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For difficult puzzles, 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)
(Guidelines for using this site here)
(useful to look up for the meaning of some unfamiliar concept)
I propose the following (tougher!) Slitherlink puzzle.
(Source: Simon Tatham's Collection)
.---------------------------------------.
| . . . . . . . . . . |
9 | 2 3 1 |
| . . . . . . . . . . |
8 | 2 3 2 |
| . . . . . . . . . . |
7 | 3 2 2 1 2 2 3 |
| . . . . . . . . . . |
6 | 1 2 1 2 |
| . . . . . . . . . . |
5 | 2 2 2 2 |
| . . . . . . . . . . |
4 | 1 2 2 2 1 1 2 2 |
| . . . . . . . . . . |
3 | 2 2 1 2 2 2 |
| . . . . . . . . . . |
2 | 2 3 1 1 |
| . . . . . . . . . . |
1 | 2 2 3 2 3 2 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i Slitherlink
Update 1 (Sept 26, 2026)
9 moves are available from the initial
patterns:
. (2)i1 forces ( r)i2 and (3b)h1
.---------------------------------------.
| . . . . . . . . . . |
9 | 2 3 1 |
| . . . . . . . . . . |
8 | 2 3 2 |
| . . . . . . . . . . |
7 | 3 2 2 1 2 2 3 |
| . . . . . . . . . . |
6 | 1 2 1 2 |
| . . . . . . . . . . |
5 | 2 2 2 2 |
| . . . . . . . . . . |
4 | 1 2 2 2 1 1 2 2 |
| . . . . . . . . . . |
3 | 2 2 1 2 2 2 |
| . . . . . . . . . . |
2 | 2 3 1 1 | |
| . . . . . . . . . . |
1 | 2 2 3 2 3 2 |
| . . . . . . . .___. . |
'---------------------------------------'
a b c d e f g h i SL
. (1)i9 must have x at (1r)i9, (1t)i9,so the
correct line in one of the remaining edges
has a "ripple effect" that impact all the
twos in the diagonal (2)d4-(2)h8 and forces
x at (1b)c3,(1l)c3. In other words, there
correct line at (1)i9 must enter (2)h8,
and that forces a line that enters (2)g7,
etc., there is a line entering (2)d4,
that forces a line leaving that cell and
entering (1)c3, so x at (1b)c3, and (1l)c3.
This implies (3t)b2, (3r)b2.
.---------------------------------------.
| . . . . . . . . . x . |
9 | 2 3 1 x |
| . . . . . . . . . . |
8 | 2 3 2 |
| . . . . . . . . . . |
7 | 3 2 2 1 2 2 3 |
| . . . . . . . . . . |
6 | 1 2 1 2 |
| . . . . . . . . . . |
5 | 2 2 2 2 |
| . . . . . . . . . . |
4 | 1 2 2 2 1 1 2 2 |
| . . . . . . . . . . |
3 | 2 2 x 1 2 2 2 |
| . .___. x . . . . . . . |
2 | 2 3 | 1 1 | |
| . . . . . . . . . . |
1 | 2 2 3 2 3 2 |
| . . . . . . . .___. . |
'---------------------------------------'
a b c d e f g h i SL
. Another consequence of x at (1t)i9, (1r)i9
is (3t)h9, (3r)g9, and so x at (1b)i9,
and x at ( r)i8
.---------------------------------------.
| . . . . . . . .___. x . |
9 | 2 3 | 1 x |
| . . . . . . . . . x . |
8 | 2 3 2 x |
| . . . . . . . . . . |
7 | 3 2 2 1 2 2 3 |
| . . . . . . . . . . |
6 | 1 2 1 2 |
| . . . . . . . . . . |
5 | 2 2 2 2 |
| . . . . . . . . . . |
4 | 1 2 2 2 1 1 2 2 |
| . . . . . . . . . . |
3 | 2 2 x 1 2 2 2 |
| . .___. x . . . . . . . |
2 | 2 3 | 1 1 | |
| . . . . . . . . . . |
1 | 2 2 3 2 3 2 |
| . . . . . . . .___. . |
'---------------------------------------'
a b c d e f g h i SL
. Looking at (2)d1, affected by x at (1b)c2, (1r)c2,
we must have ( b)c1.
.---------------------------------------.
| . . . . . . . .___. x . |
9 | 2 3 | 1 x |
| . . . . . . . . . x . |
8 | 2 3 2 x |
| . . . . . . . . . . |
7 | 3 2 2 1 2 2 3 |
| . . . . . . . . . . |
6 | 1 2 1 2 |
| . . . . . . . . . . |
5 | 2 2 2 2 |
| . . . . . . . . . . |
4 | 1 2 2 2 1 1 2 2 |
| . . . . . . . . . . |
3 | 2 2 x 1 2 2 2 |
| . .___. x . . . . . . . |
2 | 2 3 | 1 x 1 | |
| . . . x . . . . . . . |
1 | 2 2 3 2 3 2 |
| . . .___. . . . .___. . |
'---------------------------------------'
a b c d e f g h i SL
. Looking at the line ( r)i2 arriving at (2)i3,
there is this ripple effect up to (1)e7 that
forces x to (1t)e7, (1l)e7, and this implies
(3r)d8, (3b)i8.
.---------------------------------------.
| . . . . . . . .___. x . |
9 | 2 3 | 1 x |
| . . . . . . . . . x . |
8 | 2 3 | 2 x |
| . . . .___. x . . . . . |
7 | 3 2 2 x 1 2 2 3 |
| . . . . . . . . . . |
6 | 1 2 1 2 |
| . . . . . . . . . . |
5 | 2 2 2 2 |
| . . . . . . . . . . |
4 | 1 2 2 2 1 1 2 2 |
| . . . . . . . . . . |
3 | 2 2 x 1 2 2 2 |
| . .___. x . . . . . . . |
2 | 2 3 | 1 x 1 | |
| . . . x . . . . . . . |
1 | 2 2 3 2 3 2 |
| . . .___. . . . .___. . |
'---------------------------------------'
a b c d e f g h i SL
These basics moves produced 9 lines. How to proceed from here ?
I propose the following tough Slitherlink puzzle.
(Source: Simon Tatham's Collection)
.---------------------------------------.
| . . . . . . . . . . |
9 | 3 3 3 3 2 2 3 |
| . . . . . . . . . . |
8 | 3 2 1 |
| . . . . . . . . . . |
7 | 3 |
| . . . . . . . . . . |
6 | 2 2 2 |
| . . . . . . . . . . |
5 | 3 2 3 3 3 |
| . . . . . . . . . . |
4 | 2 1 2 0 |
| . . . . . . . . . . |
3 | 2 2 2 2 2 3 |
| . . . . . . . . . . |
2 | 2 2 2 |
| . . . . . . . . . . |
1 | 3 3 2 3 2 3 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i Slitherlink
Update 1 (Sept 21, 2026)
Step 1: 32 basic moves
We have in this puzzle many well-known patterns such as:
(a)
.--------------- .---------------
| . . . . | .___. . .
| 3 | | 3
| . . . . => | . . . .
| |
| . . . . | . . . .
(b)
. . . . . . . . . .
x
. . . . . => . x .___. . .
3 | 3
. . . . . . . . . .
3 3 |
. . . . . . . .___. x .
x
. . . . . . . . . .
(c)
. . . . . . . . . .
. . . . . . .___. . .
3 3
. . . . . => . x .___. x . .
3 3
. . . . . . .___. . .
. . . . . . . . . .
After 32 moves we get the following:
.---------------------------------------.
| .___. .___. .___. .___.___.___. |
9 | | 3 | 3 | 3 | | 3 | 2 | 2 3 | |
| . .___. . . . . .___.___. |
8 | | | 3 | 2 | 1 |
| . . . . . .___. . . . |
7 | 3 |
| . . . . . . . . . . |
6 | 2 2 2 |
| . . . . . . . . . . |
5 | 3 2 3 | 3 | | 3 |
| . . . . .___. .___. x .___. |
4 | 2 1 2 x 0 x |
| . . . . . . . . x .___. |
3 | 2 2 2 2 2 | 3 |
| . . . . . . . . . . |
2 | 2 2 2 |
| . . . . . . . . . . |
1 | 3 3 2 3 2 3 | |
| . . . . . . . . .___. |
'---------------------------------------'
a b c d e f g h i SL
How to continue ?
Update 2 (Sept 22, 2026)
Recall: . ( r)i6 means to place a line segment
in the right edge of the empty cell i6.
. (3l)i1 means to fill the left edge of
the cell i1 [has 3 on it] with a line segment.
.(3b)i3 means to fill the bottom edge of the
cell i3 [has 3 on it] with a line segment.
. ( t)i6 means to fill the top edge of the
cell i6 with a line segment.
Step 2: 33.( r)i6! 34.( t)i6 35.(2r)i2! 36.(3l)i1
37.(3b)i3! and 11 additional placements.
(we recall that one exclamation mark means a small
deduction; two and three exclamation marks refer
more involved deduction)
.---------------------------------------.
| .___. .___. .___. .___.___.___. |
9 | | 3 | 3 | 3 | | 3 | 2 | 2 3 | |
| . .___. . . . . .___.___. |
8 | | | 3 | 2 | 1 |
| . . . . . .___. . . . |
7 | 3 |
| . . . . . . . . .___. |
6 | 2 2 2 | | |
| . . . . . . . . .___. |
5 | 3 2 3 | | 3 | | 3 |
| . . . . .___. .___. .___. |
4 | 2 1 2 0 | |
| . . . . . .___.___. .___. |
3 | 2 2 2 2 | 2 | 3 |
| . . . . . . . . .___. |
2 | 2 | 2 2 | |
| . . . . . . . .___. . |
1 | 3 3 2 3 | 2 | 3 | |
| . . . . . .___. . .___. |
'---------------------------------------'
a b c d e f g h i SL
How to proceed from this position ?
Update 3 (Sept 23, 2026)
(see recall on notation at the beginning)
Step 3: Forced moves to avoid lines without place to go
or small loops
49.(3t)g6! 50.( b)h8 51.( l)i7 52.( b)f7 53.( b)f6
54.(3l)e5 55.( b)e7 56.( t)d5!
.---------------------------------------.
| .___. .___. .___. .___.___.___. |
9 | | 3 | 3 | 3 | | 3 | 2 | 2 3 | |
| . .___. . . . . .___.___. |
8 | | | 3 | 2 | 1 |
| . . . . . .___. .___. . |
7 | 3 | |
| . . . . .___.___.___. .___. |
6 | 2 2 2 | | |
| . . . .___. .___. . .___. |
5 | 3 2 | 3 | | 3 | | 3 |
| . . . . .___. .___. .___. |
4 | 2 1 2 0 | |
| . . . . . .___.___. .___. |
3 | 2 2 2 2 | 2 | 3 |
| . . . . . . . . .___. |
2 | 2 | 2 2 | |
| . . . . . . . .___. . |
1 | 3 3 2 3 | 2 | 3 | |
| . . . . . .___. . .___. |
'---------------------------------------'
a b c d e f g h i SL
How to continue from here ?
Update 4 (Sept 25, 2026)
Step 4: 57.(3t)f1!! [otherwise, trouble at (3)d1]
and 8 additional placements. We get
.---------------------------------------.
| .___. .___. .___. .___.___.___. |
9 | | 3 | 3 | 3 | | 3 | 2 | 2 3 | |
| . .___. . . . . .___.___. |
8 | | | 3 | 2 | 1 |
| . . . . . .___. .___. . |
7 | 3 | |
| . . . . .___.___.___. .___. |
6 | 2 2 2 | | |
| . . . .___. .___. . .___. |
5 | 3 2 | 3 | | 3 | | 3 |
| . . . . .___. .___. .___. |
4 | 2 1 2 0 | |
| . . . . . .___.___. .___. |
3 | 2 2 2 2 | 2 | 3 |
| . . . . . . . . .___. |
2 | | 2 | 2 2 | |
| . .___. .___. .___. .___. . |
1 | | 3 | 3 | 2 3 | 2 | 3 | |
| . . .___. .___.___. . .___. |
'---------------------------------------'
a b c d e f g h i SL
Now (2r)c5 is impossible
[it would force (2l)b6, (2t)b6 and trouble at cell (3)b7]
So,
66.(3t)b7! 67.(3l)b7 68.( l)a7
We reach the following situation
.---------------------------------------.
| .___. .___. .___. .___.___.___. |
9 | | 3 | 3 | 3 | | 3 | 2 | 2 3 | |
| . .___. . . . . .___.___. |
8 | | | 3 | 2 | 1 |
| . .___. . . .___. .___. . |
7 | | | 3 | |
| . . . . .___.___.___. .___. |
6 | 2 2 2 | | |
| . . . .___. .___. . .___. |
5 | 3 2 | 3 | | 3 | | 3 |
| . . . . .___. .___. .___. |
4 | 2 1 2 0 | |
| . . . . . .___.___. .___. |
3 | 2 2 2 2 | 2 | 3 |
| . . . . . . . . .___. |
2 | | 2 | 2 2 | |
| . .___. .___. .___. .___. . |
1 | | 3 | 3 | 2 3 | 2 | 3 | |
| . . .___. .___.___. . .___. |
'---------------------------------------'
a b c d e f g h i SL
How to advance ?
Update 5 (Sept 26, 2026)
Step 5: (2t)a6 is not possible ... problem at (2)c5.
69.(2l)a6! 70.(3b)a5 71.(3r)a5 72.( t)e2!
[impossible ( l)f3] 73.(2l)c5! We get:
.---------------------------------------.
| .___. .___. .___. .___.___.___. |
9 | | 3 | 3 | 3 | | 3 | 2 | 2 3 | |
| . .___. . . . . .___.___. |
8 | | | 3 | 2 | 1 |
| . .___. . . .___. .___. . |
7 | | | 3 | |
| . . . . .___.___.___. .___. |
6 | | 2 2 2 | | |
| . . . .___. .___. . .___. |
5 | 3 | | 2 x | 3 | | 3 | | 3 |
| .___. . . .___. .___. .___. |
4 | 2 1 2 0 | |
| . . . . . .___.___. .___. |
3 | 2 2 2 2 | 2 | 3 |
| . . . . .___. . . .___. |
2 | | 2 | 2 2 | |
| . .___. .___. .___. .___. . |
1 | | 3 | 3 | 2 3 | 2 | 3 | |
| . . .___. .___.___. . .___. |
'---------------------------------------'
a b c d e f g h i SL
Getting close to done. How to proceed ?
In the next grid, find the maximum number of lines and forbidden edges possible.
. . . . . . |
|
. . .___. . . |
| 3 3 |
. . . . . . |
2 |
. . . . . . |
----------------------' SL
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com