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 tough Slitherlink puzzle: very distinct features!
(Source: Simon Tatham's Collection)
.---------------------------------------.
| . . . . . . . . . . |
9 | 3 2 3 3 |
| . . . . . . . . . . |
8 | 1 1 |
| . . . . . . . . . . |
7 | 3 1 2 2 |
| . . . . . . . . . . |
6 | 2 0 2 1 1 2 2 |
| . . . . . . . . . . |
5 | 3 2 3 2 3 |
| . . . . . . . . . . |
4 | 1 1 2 2 |
| . . . . . . . . . . |
3 | 3 1 1 2 2 3 |
| . . . . . . . . . . |
2 | 2 1 2 3 2 2 |
| . . . . . . . . . . |
1 | 3 2 3 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i
Update 1 (March 13, 2026)
Part 1: After 17 basic moves, including the pattern
__
3|
2
2
|3
--
we get
.---------------------------------------.
| . . . . . . . . .___. |
9 | 3 2 3 3 | |
| . . . . . . . . . . |
8 | 1 1 |
| . . .___. . . . . . . |
7 | | 3 | 1 2 2 |
| . .___. .___. . . . . . |
6 | 2 0 2 1 1 2 2 |
| . .___. .___. . . . .___. |
5 | 3 | 2 | 3 2 3 | |
| . . . . . . . . . . |
4 | 1 1 2 2 |
| . . . . . . . . . . |
3 | 3 1 1 2 2 3 |
| . . . . . . . . . . |
2 | 2 1 2 | 3 2 2 |
| . . . . . .___. . . . |
1 | 3 2 3 | |
| . . . . . . . . .___. |
'---------------------------------------'
a b c d e f g h i
[4 additional moves are available before
the first deduction is needed]
Update 2 (March 14, 2026)
We reach the following position after 21 moves.
Notice the marked recent moves that follow from
line (3r)b5 [line to the right of cell (3)b5]
reaching the top right coner of cell (1)b4, forcing
"x" at the bottom and left of that cell, and thus
forcing 18.( t)a4! 19.(3t)a3 20.(3r)a3 and 21.(2l)a2.
.---------------------------------------.
| . . . . . . . . .___. |
9 | 3 2 3 3 | |
| . . . . . . . . . . |
8 | 1 1 |
| . . .___. . . . . . . |
7 | | 3 | 1 2 2 |
| . .___. .___. . . . . . |
6 | 2 0 2 1 1 2 2 |
| . .___. .___. . . . .___. |
5 | 3 | 2 | 3 2 3 | |
| ._!_. . . . . . . . . |
4 | x 1 1 2 2 |
| .___. x . . . . . . . . |
3 | 3 | 1 1 2 2 3 |
| . . . . . . . . . . |
2 |!| 2 1 2 | 3 2 2 |
| . . . . . .___. . . . |
1 | 3 2 3 | |
| . . . . . . . . .___. |
'---------------------------------------'
a b c d e f g h i
How to continue ?
Update 3 (March 15, 2026)
Part 2: The top right corner has a nice pattern
involving several cells:
(3)e9,(2)f9,(3)g9,(1)e8,(3)i9,(2)h7,(3t)i5,(3r)i5.
That pattern implies (3l)i9 as it is shown next.
Proof:
.---------------------------------------.
| . . . . . . . .___.___. |
9 | 3 2 3 3 | |
| . . . . . . . . ._?_. |
8 | 1 1 |
| . . .___. . . . . . . |
7 | | 3 | 1 2 2 |
| . .___. .___. . . . . . |
6 | 2 0 2 1 1 2 2 |
| . .___. .___. . . . .___. |
5 | 3 | 2 | 3 2 3 | |
a b c d e f g h i
.---------------------------------------.
| . . . . . . . .___.___. |
9 | 3 2 | 3 3 | |
| . . . . . . x .___. ._?_. |
8 | 1 1 |
| . . .___. . . . . . . |
7 | | 3 | 1 2 2 |
| . .___. .___. . . . . . |
6 | 2 0 2 1 1 2 2 |
| . .___. .___. . . . .___. |
5 | 3 | 2 | 3 2 3 | |
a b c d e f g h i
Now (2t)f9 is not possible because it would
imply (3t)e9, (3l)e9, (3b)e9 and no place to
continue, so
.---------------------------------------.
| . . . . . . x .___.___.___. |
9 | 3 2 | 3 3 | |
| . . . . . . x .___. ._?_. |
8 | 1 1 | | |
| . . .___. . . . . . . |
7 | | 3 | 1 2 2 |
| . .___. .___. . . . . . |
6 | 2 0 2 1 1 2 2 |
| . .___. .___. . . . .___. |
5 | 3 | 2 | 3 2 3 | |
a b c d e f g h i
Now the line entering the top left corner
of (2)i7 should continue at (2r)i6 and that
is not possible due to (3t)i5, (3r)i5. //////
So,
22. (3l)i9!!
With this move we can continue all the way
to move 46, reaching the following
.---------------------------------------.
| . . . . .___. .___. .___. |
9 | 3 | 2 | 3 | | 3 | |
| . . . .___. . . . . . |
8 | 1 1 | | |
| . . .___. . . . . . . |
7 | | 3 | 1 2 2 |
| . .___. .___.___. . . . . |
6 | | 2 0 2 1 1 2 2 |
| .___.___. .___. . . . .___. |
5 | 3 | 2 | 3 | 2 3 | |
| .___.___. . . . . . . . |
4 | | 1 1 | 2 2 |
| .___. . . . . . . . . |
3 | 3 | 1 | 1 2 2 3 |
| .___. . . . . . . . . |
2 | | 2 1 | 2 | 3 2 2 |
| . .___. . . .___. . . . |
1 | | | 3 | 2 3 | |
| .___. .___. . . . . .___. |
'---------------------------------------'
a b c d e f g h i
How to advance from here ?
Update 4 (March 16, 2026)
Part 3: Looking at cell (3)e9, we must have
47.(3b)e9!!
since the other way leaves 3 lines to match in
a closed region, which is impossible. After 11
easy moves we get the following configuration
.---------------------------------------.
| .___.___.___.___.___. .___. .___. |
9 | | 3 | 2 | 3 | | 3 | |
| . .___.___.___.___. . . . . |
8 | | | 1 1 | | |
| . . .___. . . . . . . |
7 | | | | 3 | 1 2 2 |
| . .___. .___.___. . . . . |
6 | | 2 0 2 1 1 2 2 |
| .___.___. .___. . . . .___. |
5 | 3 | 2 | 3 | 2 3 | |
| .___.___. . . . . . . . |
4 | | 1 1 | 2 2 |
| .___. . . . . . . . . |
3 | 3 | 1 | 1 2 2 3 |
| .___. . . . . . . . . |
2 | | 2 1 | 2 | 3 2 2 |
| . .___. . . .___. . . . |
1 | | | 3 | 2 3 | |
| .___. .___. . . . . .___. |
'---------------------------------------'
We have reached the most difficult position
of this puzzle. How to make progress ?
Update 5 (March 17, 2026)
Part 4: If (3r)f2 then (2r)g1, (2b)g1, ( b)f1,
( b)e1 and "x" at (1t)e3,(1l)e3 leaving 3 lines
to match in a closed region... impossible!
(see below)
.---------------------------------------.
| .___.___.___.___.___. .___. .___. |
9 | | 3 | 2 | 3 | | 3 | |
| . .___.___.___.___. . . . . |
8 | | | 1 1 | | |
| . . .___. . . . . . . |
7 | | | | 3 | 1 2 2 |
| . .___. .___.___. . . . . |
6 | | 2 0 2 1 1 2 2 |
| .___.___. .___. . . . .___. |
5 | 3 | 2 | 3 | 2 3 | |
| .___.___. . . . . . . . |
4 | | 1 1 | 2 2 |
| .___. . . . x . . . . . |
3 | 3 | 1 | x 1 2 2 3 |
| .___. . . . . . . . . |
2 | | 2 1 | 2 | 3?| 2 2 |
| . .___. . . .___. . . . |
1 | | | 3 | 2 | 3 | |
| .___. .___. .___.___.___. .___. |
'---------------------------------------'
a b c d e f g h i
So 59.(3t)f2 !! and 15 placements follow.
We reach the following configuration
.---------------------------------------.
| .___.___.___.___.___. .___. .___. |
9 | | 3 | 2 | 3 | | 3 | |
| . .___.___.___.___. . . . . |
8 | | | 1 1 | | |
| . . .___. . . . . . . |
7 | | | | 3 | 1 2 2 |
| . .___. .___.___. . . . . |
6 | | 2 0 2 1 1 2 2 |
| .___.___. .___. . . . .___. |
5 | 3 | 2 | 3 | 2 3 | |
| .___.___. . . . . . . . |
4 | | 1 1 | | 2 2 |
| .___. . . . . . . . . |
3 | 3 | 1 | | 1 2 2 3 | |
| .___. . . . .___.___. .___. |
2 | | 2 1 | | 2 | 3 2 2 |
| . .___. . . .___.___.___.___. |
1 | | | 3 | | | 2 3 | |
| .___. .___. .___.___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
We are getting close to done. How to continue ?
Update 6 (March 18, 2026)
Part 5: (3l)i3 is impossible because it forces
( r)i4, (2l)h3, (2r)h4, (3l)i5 forming
an impossible loop. So
75.(2b)h3!! and 7 placements lead to the following
.---------------------------------------.
| .___.___.___.___.___. .___. .___. |
9 | | 3 | 2 | 3 | | 3 | |
| . .___.___.___.___. . . . . |
8 | | | 1 1 | | |
| . . .___. . .___. . . . |
7 | | | | 3 | | 1 2 2 |
| . .___. .___.___. . . . . |
6 | | 2 0 2 1 1 2 2 x |
| .___.___. .___. . . . .___. |
5 | 3 | 2 | 3 | 2 3 | |
| .___.___. . . . . .___.___. |
4 | | 1 1 | | 2 2 |
| .___. . . . . .___.___.___. |
3 | 3 | 1 | | 1 2 2 3 | |
| .___. . . . .___.___.___.___. |
2 | | 2 1 | | 2 | 3 2 2 |
| . .___. . . .___.___.___.___. |
1 | | | 3 | | | 2 3 | |
| .___. .___. .___.___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
We need a last deduction to finish this puzzle.
Update 7 (March 19, 2026)
We need a line at ( l)f4, otherwise (2l)g4
[marked with question mark below], (2l)h5,
(2l)i6, (2t)i7!, (2l)i7, ( t)h8 ...
.---------------------------------------.
| .___.___.___.___.___. .___. .___. |
9 | | 3 | 2 | 3 | | 3 | |
| . .___.___.___.___. . .___. . |
8 | | | 1 1 | | |
| . . .___. . .___. . .___. |
7 | | | | 3 | | 1 2 | 2 |
| . .___. .___.___. . . . . |
6 | | 2 0 2 1 1 2 | 2 |
| .___.___. .___. . . . .___. |
5 | 3 | 2 | 3 | | 2 3 | |
| .___.___. . . . . .___.___. |
4 | | 1 1 | | ?| 2 2 |
| .___. . . . . .___.___.___. |
3 | 3 | 1 | | 1 2 2 3 | |
| .___. . . . .___.___.___.___. |
2 | | 2 1 | | 2 | 3 2 2 |
| . .___. . . .___.___.___.___. |
1 | | | 3 | | | 2 3 | |
| .___. .___. .___.___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
and we have a problem (2l)h7 (no place to go).
So, 83.( l)f4! and the final 13 moves are easy.
Final configuration:
.---------------------------------------.
| .___.___.___.___.___. .___. .___. |
9 | | 3 | 2 | 3 | | 3 | |
| . .___.___.___.___. . . . . |
8 | | | 1 1 | | | | |
| . . .___. . .___. .___. . |
7 | | | | 3 | | 1 2 2 | |
| . .___. .___.___. .___.___.___. |
6 | | 2 0 2 1 1 | 2 2 |
| .___.___. .___. . .___.___.___. |
5 | 3 | 2 | 3 | 2 3 | |
| .___.___. . . .___.___.___.___. |
4 | | 1 1 | | | 2 2 |
| .___. . . . .___.___.___.___. |
3 | 3 | 1 | | 1 2 2 3 | |
| .___. . . . .___.___.___.___. |
2 | | 2 1 | | 2 | 3 2 2 |
| . .___. . . .___.___.___.___. |
1 | | | 3 | | | 2 3 | |
| .___. .___. .___.___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
I propose the following Slitherlink puzzle (many patterns and nice ideas).
(Source: Simon Tatham's Collection)
.---------------------------------------.
| . . . . . . . . . . |
9 | 2 3 3 |
| . . . . . . . . . . |
8 | 2 2 2 |
| . . . . . . . . . . |
7 | 2 2 1 3 1 |
| . . . . . . . . . . |
6 | 1 2 |
| . . . . . . . . . . |
5 | 3 3 3 2 |
| . . . . . . . . . . |
4 | 2 3 3 |
| . . . . . . . . . . |
3 | 3 2 |
| . . . . . . . . . . |
2 | 2 1 1 |
| . . . . . . . . . . |
1 | 2 3 2 2 2 1 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i
Update 1 (March 12, 2026)
For his puzzle, the part 1 of basic moves is
long. A couple moves (13) are displayed below,
but one can go a lot further without difficulties.
.---------------------------------------.
| . . . . . . . . . . |
9 | 2 3 3 |
| . . . . . . . . . . |
8 | 2 2 2 |
| . . . . . . . .___. . |
7 | 2 2 1 | 3 1 |
| . . . . . . . .___. . |
6 | 1 x 2 | |
| . . . . . . .___. . . |
5 | 3 | 3 | 3 | 2 | |
| . . . . . .___. . . . |
4 | 2 x 3 | 3 |
| . . . . . . . . . . |
3 | | 3 2 |
| . . . . .___. . . . . |
2 | 2 1 1 |
| . . . . . . . . . . |
1 | 2 3 2 2 2 1 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i
Update 2 (March 13, 2026)
After 29 (basic) moves:
.---------------------------------------.
| . . . . . . . . .___. |
9 | 2 3 3 | |
| . . . . . . . . . . |
8 | 2 2 2 |
| . . . . . . x . .___. . |
7 | 2 2 x 1 | 3 1 |
| . . . . . . . .___. . |
6 | 1 x | 2 | |
| . .___. . .___. .___. .___. |
5 | | 3 | 3 | 3 | 2 | |
| . . . .___. .___. .___. . |
4 | | 2 x 3 | 3 | |
| . . .___. . .___. .___. . |
3 | | 3 2 | |
| . . . . .___. .___. . . |
2 | 2 x 1 1 |
| . . . . . . x . . . . |
1 | 2 3 2 2 2 1 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i
Update 3 (March 14, 2026)
Part 2: Small deductions
. Looking at the cell (1)i7, we must have
30.(2r)i8!
. Looking at the cell (2)h8, we must have
31.( l)i9!
. Looking at the cell (1)a6, we must have
32.(2l)a7! and 5 more placements to reach:
.---------------------------------------.
| . . . . . . . . .___. |
9 | 2 3 3 | | |
| . . . . . . . .___. . |
8 | 2 2 2 | |
| . . . . . . x . .___.___. |
7 | | 2 2 x 1 | 3 1 |
| . . . . . . . .___. . |
6 | 1 x x | 2 | |
| . x .___. . .___. .___. .___. |
5 | | 3 | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | 2 x 3 | 3 | | |
| . . .___. . .___. .___. . |
3 | | 3 2 | | |
| . . . . .___. .___. . . |
2 | 2 x 1 1 |
| . . . . . . x . . . . |
1 | 2 3 2 2 2 1 |
| . . . . . . . . . . |
'---------------------------------------'
a b c d e f g h i
How to make progress now ?
Update 4 (March 15, 2026)
Part 3: Small deductions that give lots of placements
Looking at cell (2)e1, a line must enter
into it from (2t)d1 and leave at (2b)f1
38.(2t)d1! 39.(2b)f1
.---------------------------------------.
| . . . . . . . . .___. |
9 | 2 3 3 | | |
| . . . . . . . .___. . |
8 | 2 2 2 | |
| . . . . . . x . .___.___. |
7 | | 2 2 x 1 | 3 1 |
| . . . . . . . .___. . |
6 | 1 x x | 2 | |
| . x .___. . .___. .___. .___. |
5 | | 3 | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | 2 x 3 | 3 | | |
| . . .___. . .___. .___. . |
3 | | 3 2 | | |
| . . . . .___. .___. . . |
2 | 2 x 1 1 |
| . . . .___. . x . . . . |
1 | 2 3 2 2 2 1 |
| . . . . . .___. . . . |
'---------------------------------------'
a b c d e f g h i
Also, it is easy to see that "x" at (3r)c1
leads into an impossible situation with a
line at (2t)e1 without a place to go. So,
40.(3r)c1!
and now one can continue without difficulties
up to move 69, reaching the following
.---------------------------------------.
| . . . . . . . . .___. |
9 | 2 3 3 | | |
| . . . . . . . .___. . |
8 | 2 2 2 | |
| . . . . . . x . .___.___. |
7 | | 2 2 x 1 | 3 1 |
| . X . . . . . . .___. . |
6 | | 1 x | | 2 | |
| . x .___. . .___. .___. .___. |
5 | | | 3 | | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | | | 2 3 | 3 | | |
| . . .___. .___.___. .___. . |
3 | | | | | 3 2 | | |
| . . .___. .___.___.___. .___. |
2 | | | | 2 1 1 | |
| . . . .___.___. . . .___. |
1 | | | 2 | 3 | 2 2 | 2 1 | |
| .___. .___. . .___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
How to continue from here ?
Update 5 (March 16, 2026)
Part 4: Looking at cell (2)b7, a line must
come from the top left corner and leave at
the bottom right corner. So
70.( b)c7!
.---------------------------------------.
| . . . . . . . . .___. |
9 | 2 3 3 | | |
| . . . . . . . .___. . |
8 | 2 2 2 | |
| . . . . . . x . .___.___. |
7 | | 2 2 x 1 | 3 1 |
| . X . .___. . . . .___. . |
6 | | 1 x | | 2 | |
| . x .___. . .___. .___. .___. |
5 | | | 3 | | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | | | 2 3 | 3 | | |
| . . .___. .___.___. .___. . |
3 | | | | | 3 2 | | |
| . . .___. .___.___.___. .___. |
2 | | | | 2 1 1 | |
| . . . .___.___. . . .___. |
1 | | | 2 | 3 | 2 2 | 2 1 | |
| .___. .___. . .___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
The line leaving (2)b7 cannnot be (2t)a7,
because then (2t)b7,(2r)b7 implies (2t)c8,
(2r)c8 and we have an impossible situation
at (3)d9. So
71.( r)a8! and 3 additional placements.
We get
.---------------------------------------.
| . . . . . . . . .___. |
9 | 2 3 3 | | |
| . . . . . . . .___. . |
8 | | | 2 2 2 | |
| . . . . . . x . .___.___. |
7 | | 2 | 2 x 1 | 3 1 |
| . .___.___. . . . .___. . |
6 | | 1 | | 2 | |
| . .___. . .___. .___. .___. |
5 | | | 3 | | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | | | 2 3 | 3 | | |
| . . .___. .___.___. .___. . |
3 | | | | | 3 2 | | |
| . . .___. .___.___.___. .___. |
2 | | | | 2 1 1 | |
| . . . .___.___. . . .___. |
1 | | | 2 | 3 | 2 2 | 2 1 | |
| .___. .___. . .___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
How to continue from here ?
Update 6 (March 17, 2026)
[notice that ( b)a9 may be possible, so
we cannot use (2)b9 to get ( t)c9]
Part 5: We must have a line entering the
bottom right corner of (2)c8 and
reaching ( t)a9, so
75.( b)d8! 76.( t)a9 77.( l)a9
.---------------------------------------.
| .___. . . . . . . .___. |
9 | | 2 3 3 | | |
| . . . . . . . .___. . |
8 | | | 2 2 2 | |
| . . . .___. . x . .___.___. |
7 | | 2 | 2 x 1 | 3 1 |
| . .___.___. . . . .___. . |
6 | | 1 | | 2 | |
| . .___. . .___. .___. .___. |
5 | | | 3 | | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | | | 2 3 | 3 | | |
| . . .___. .___.___. .___. . |
3 | | | | | 3 2 | | |
| . . .___. .___.___.___. .___. |
2 | | | | 2 1 1 | |
| . . . .___.___. . . .___. |
1 | | | 2 | 3 | 2 2 | 2 1 | |
| .___. .___. . .___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
Also, due to (3)d9, the line that arrives
at the bottom right corner of (2)c8, cannot
go (2r)c8, (2t)c8, so
78.(2b)c8 and 3 placements. We get the following
configuration
.---------------------------------------.
| .___. . . . . . . .___. |
9 | | 2 | 3 3 | | |
| . . . .___. . . .___. . |
8 | | | | 2 2 2 | |
| . . .___.___. . x . .___.___. |
7 | | 2 | 2 x 1 | 3 1 |
| . .___.___. . . . .___. . |
6 | | 1 | | 2 | |
| . .___. . .___. .___. .___. |
5 | | | 3 | | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | | | 2 3 | 3 | | |
| . . .___. .___.___. .___. . |
3 | | | | | 3 2 | | |
| . . .___. .___.___.___. .___. |
2 | | | | 2 1 1 | |
| . . . .___.___. . . .___. |
1 | | | 2 | 3 | 2 2 | 2 1 | |
| .___. .___. . .___.___.___.___. |
'---------------------------------------'
a b c d e f g h i
How to finish the puzzle ?
Update 7 (March 18, 2026)
Part 6: (3t)d9 leaves the impossible situation
of 3 lines to match in a closed region.
So,
82.( t)c9! and the remaning moves are easy
[with ending at (2)b9]
Final configuration:
.---------------------------------------.
| .___. .___. .___. .___. .___. |
9 | | | 2 | | 3 | | 3 | | | | |
| . . . .___. .___. .___. . |
8 | | | | 2 2 2 | |
| . . .___.___. . . .___.___. |
7 | | 2 | 2 | 1 | 3 1 |
| . .___.___. .___.___. .___. . |
6 | | 1 | | 2 | |
| . .___. . .___. .___. .___. |
5 | | | 3 | | 3 | 3 | 2 | | |
| . . . .___. .___. .___. . |
4 | | | | 2 3 | 3 | | |
| . . .___. .___.___. .___. . |
3 | | | | | 3 2 | | |
| . . .___. .___.___.___. .___. |
2 | | | | 2 1 1 | |
| . . . .___.___. . . .___. |
1 | | | 2 | 3 | 2 2 | 2 1 | |
| .___. .___. . .___.___.___.___. |
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Created: February 12, 2024
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