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 this newly created Hidoku puzzle (for a manual solution !)
.---------------------------.
7 | 16 __ __ __ __ __ 49|
6 | __ 19 __ __ __ __ __|
5 | __ 27 __ __ __ __ __|
4 | __ 24 __ __ __ __ 10|
3 | 29 __ __ __ __ __ __|
2 | __ __ __ 34 39 __ 42|
1 | __ __ 35 __ __ __ 01|
'---------------------------'
a b c d e f g
Update 1 (Sept 01, 2026)
Step 1: The positions 10 and 16
makes possible to get 4 numbers
(marked with *).
.---------------------------.
7 | 16 *15 __ __ __ __ 49|
6 |*17 19 __ __ __ __ __|
5 |*18 27 __ __ __ __ __|
4 |*28 24 __ __ __ __ 10|
3 | 29 __ __ __ __ __ __|
2 | __ __ __ 34 39 __ 42|
1 | __ __ 35 __ __ __ 01|
'---------------------------'
a b c d e f g
How to advance from here ?
Update 2 (Sept 3, 2026)
Step 2: After 4 numbers, a huge barrier
seems to exist for the next one! We have
to look for weaknesses and the natural
place for that is the lower right
corner. I have found a strong but
very complex move:
(40)f3 -> (43)f2, (44)e3, (38)d3 and path 01-10 leaves no place for 33
/
(41)g3
|| \
|| (40)f2 -> path 2-10, locked numbers (06,33,38)c2.d2.e2 and path 35->39 are in conflict
||
|| (02)f2 -> (40)e3, (43)g3!, and path 2-10 is tight -> no place for 38
|| /
(41)f3 (43)f2 -> (40)e3, (44)g3, (45)f4, (38)d3!, and path 2-10 leaves no place for 33
|| \ /
|| (02)f1 (3)f2 -> (40)e3, and path 3-10 leaves place for 38
|| \ /
|| (43)g3
|| \
|| (3)e1!!,(4)d1!,(5)c2, (44)f4!, now path 35-39 leaves no place for 33
||
(41)f2->(02)f1, (03)e1, (04)d1, (05)c2, (36)b2!, (37)c3,(38)d3, (33)e3, and path 5->10 is impossible.
Since those three possible places for 41 each gives a contradiction (each as described), we must have
5.(41)f1!!! [three due to the complexity, but I would happier with a simpler move]
6.(02)f2 7.(40)e1 8.(38)d1 9.(37)c2
So, we get
.---------------------------.
7 | 16 *15 __ __ __ __ 49|
6 |*17 19 __ __ __ __ __|
5 |*18 27 __ __ __ __ __|
4 |*28 24 __ __ __ __ 10|
3 | 29 __ __ __ __ __ __|
2 | __ __ *37 34 39 *02 42|
1 | __ __ 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
The situation has improved a lot,
it seems. How to continue ?
Update 3 (Sept 4, 2026)
Step 3: Now, small deductions get
many placements. The first one is
10.(36)b1! [(36)b2 leads to trouble
with that corner at b1]. After 7
more placements, we get
.---------------------------.
7 | 16 *15 __ __ __ __ 49|
6 |*17 19 __ __ __ __ __|
5 |*18 27 *23 __ __ __ __|
4 |*28 24 *26 __ __ __ 10|
3 | 29 *25 *33 __ __ __ __|
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
How to make progress now ?
Update 4 (Sept 6, 2026)
Step 4: The following move gives only
two numbers but it contains the main
ideas involved in the resolution of
this puzzle.
(21)d6, (13)d7,(12)e6,(11)f5,(22)d5, and conflicting paths 02-10,42-49.
/
(20)c6 (22)d6, (13)d7,(12)e6,(11)f5,(21)d5, and conflicting paths 02-10,42-49.
\ /
(21)d5
\
(22)d4, path 42-49 must pass through one of the cells e4, f4, and
use at least one cell of line 3. The path 2-10 has 7 numbers, so
it must use either e4 or f4. So, for the path 10-14, we must have
(11)f5!, which narrows the ways for the other two paths. One of
them must pass through f5, g5 and the other must use the cell e5.
So, (12)e6! is forced. Now the only way for the path 2-10 is
to use both passages, which makes the path 42-49 impossible.
------
The two next grids are for the analysis for the last part
(the most interesting, since it involves conflict of three paths)
.---------------------------.
7 | 16 *15 *14 __ __ __ 49|
6 |*17 19 ?20 __ __ __ __|
5 |*18 27 *23 ?21 __ __ __|
4 |*28 24 *26 *22 __ __ 10|
3 | 29 *25 *33 __ __ __ __| 03,43
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
.---------------------------.
7 | 16 *15 *14 __ __ __ 49|
6 |*17 19 ?20 __ *12 __ __|
5 |*18 27 *23 ?21 __ *11 __|
4 |*28 24 *26 *22 __ __ 10|
3 | 29 *25 *33 __ __ __ __| 03,43
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
----
So, 18.(20)c7!!! 19.(14)c6
.---------------------------.
7 | 16 *15 *20 __ __ __ 49|
6 |*17 19 *14 __ __ __ __|
5 |*18 27 *23 __ __ __ __|
4 |*28 24 *26 __ __ __ 10|
3 | 29 *25 *33 __ __ __ __|
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
Still needs work, but a lot less than
the two previous moves.
Update 5 (Sept 7, 2026)
Step 5: Either (21)d6 or (21)d7.
(21)d6, then (22)d5, (13)d7, (12)e6,(11)f5 and
we reach a familiar conflicting situation between
the paths 42-49 and 2-10. In detail:
The path 42-49 must pass through e5, f6, and
use at least one cell from line e3, one cell
from line e4, so the path 2-10 has at most 5
cells available in lines 3,4, so it must use
cells g5, g6, making impossible for such
path to exist.
.---------------------------.
7 | 16 *15 *20 *13 __ __ 49|
6 |*17 19 *14 ?21 *12 __ __|
5 |*18 27 *23 *22 __ *11 __|
4 |*28 24 *26 __ __ __ 10|
3 | 29 *25 *33 __ __ __ __|
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
So, 20.(21)d7!! 21.(22)d6 22.(13)d5
We have the following configuration
.---------------------------.
7 | 16 *15 *20 *21 __ __ 49|
6 |*17 19 *14 *22 __ __ __|
5 |*18 27 *23 *13 __ __ __|
4 |*28 24 *26 __ __ __ 10|
3 | 29 *25 *33 __ __ __ __|
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
Now we are a deduction away from
finishing easily the puzzle.
Update 6 (Sept 9, 2026)
Step 6: Last complex move
(11)f4 -> paths 2-10,42-49 leave no room for number 12.
/
\
(11)f5 -> path 42-49 must pass through e5 or g5, and
also takes at least one cell from row 3, and
another cell from row 4. Then, for the path
2-10 we have at most 5 cells available from
rows 3,4. But then the digits 8,9 will not
reach back to 10.
=> 23.(11)f3!! after this move the puzzle is solved easily.
.---------------------------.
7 | 16 *15 *20 *21 __ __ 49|
6 |*17 19 *14 *22 __ __ __|
5 |*18 27 *23 *13 __ __ __|
4 |*28 24 *26 __ __ __ 10|
3 | 29 *25 *33 __ __ *11 __|
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
I rate this puzzle as very tough due
to the complexity of moves 5 and 18.
In particular, a good replacement
for move 5 would be nice, but it
seems unlikely.
The final configuration is
.---------------------------.
7 | 16 *15 *20 *21 47 48 49|
6 |*17 19 *14 *22 46 07 08|
5 |*18 27 *23 *13 *06 45 09|
4 |*28 24 *26 *05 *12 *44 10|
3 | 29 *25 *33 *04 *03 *11 *43|
2 |*30 *32 *37 34 39 *02 42|
1 |*31 *36 35 *38 *40 *41 01|
'---------------------------'
a b c d e f g
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com