Welcome!
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, 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 ?
Update 2 (Sept 27, 2026)
Step 2: (3b)b2 creates immmediate impossible situation,
so 10.(3l)b2! with 8 more placements to get
.---------------------------------------.
| . . . . . . . .___. 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 | x 2 2 2 2 |
| . x . . . . . . . . . |
4 | x 1 x 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
Now (1t)c3 forces an impossible situation at (2)d4, so
19.(2r)b4! and 5 placements. We arrive at
.---------------------------------------.
| . . . . . . . .___. . |
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
How to advance from here ?
Update 3 (Sept 30, 2026)
It is tough to advance!
Step 3: If (2t)d4, then we have a long sequence
of forced moved leading to trouble with
three lines in a closed region (see below)
to the left.
.---------------------------------------.
| . . . . .___.___.___.___. x . |
9 | | 2 3 | 1 x |
| . . . . . .___.___.___. x . |
8 | 2 | 3 | | 2 x x |
| . . . .___. x . . x .___. x . |
7 | 3 2 2 x 1 | 2 x 2 | 3 | x |
| . . . . . x .___.___. x . . |
6 | | 1 x 2 x 1 x 2 |
| . .___. .___.___.___. x . . . |
5 | x x 2 | 2 x | 2 2 |
| . x . x . ._?_.___. x .___.___. . |
4 | x 1 x 2 | | 2 2 | 1 x 1 x 2 2 |
| .___.___. x . . . x . x . . . |
3 | | 2 2 x 1 | 2 | x 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
So, 25.( r)c5!! 26.(2r)d4 27.(2b)e4 28.(2l)e5
.---------------------------------------.
| . . . . . . . .___. x . |
9 | 2 3 | 1 x |
| . . . . . . . . . x . |
8 | 2 3 | 2 x |
| . . . .___. x . . . . . |
7 | 3 2 2 x 1 2 2 3 |
| . . . . . . . . . . |
6 | x 1 2 1 2 |
| . .___. x . . . . . . . |
5 | x x 2 | | | 2 2 2 |
| . x . x . . . x . . . . . |
4 | x 1 x 2 | | 2 | 2 x 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
Still looks very tough. How to make progress ?
Update 4 (Oct 3, 2026)
Step 4: If ( r)a6 then there is a forced sequence
(final configuration below) leading to
.---------------------------------------.
| .___.___.___.___.___.___. .___. x . |
9 | | 2 3 | 1 x |
| .___.___.___. .___. . . . x . |
8 | 2 | 3 | 2 x |
| .___.___. .___. x . . . . . |
7 | | 3 2 | 2 x 1 2 2 3 |
| .___. .___. . . . . . . |
6 | |? x 1 2 1 2 |
| . .___. x . . . . . . . |
5 | x x 2 | | | 2 2 2 |
| . x . x . . . x . . . . . |
4 | x 1 x 2 | | 2 | 2 x 1 1 2 2 |
| .___.___. . .___. . . . . |
3 | | 2 2 1 | 2 2 2 |
| . .___. .___. x . . . . . |
2 | | 2 | 3 | 1 x | 1 | |
| . . . . x . . . . . . |
1 | | | | 2 | 2 | 3 2 3 2 |
| .___. .___._!_. x .___. .___. . |
'---------------------------------------'
a b c d e f g h i SL
We have a total of 3 lines in column e, and
this is impossible. So,
30.( b)a6!! 31.( l)a6 32.(3r)a7 33.(3t)a7
.---------------------------------------.
| . . . . . . . .___. x . |
9 | 2 3 | 1 x |
| . . . . . . . . . x . |
8 | 2 x 3 | 2 x |
| .___. x . .___. x . . . . . |
7 | 3 | 2 2 x 1 2 2 3 |
| . . . . . . . . . . |
6 | | x x 1 2 1 2 |
| ._!_.___. x . . . . . . . |
5 | x x 2 | | | 2 2 2 |
| . x . x . . . x . . . . . |
4 | x 1 x 2 | | 2 | 2 x 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
Now (3r)h1 implies forced moves that lead
quickly into trouble at (2)d1 [not shown].
So, 34.(2b)i1! and 7 additional placements.
We reach the following configuration
.---------------------------------------.
| . . . . . . . .___. . |
9 | 2 3 | 1 |
| . . . . . . . . . . |
8 | 2 x 3 | 2 x |
| .___. x . .___. x . . . . . |
7 | 3 | 2 2 x 1 2 2 3 |
| . . . . . . . . . . |
6 | | x 1 2 1 2 |
| .___.___. x . . . . . . . |
5 | 2 | | | 2 2 2 |
| . . . . . . . x . . . |
4 | 1 2 | | 2 | 2 1 x 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
Still not easy. How to continue ?
Update 5 (Oct 4, 2026)
Step 5: If (1b)e6, then (2b)f6, (1b)f4, (2t)g5,
(2r)g5, (1r)e7, (1b)f7 and this line has no
place to go.
.---------------------------------------.
| . . . . . . . .___. . |
9 | 2 3 | 1 |
| . . . . . . . . . . |
8 | 2 x 3 | 2 x |
| .___. x . .___. x . . . . . |
7 | 3 | 2 2 x 1 | 2 2 3 |
| . . . . . x .___. . . . |
6 | | x 1 2 1 2 |
| .___.___. x . ._?_.___.___. . . |
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
So, 42.(2r)e5!!
.---------------------------------------.
| . . . . . . . .___. . |
9 | 2 3 | 1 |
| . . . . . . . . . . |
8 | 2 x 3 | 2 x |
| .___. x . .___. x . . . . . |
7 | 3 | 2 2 x 1 2 2 3 |
| . . . . . . . . . . |
6 | | x 1 2 1 2 |
| .___.___. x . . . . . . . |
5 | 2 | | | 2 | 2 2 |
| . . . . . . . x . . . |
4 | 1 2 | | 2 | 2 1 x 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
and this unlocks the puzzle (easy moves up to
move 94). The final configuration is
.---------------------------------------.
| .___.___.___.___.___. .___.___. . |
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
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com