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This is a place chosen to make available some ideas (on puzzles, patterns, etc)
that seemed unsuitable for posting in a Forum, but some people may find interesting.
For difficult puzzles (like the next one), possible solutions will not be shown (only hints).
For other puzzles, the solution wil be hidden so that a serious attempt can be made
without direct access to a solution.
(hopefully this will make the puzzles more interesting for newcomers).
I propose this interesting and hard Slitherlink puzzle.
(puzzle from Simon Tatham's Collection)
.-----------------------------------.
| . . . . . . . . . |
| 2 2 3 | 8
| . . . . . . . . . |
| 2 2 2 2 | 7
| . . . . . . . . . |
| 2 2 3 3 3 | 6
| . . . . . . . . . |
| 3 | 5
| . . . . . . . . . |
| 3 2 2 2 0 1 | 4
| . . . . . . . . . |
| 1 3 1 | 3
| . . . . . . . . . |
| 2 2 | 2
| . . . . . . . . . |
| 3 2 1 3 | 1
| . . . . . . . . . |
'-----------------------------------'
a b c d e f g h
Update (Nov 24, 2025)
We have many basic moves at the start.
Most of them are in the following grid
.-----------------------------------.
| . .___. . . .___.___.___. |
| 2 2 3 | | 8
| . . . . . . .___.___. |
| | 2 2 2 2 | 7
| . . . . . . . .___. |
| 2 2 3 3 3 | | 6
| . . . . . . . . . |
| |3 | 5
| . . . . . . .___. . |
| 3 2 2 2 0 1 | 4
| . . . . . .___. . . |
| 1 | 3 1 | 3
| . . . . . . . . . |
| 2 2 | 2
| . . . . . . . . . |
| | 3 2 1 3 | | 1
| .___. . . . . . .___. |
'-----------------------------------'
a b c d e f g h
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.
In the game called Slitherlink, can you show all the details
proving that the following configuration is impossible ?
(My solution has a trivial initial observation, an easy Case 1 and Case 2 divided in two sub-cases)
We analyze the possible outcomes from this configuration but can already discard
all configurations in which the lower "2"-cell has vertical lines, or horizontal lines,
in both edges.
Also, this configuration
.------------------- | . . . . . | 2 | . . . . . | 2 | .___. . . . | | 2 |A. . . . . | x | . . . . .
and this
.------------------- | . . . . . | 2 | . . . . . | 2 | . . . . . | 2 | |A.___. . . . | x | . . . . .
are clearly impossible,
(dead end at corner A).
Case 1:
.-------------------
| . . . . .
| 2
| . . . . .
| 2
| .___. . . .
| 2 |
| . . . . .
| x
| . . . . .
Now the following is forced
.-------------------
| . .___.___. .
| x 2 |
| . .___. x . .
| | x 2 |
| .___. x . . .
| 2 |
| . . . . .
| x
| . . . . .
and this leads to an impossibility in the cell at the corner, reached by three lines.
.------------------- | . . . . . | 2 | . . . . . | 2 | . . . . . | | 2 | .___. . . . | x | . . . . .
The following is a forced move
.------------------- | . . . . . | 2 | . .B . . . | | 2 | . x .A . . . | | 2 x | .___. . . . | x | . . . . .
Case 2.1: If a vertical line exists at AB, it forces
.------------------- | . . . . . | | 2 | .C . . . . | | | 2 | . x .___.D . . | | 2 x | .___. . . . | x | . . . . .
and any continuation for the line meeting corner C will create a loop (impossible).
Case 2.2: the other possibility is to have the edge AB blocked, and then the bottom edge AD
of the "2"-cell in the middle needs to be blocked too, forcing the following configuration to be reached.
.------------------- | . .___.___. . | x 2 | | . .___. x . . | | x 2 | | . x . x . . . | | 2 x | .___. . . . | x | . . . . .
Now, we have an impossible situation in the cell at the corner, reached by three lines. □
The following Jigsaw Sudoku Layout is invalid. Why ?
(image created using SudokuExplainer)
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com