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I propose the following (tough) Slitherlink puzzle.
(Source: Simon Tatham's Collection)
.---------------------------------------.
| . . . . . . . . . . |
9 | 3 2 3 1 1 2 |
| . . . . . . . . . . |
8 | 2 2 3 |
| . . . . . . . . . . |
7 | 2 1 |
| . . . . . . . . . . |
6 | 3 3 1 |
| . . . . . . . . . . |
5 | 1 2 2 |
| . . . . . . . . . . |
4 | 2 3 3 2 1 |
| . . . . . . . . . . |
3 | 3 3 2 2 |
| . . . . . . . . . . |
2 | 2 1 3 1 3 |
| . . . . . . . . . . |
1 | 1 3 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i Slitherlink
Update 1 (Oct 28, 2026)
After (23) basic moves, we get
.---------------------------------------.
| .___. . . . . . . . . |
9 | | 3 2 3 1 1 2 |
| . . . . . . . . . . |
8 | 2 2 3 |
| . . . . . .___. . . . |
7 | 2 | 1 |
| . . .___. .___. . . . . |
6 | | 3 | 3 | 1 |
| . .___. .___. . . . . . |
5 | 1 2 2 |
| . . .___. .___. . . . . |
4 | 2 | 3 | | 3 | 2 1 |
| . . . . . . . . . . |
3 | 3 | 3 | 2 2 |
| . . . .___. . . . . . |
2 | 2 1 3 1 3 |
| . . . .___. . . . . . |
1 | 1 3 | |
| . . . . .___. . . . . |
'---------------------------------------'
a b c d e f g h i Slitherlink
How to continue ?
Update 2 (Oct 30, 2026)
Looking at (3)a3 and (2)b4, we see that
we cannot have both (3t)a3, (3r)a3, so
24.(3l)a3 25.(3b)a3
.---------------------------------------.
| .___. . . . . . . . . |
9 | | 3 2 3 1 1 2 |
| . . . . . . . . . . |
8 | 2 2 3 |
| . . . . . .___. . . . |
7 | 2 | 1 |
| . . .___. .___. . . . . |
6 | | 3 | 3 | 1 |
| . .___. .___. . . . . . |
5 | 1 2 2 |
| . . .___. .___. . . . . |
4 | 2 | 3 | | 3 | 2 1 |
| . . . . . . . . . . |
3 | | 3 | 3 | 2 2 |
| .___. . .___. . . . . . |
2 | 2 1 3 1 3 |
| . . . .___. . . . . . |
1 | 1 3 | |
| . . . . .___. . . . . |
'---------------------------------------'
a b c d e f g h i SL
Also, (2b)b9 is not possible (why ?), so
26.( r)a8! 27.(2r)b9
.---------------------------------------.
| .___. . . . . . . . . |
9 | | 3 2 | 3 1 1 2 |
| . . . . . . . . . . |
8 | | 2 2 3 |
| . . . . . .___. . . . |
7 | 2 | 1 |
| . . .___. .___. . . . . |
6 | | 3 | 3 | 1 |
| . .___. .___. . . . . . |
5 | 1 2 2 |
| . . .___. .___. . . . . |
4 | 2 | 3 | | 3 | 2 1 |
| . . . . . . . . . . |
3 | | 3 | 3 | 2 2 |
| .___. . .___. . . . . . |
2 | 2 1 3 1 3 |
| . . . .___. . . . . . |
1 | 1 3 | |
| . . . . .___. . . . . |
'---------------------------------------'
a b c d e f g h i SL
How to advance from here ?
Update 3 (Nov 1, 2026)
It is easy to check that (3b)a9 cannot be true
[it gives quickly a small closed loop].
So, 28.(3r)a9! and 14 placements.
The resulting grid after move 41 is the following
.---------------------------------------.
| .___. .___. . . . . . . |
9 | | 3 | 2 | 3 | 1 1 2 |
| . . . .___.___. . . . . |
8 | | | | 2 2 3 |
| . . .___.___. .___. . . . |
7 | | | 2 | 1 |
| . . .___. .___. . . . x . |
6 | | | | 3 | 3 | 1 |
| . .___. .___. . . . . . |
5 | | x 1 2 2 |
| . . x .___. .___. . . . . |
4 | 2 | 3 | | 3 | 2 1 |
| . . . . . . . . . . |
3 | | 3 | 3 | 2 2 |
| .___. . x .___. . . . . . |
2 | x 2 1 3 1 3 |
| . . . .___. . . . . . |
1 | 1 3 | |
| . . . . .___. x . . . . |
'---------------------------------------'
a b c d e f g h i SL
How to continue ?
Update 4 (Nov 2, 2026)
(2t)f8 leads quickly to trouble, at ( b)g9, (2b)h9
so 42.(2l)f8! with 16 placements.
We reach the following after move 58:
.---------------------------------------.
| .___. .___. . . .___.___.___. |
9 | | 3 | 2 | 3 | 1 1 | 2 | |
| . . . .___.___. .___.___. . |
8 | | | | 2 | 2 3 | | |
| . . .___.___. .___. .___. . |
7 | | | | 2 | | 1 | |
| . . .___. .___. . . . . |
6 | | | | 3 | 3 | 1 | |
| . .___. .___.___. . . . . |
5 | | 1 2 2 | |
| . . .___. .___. . . . . |
4 | 2 | 3 | | 3 | 2 1 |
| . . . . . . . . . . |
3 | | 3 | 3 | 2 2 |
| .___. . .___. . . . . . |
2 | 2 1 3 1 3 |
| . . . .___. . . . . . |
1 | 1 3 | |
| . . . . .___. x . . . . |
'---------------------------------------'
a b c d e f g h i SL
How to advance from here ?
Update 5 (Nov 3, 2026)
Now, ( l)a4 leads to small loop at c1.d1.e1, so
59.(3t)a3!! with 3 placements, reaching the following
.---------------------------------------.
| .___. .___. . . .___.___.___. |
9 | | 3 | 2 | 3 | 1 1 | 2 | |
| . . . .___.___. .___.___. . |
8 | | | | 2 | 2 3 | | |
| . . .___.___. .___. .___. . |
7 | | | | 2 | | 1 | |
| . . .___. .___. . . . . |
6 | | | | 3 | 3 | 1 | |
| . .___. .___.___. . . . . |
5 | | 1 2 2 | |
| .___. .___. .___. . . . . |
4 | | 2 | 3 | | 3 | 2 x 1 |
| .___. . . . . . . . x . |
3 | | 3 | | 3 | 2 2 |
| .___. . .___. . . . . . |
2 | 2 1 3 1 3 |
| . . . .___. . . . . . |
1 | 1 3 | |
| . . . . .___. x . . . . |
'---------------------------------------'
a b c d e f g h i SL
This is getting close to an easy solve. In my
account only two more steps are needed. How
to continue ?
Update 6 (Nov 5, 2026)
Now 63.(3t)e1! [otherwise, 3 lines would
be left in a closed region]. This gives 9
placements and we are almost done at
.---------------------------------------.
| .___. .___. . . .___.___.___. |
9 | | 3 | 2 | 3 | 1 1 | 2 | |
| . . . .___.___. .___.___. . |
8 | | | | 2 | 2 3 | | |
| . . .___.___. .___. .___. . |
7 | | | | 2 | | 1 | |
| . . .___. .___. . . . . |
6 | | | | 3 | 3 | 1 | |
| . .___. .___.___. . . . . |
5 | | 1 2 2 | |
| .___. .___. .___. . . . . |
4 | | 2 | 3 | | 3 | 2 x 1 |
| .___. . . . . . . . x . |
3 | | 3 | | 3 | 2 2 |
| .___. . .___. . . . . . |
2 | | | 2 x 1 3 1 3 |
| .___. .___.___.___. x . . . . |
1 | | 1 3 | |
| .___.___.___.___.___. . . . . |
'---------------------------------------'
a b c d e f g h i SL
How to finish this puzzle ?
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com