347 8 | 9 14-7 2347 | 8
| 7 8 9 | 124 2346 16 | 124 5 234 | 7
+-------------------+-------------------+-------------------+
| 5 3 27 | 24 1 9 | 6 8 47 | 6
| 9 6 27 | 8 24 3 | 1457 147 1457 | 5
| 8 1 4 | 6 5 7 | 3 2 9 | 4
+-------------------+-------------------+-------------------+
| 246 9 5 | 3 267 16 | 8 147 1247 | 3
| 26 27 8 | 12579 2679 4 | 1257 3 1257 | 2
| 3 247 1 | 257 8 25 | 2457 9 6 | 1
+-------------------+-------------------+-------------------+
a b c d e f g h i Sudoku_X
Now there is a powerful move to be found that removes (7)h8.
This move gives only one placement, but activates another fish.
Update (Nov 22, 2025)
After the placement due to the previous step, exploring the diagonal
a1-i9, that can be viewed as a kraken column, or almost ALS w-wing,
Either (4)h8,
OR
ALS W-wing (7=264)a23.b2 - (4)h3 '=' (4)h5 - (4=27)e5.b2
we get the folowing (with an x-wing (2) available):
+-------------------+--------------------+-------------------+
| 1 24 3 | 4579-2 479-2 25 | 47-2 6 8 | 9
| 24 5 6 | 1247 2347 8 | 9 14 2347 | 8
| 7 8 9 | 124 346 16 | 124 5 234 | 7
+-------------------+--------------------+-------------------+
| 5 3 27 | 24 1 9 | 6 8 47 | 6
| 9 6 27 | 8 24 3 | 1457 147 1457 | 5
| 8 1 4 | 6 5 7 | 3 2 9 | 4
+-------------------+--------------------+-------------------+
| 246 9 5 | 3 267 16 | 8 147 1247 | 3
| 26 7 8 | 1259 269 4 | 125 3 125 | 2
| 3 24 1 | 57-2 8 25 | 457-2 9 6 | 1
+-------------------+--------------------+-------------------+
a b c d e f g h i Sudoku_X
After those eliminations, a seemingly unimportant fish helps a lot!
Update (Nov 23, 2025)
+---------------+-----------------+----------------+
| 1 24 3 | 4579 479 25 | 47 6 8 | 9
| 24 5 6 | 124-7 2347 8 | 9 14 2347 | 8
| 7 8 9 | 124 346 16 | 124 5 234 | 7
+---------------+-----------------+----------------+
| 5 3 27 | 24 1 9 | 6 8 47 | 6
| 9 6 27 | 8 24 3 | 1457 147 1457 | 5
| 8 1 4 | 6 5 7 | 3 2 9 | 4
+---------------+-----------------+----------------+
| 246 9 5 | 3 267 16 | 8 147 1247 | 3
| 26 7 8 | 1259 269 4 | 125 3 125 | 2
| 3 24 1 | 57 8 25 | 457 9 6 | 1
+---------------+-----------------+----------------+
a b c d e f g h i Sudoku_X
A turbot fish on 7 eliminates (7)d8, turning on simultaneously
two naked triples at row 8 and at column d.
With these eliminations together with two other basic moves,
we get
+----------------+----------------+----------------+
| 1 24 3 | 579 479 25 | 47 6 8 | 9
| 24 5 6 | 124 37 8 | 9 14 37 | 8
| 7 8 9 | 14 34 6 | 124 5 234 | 7
+----------------+----------------+----------------+
| 5 3 27 | 24 1 9 | 6 8 47 | 6
| 9 6 27 | 8 24 3 | 1457 147 15 | 5
| 8 1 4 | 6 5 7 | 3 2 9 | 4
+----------------+----------------+----------------+
| 246 9 5 | 3 267 1 | 8 47 247 | 3
| 26 7 8 | 59 269 4 | 125 3 15 | 2
| 3 24 1 | 57 8 25 | 457 9 6 | 1
+----------------+----------------+----------------+
a b c d e f g h i Sudoku_X
The end is near. How to finish the puzzle ?
Update (Nov 24, 2025)
Now, an XYZ-wing elimination gives 4 placements, and
among them (7)g9 is the key to finish the puzzle in
the next move.
Update (Nov 27, 2025)
+-------------+-------------+-------------+
| 1 24 3 | 59 49 25 | 7 6 8 | 9
| 24 5 6 | 124 7 8 | 9 14 3 | 8
| 7 8 9 | 14 3 6 | 124 5 24 | 7
+-------------+-------------+-------------+
| 5 3 27 | 24 1 9 | 6 8 47 | 6
| 9 6 27 | 8 24 3 | 145 147 15 | 5
| 8 1 4 | 6 5 7 | 3 2 9 | 4
+-------------+-------------+-------------+
| 246 9 5 | 3 26 1 | 8 47 247 | 3
| 26 7 8 | 59 269 4 | 125 3 15 | 2
| 3 24 1 | 7 8 25 | 45 9 6 | 1
+-------------+-------------+-------------+
a b c d e f g h i Sudoku_X
Now we can finish the puzzle if we can show that (2)g2 is true.
How can we prove that using a uniqueness argument ?
Update (Nov 28, 2025)
+-------------+-------------+--------------+
| 1 24 3 | 59 49 25 | 7 6 8 | 9
| 24 5 6 | 124 7 8 | 9 14 3 | 8
| 7 8 9 | 14 3 6 | 124 5 24 | 7
+-------------+-------------+--------------+
| 5 3 27 | 24 1 9 | 6 8 47 | 6
| 9 6 27 | 8 24 3 | 145 147 15 | 5
| 8 1 4 | 6 5 7 | 3 2 9 | 4
+-------------+-------------+--------------+
| 246 9 5 | 3 26 1 | 8 47 247 | 3
| 26 7 8 | 59 269 4 |(125) 3 (15) | 2
| 3 24 1 | 7 8 25 |(45) 9 6 | 1
+-------------+-------------+--------------+
a b c d e f g h i Sudoku_X
The ALS (1245)g12.i2 interacts with the UR (15)g25,i25:
UR
(2=154)g12.i2 - (4)g5 ==== (2)g2 => +2 g2; ste