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Before moving on (other types of puzzles),
I propose this interesting Slitherlink puzzle.
(Source: Simon Tatham's Collection)
.---------------------------------------.
| . . . . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | 3 2 2 3 2 2 |
| . . . . . . . . . . |
7 | 2 2 2 |
| . . . . . . . . . . |
6 | 3 1 3 2 3 2 |
| . . . . . . . . . . |
5 | 1 1 1 |
| . . . . . . . . . . |
4 | 3 2 1 |
| . . . . . . . . . . |
3 | 1 1 2 2 |
| . . . . . . . . . . |
2 | 3 3 2 1 |
| . . . . . . . . . . |
1 | 2 2 2 2 3 2 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i Slitherlink
Update 1 (June 02, 2026)
Step 1 (part of it): after 26 basic moves
[includes 2-2-2 and 3-3 in a diagonal,
and 2 at corners, and consequences]
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | | 3 2 2 3 2 2 |
| . . . . . . . . . . |
7 | 2 2 2 |
| . . . . . . . . . . |
6 | 3 1 3 2 3 | 2 |
| . . . . . .___. . . . |
5 | 1 1 1 |
| .___. . . . . . . . . |
4 | | 3 | 2 1 |
| . x .___. x . . . . . . . |
3 | | 1 x 1 x 2 2 | |
| . .___. . .___. . . . . |
2 | | | 3 | 3 2 1 | |
| . .___. . . . . . . . |
1 | | 2 2 2 2 3 | | 2 | |
| .___.___. . . .___. .___.___. |
'---------------------------------------'
a b c d e f g h i
Update 2 (June 3, 2026) More basics moves:
After 30 moves [total of 44 basic moves]
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | | 3 2 2 3 2 2 |
| . . . . . . . . . . |
7 | | 2 2 2 |
| . . x . . . . . . . . |
6 | | 3 1 x 3 2 3 | 2 |
| .___. . . . .___. x . . . |
5 | 1 1 x 1 |
| .___. . . . . . . . . |
4 | | 3 | 2 1 |
| . .___. x . . . . . . . |
3 | | 1 1 x x 2 2 | |
| . .___. . x .___. . . . . |
2 | | | 3 | 3 2 | 1 | |
| . .___. . . . . . . . |
1 | | 2 2 2 2 3 | | 2 | |
| .___.___. . . .___. .___.___. |
'---------------------------------------'
a b c d e f g h i
Update 3 (June 04, 2026)
31.(2l)c4! [line to the left of cell (2)c4;
otherwise, a loop is formed!]
this gives 10 line placements to get at move 41:
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | | 3 2 2 3 2 2 |
| . . . . . . . . . . |
7 | | 2 2 2 |
| . . x . . . . . . . . |
6 | | 3 1 x 3 2 3 | 2 |
| .___. . . . .___. x . . . |
5 | 1 1 x 1 |
| .___. . . . . . . . . |
4 | | 3 | | 2 1 |
| . .___. . .___. . . . . |
3 | | 1 1 2 2 | |
| . .___.___. .___.___. . . . |
2 | | | 3 | | 3 2 | 1 | |
| . .___. . .___.___. . . . |
1 | | 2 | 2 | 2 2 3 | | 2 | |
| .___.___. .___.___.___. x .___.___. |
'---------------------------------------'
a b c d e f g h i
42.( t)d4! 43.(3l)d6 44.(3b)d6
and the situation after all these basics is
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | | 3 2 2 3 2 2 |
| . . . . . . . . . . |
7 | | 2 2 2 |
| . . x . . . . . . . . |
6 | | 3 1 x | 3 2 3 | 2 |
| .___. . x .___. .___. x . . . |
5 | 1 x 1 x 1 |
| .___. . .___. . . . . . |
4 | | 3 | | 2 1 |
| . .___. . .___. . . . . |
3 | | 1 1 2 2 | |
| . .___.___. .___.___. . . . |
2 | | | 3 | | 3 2 | 1 | |
| . .___. . .___.___. . . . |
1 | | 2 | 2 | 2 2 3 | | 2 | |
| .___.___. .___.___.___. .___.___. |
'---------------------------------------'
a b c d e f g h i
How to advance now ?
Update 4 (June 6, 2026)
Step 2: The line ( t)d4 to the right, has 3 possible
places to go:
. ( r)d5 is impossible because of the 2-2 diagonal
e6-f7 effect that leaves cell (3)g8 without lines
at (3l)g8, (3b)g8 [figure below]
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | | 3 2 2 x 3 2 2 | ... impossible
| . . . . . .___. x . . . |
7 | | 2 2 | 2 |
| . . x . . .___. . . . . |
6 | | 3 1 x | 3 x 2 | 3 | 2 |
| .___. . x .___. x .___. x . . . |
5 | 1 x ?| 1 x 1 |
| .___. . .___. . . . . . |
a b c d e f g h i
. ( r)d4 implies [thanks to x at (1b)e5,(1l)e5]
(3t)f6! [forbidding (2l)g7,(2b)g7
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | | 3 2 2 3 2 2 |
| . . . . . . . . . . |
7 | | 2 2 x 2 |
| . . x . . . .___. x . . . |
6 | | 3 1 x | 3 2 3 | 2 |
| .___. . x .___. .___. x . . . |
5 | 1 x x 1 x 1 |
| .___. . .___. x . . . . . |
4 | | 3 | | 2 | 1 |
| . .___. . .___. . . . . |
3 | | 1 1 2 2 | |
| . .___.___. .___.___. . . . |
2 | | | 3 | | 3 2 | 1 | |
| . .___. . .___.___. . . . |
1 | | 2 | 2 | 2 2 3 | | 2 | |
| .___.___. .___.___.___. .___.___. |
'---------------------------------------'
a b c d e f g h i
However, the line (3b)d6, x at (1l)e5
implies that a line must leave the top-right
corner of (2)g7, and so (3t)g8, (3r)h8,
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . .___. . . |
8 | | 3 2 2 3 | 2 2 |
| . . . . . . . . . . |
7 | | 2 2 x 2 |
| . . x . . . .___. x . . . |
6 | | 3 1 x | 3 2 3 | 2 |
| .___. . x .___. .___. x . . . |
5 | 1 x x 1 x 1 |
| .___. . .___. x . . . . . |
4 | | 3 | | 2 | 1 |
| . .___. . .___. . . . . |
3 | | 1 1 2 2 | |
| . .___.___. .___.___. . . . |
2 | | | 3 | | 3 2 | 1 | |
| . .___. . .___.___. . . . |
1 | | 2 | 2 | 2 2 3 | | 2 | |
| .___.___. .___.___.___. .___.___. |
'---------------------------------------'
a b c d e f g h i
which contradicts the need of lines
(2t)g7, (2r)g7
So, 45. (1b)e5!! and now it is easy to advance
up to (at least) move 65, reaching
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . . . . . . . . . |
8 | | 3 2 2 3 2 2 |
| .___. . . . . . . . . |
7 | | | 2 | 2 2 |
| .___. . . . . . . . . |
6 | | 3 1 | 3 | 2 | 3 | 2 |
| .___.___. .___. .___. . . . |
5 | | 1 1 1 | |
| .___. . .___.___.___.___.___. . |
4 | | 3 | | 2 | 1 | | |
| . .___. .___.___.___. . . . |
3 | | 1 1 2 | | 2 | |
| . .___.___. .___.___. .___. . |
2 | | | 3 | | 3 2 | 1 | |
| . .___. . .___.___. . . . |
1 | | 2 | 2 | 2 2 3 | | 2 | |
| .___.___. .___.___.___. .___.___. |
'---------------------------------------'
a b c d e f g h i
How to continue from here ?
Upate 5 (June 7, 2026)
Step 3: ( l)d7 forces an impossible loop or
a line without place to go. In detail:
(3l)d8, (3t)c8 are forced
.---------------------------------------.
| . .___. . . . . . . . |
9 | 2 2 2 3 1 |
| . . .___. . . . . . . |
8 | | | 3 2 2 3 2 2 |
| .___. . . . . . . . . |
7 | | |? | 2 | 2 2 |
| .___. . . . . . . . . |
6 | | 3 1 | 3 | 2 | 3 | 2 |
| .___.___. .___. .___. . . . |
a b c d e f g h i
and now (3b)c8 gives a forced loop and
(3r)c8 gives a line without place to go. So,
66.( b)c7!!
and in all the remaining moves we have
only a few easy deductions to make.
The final configuration on move 94 is
.---------------------------------------.
| .___.___. . .___. . . .___. |
9 | | 2 2 | 2 | 3 | 1 | | |
| . . .___. . . .___. . . |
8 | | 3 | 2 | 2 | | 3 | 2 | 2 | |
| .___. .___. . . . . . . |
7 | | | | 2 | 2 | 2 | | | |
| .___. .___. . . . . . . |
6 | | 3 1 | 3 | 2 | 3 | 2 | | | |
| .___.___. .___. .___. .___. . |
5 | | 1 1 1 | |
| .___. . .___.___.___.___.___. . |
4 | | 3 | | 2 | 1 | | |
| . .___. .___.___.___. . . . |
3 | | 1 1 2 | | 2 | |
| . .___.___. .___.___. .___. . |
2 | | | 3 | | 3 2 | 1 | |
| . .___. . .___.___. . . . |
1 | | 2 | 2 | 2 2 3 | | 2 | |
| .___.___. .___.___.___. .___.___. |
'---------------------------------------'
a b c d e f g h i
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com