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I propose this Sudoku-X puzzle to be solved manually.
(generated and displayed with Sudoku6Explainer)
+-------+-------+
| . . . | 6 . . |
| . . . | . . 1 |
+-------+-------+
| . . . | . . 6 |
| . . . | . . 4 |
+-------+-------+
| . . . | . . 5 |
| . . . | 3 . . |
+-------+-------+ X
There is a nice solution without using pencilmarks.
I propose the following interesting Slitherlink puzzle.
(Source: Simon Tatham's Collection)
.---------------------------------------.
| . . . . . . . . . . |
9 | 2 2 1 2 3 |
| . . . . . . . . . . |
8 | 1 1 3 2 |
| . . . . . . . . . . |
7 | 3 2 2 1 2 |
| . . . . . . . . . . |
6 | 3 2 3 1 2 |
| . . . . . . . . . . |
5 | 3 2 2 |
| . . . . . . . . . . |
4 | 3 1 3 |
| . . . . . . . . . . |
3 | 1 1 2 3 |
| . . . . . . . . . . |
2 | 2 0 1 |
| . . . . . . . . . . |
1 | 2 1 1 1 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i Slitherlink
Update 1 (July 15, 2026)
Two natural places for starting moves:
the three "3" in diagonal and the "0" cell
with "1s" below
.---------------------------------------.
| . . . . . . . . . . |
9 | 2 2 1 2 3 |
| . . x . . . . . . . . |
8 | 1 x 1 3 2 |
| .___. . . . . . . . . |
7 | | 3 2 2 1 2 |
| .___.___. . . . . . . . |
6 | 3 | 2 3 1 2 |
| .___.___. . . . . . . . |
5 | | 3 2 2 |
| .___. . . . . . . . . |
4 | 3 1 3 |
| . . . . . . . . . . |
3 | 1 1 2 | 3 |
| . . . .___. . . . . . |
2 | | 2 0 1 |
| . . .___. x . x . x . . . . |
1 | 2 1 x 1 x 1 |
| . . .___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
How many moves can be found directly ?
Update 2 (July 17, 2026)
For me, basic moves stops at move 37.
After the 18 moves above, the following
observations were used:
. line (3t)a7 has to go up [2 placements]
. (2r)b1 impossible [1 placement]
. (2r)d3 and (2b)b3 imply 22.(3r)c4, 23.(3b)c4,
and 24.( b)e4
. We cannot have (1t)b3 (quick contradiction) [9 placements]
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 1 2 3 |
| . . . . . . . . . . |
8 | | 1 1 3 2 |
| .___. . . . . . . . . |
7 | | 3 2 2 1 2 |
| .___.___. . . . . . . . |
6 | 3 | 2 3 1 2 |
| .___.___. . . . . . . . |
5 | | 3 | 2 2 |
| .___.___. . . . . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. . . . . |
3 | 1 1 2 | 3 |
| .___.___. .___. . . . . . |
2 | | | | 2 0 1 |
| .___. .___. . . . . . . |
1 | | 2 1 1 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
. Line arriving at cell (2)d6 must continue
and reach lower-left corner of (3)f8, so
34.(3t)f8, 35.(3r)f8. Two more placements
are available.
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 1 2 3 |
| . . . . . .___. . . . |
8 | | 1 1 3 | 2 |
| .___. . . . . . . . . |
7 | | 3 2 2 1 2 |
| .___.___. . . . . . . . |
6 | 3 | 2 3 1 2 |
| .___.___. . . . . . . . |
5 | | 3 | 2 2 |
| .___.___. . . . . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. . . . . |
3 | 1 1 2 | 3 |
| .___.___. .___. . . . . . |
2 | | | | 2 0 1 |
| .___. .___. . . . . . . |
1 | | 2 1 1 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
How to continue ?
Update 3 (July 19, 2026)
After 36.(3t)g3, 37.(3r)g3 [due to x at (1l)f2, (1b)f2]
we get the position
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 1 2 3 |
| . . . . . .___. . . . |
8 | | 1 1 3 | 2 |
| .___. . . . . . . . . |
7 | | 3 2 2 1 2 |
| .___.___. . . . . . . . |
6 | 3 | 2 3 1 2 |
| .___.___. . . . . . . . |
5 | | 3 | 2 2 |
| .___.___. . . . . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. .___. . . |
3 | 1 1 2 | 3 | |
| .___.___. .___. . . . . . |
2 | | | | 2 0 x 1 |
| .___. .___. . x . x . . . . |
1 | | 2 1 1 x 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
Step 1: (2l)b9 leads to contradiction at (2)f9,
.---------------------------------------.
| . .___.___. x . x . x . . . . |
9 | |?2 2 | 1 x x 2 contr 3 |
| . . . x . x . x .___. . . . |
8 | | 1 x | x 1 3 | 2 |
| .___. . . . . . . . . |
7 | | 3 2 2 1 2 |
| .___.___. . . . . . . . |
6 | 3 | 2 3 1 2 |
| .___.___. . . . . . . . |
5 | | 3 | 2 2 |
| .___.___. . . . . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. .___. . . |
3 | 1 1 2 | 3 | |
| .___.___. .___. . . . . . |
2 | | | | 2 0 x 1 |
| .___. .___. . x . x . . . . |
1 | | 2 1 1 x 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
so 38.( b)a9! and 4 additional placements.
.---------------------------------------.
| .___.___. . . . . . . . |
9 | | 2 | 2 1 2 3 |
| .___. .___. . .___. . . . |
8 | | 1 1 3 | 2 |
| .___. . . . . . . . . |
7 | | 3 2 2 1 2 |
| .___.___. . . . . . . . |
6 | 3 | 2 3 1 2 |
| .___.___. . . . . . . . |
5 | | 3 | 2 2 |
| .___.___. . . . . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. .___. . . |
3 | 1 1 2 | 3 | |
| .___.___. .___. . . . . . |
2 | | | | 2 0 1 |
| .___. .___. . . . . . . |
1 | | 2 1 1 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
How to make progress now ?
Update 4 (July 20, 2026)
Step 2: (1b)d9 leads to 3 lines in a
closed region (see below)
.---------------------------------------.
| .___.___. . x . . . . . . |
9 | | 2 | 2 x 1 2 3 |
| .___. .___._?_. .___. x . . . |
8 | | 1 1 x 3 | 2 |
| .___. . . . x .___. x . . . |
7 | | 3 | 2 | 2 x 1 2 |
| .___.___. . . x . x .___. . . |
6 | 3 | 2 | 3 | 1 2 |
| .___.___. . . .___. . . . |
5 | | 3 | 2 2 |
| .___.___. . . . . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. .___. . . |
3 | 1 1 2 | 3 | |
| .___.___. .___. . . . . . |
2 | | | | 2 0 1 |
| .___. .___. . . . . . . |
1 | | 2 1 1 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
So: 43.(1r)d9! with 10 additional placements.
We get the following
.---------------------------------------.
| .___.___. . .___. . . . . |
9 | | 2 | 2 1 | 2 x 3 |
| .___. .___. . .___. . . . |
8 | | 1 | 1 3 | 2 | |
| .___. . . . .___. . . . |
7 | | 3 | 2 | 2 1 x 2 |
| .___.___. . . . .___. x . . |
6 | 3 | 2 | 3 | 1 2 |
| .___.___. . . .___. . . . |
5 | | 3 | 2 2 |
| .___.___. . . . . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. .___. . . |
3 | 1 1 2 | 3 | |
| .___.___. .___. . . . . . |
2 | | | | 2 0 1 |
| .___. .___. . . . . . . |
1 | | 2 1 1 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
Now, how to proceed ?
Update 5 (July 21, 2026)
Step 3: We have the meeting of lines ( l)d5,
(r)d8, (2l)e7, (1r)d9. One must avoid
( b)e9, since it originates a loop
connecting ( l)d5 to ( r)c8. So
54.(1l)e8! with 10 additional placements.
All this leads to
.---------------------------------------.
| .___.___. . .___. . .___. . x
9 | | 2 | 2 1 | | 2 | 3 | |
| .___. .___. . .___. . . . |
8 | | 1 | | 1 3 | 2 | |
| .___. . . . .___. . . . |
7 | | 3 | | 2 | 2 | 1 2 |
| .___.___. .___. . .___. . . |
6 | 3 | 2 | 3 | 1 2 |
| .___.___. .___. .___. . . . |
5 | | 3 | | 2 2 |
| .___.___. . .___. . . . . |
4 | | 3 | 1 3 |
| . . .___. .___. .___. . . |
3 | 1 1 2 | 3 | |
| .___.___. .___. . . . . . |
2 | | | | 2 0 1 |
| .___. .___. . . . . . . |
1 | | 2 1 1 1 |
| . .___.___.___.___.___.___. . . |
'---------------------------------------'
a b c d e f g h i SL
One more inference is enough to solve the
puzzle with simple forced moves (singles).
Update 6 (July 22, 2026)
(1r)h6 leads quickly to trouble at (3)i4.
So 65.(1b)h6! and the remaining moves are easy.
The final configuration after 88 moves is
.---------------------------------------.
| .___.___. . .___. . .___. . |
9 | | 2 | 2 1 | | 2 | 3 | |
| .___. .___. . .___. . . . |
8 | | 1 | | 1 3 | 2 | | |
| .___. . . . .___. . .___. |
7 | | 3 | | 2 | 2 | 1 2 | |
| .___.___. .___. . .___. . . |
6 | 3 | 2 | 3 | 1 2 | |
| .___.___. .___. .___. .___.___. |
5 | | 3 | | | 2 2 |
| .___.___. . .___. .___. .___. |
4 | | 3 | 1 | | | 3 | |
| . . .___. .___. .___. . . |
3 | 1 1 2 | 3 | | | |
| .___.___. .___. . .___. . . |
2 | | | | 2 0 1 | | | |
| .___. .___. . . .___.___. . |
1 | | 2 1 1 1 | |
| . .___.___.___.___.___.___.___.___. |
'---------------------------------------'
a b c d e f g h i SL
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com