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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 (like the next one), 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).
This new Hidoku puzzle ("Tightly tied knot ?") has an easy start, but becomes tough later.
,------------------------------------,
| __ 49 __ 69 __ 81 __ __ __ | 9
| 47 __ 52 54 __ __ 79 77 __ | 8
| __ __ 42 __ 56 67 __ 73 __ | 7
| __ __ __ __ 15 __ __ 65 64 | 6
| __ __ 35 __ 01 __ __ __ 62 | 5
| __ __ __ __ 29 __ __ __ __ | 4
| __ __ __ __ __ 27 __ __ __ | 3
| __ __ 32 __ __ __ 24 21 __ | 2
| __ 09 __ __ __ __ __ 22 __ | 1
'------------------------------------'
a b c d e f g h i JCO#6 (Hidoku)
Update (Nov 6, 2025)
After 28 placements:
,------------------------------------,
|*48 49 *53 69 *70 81 *80 *78 *76 | 9
| 47 *50 52 54 *68 *71 79 77 *75 | 8
|*46 *51 42 *55 56 67 *72 73 *74 | 7
| __ __ __ __ 15 *57 *66 65 64 | 6
| __ __ 35 __ 01 *16 *58 *63 62 | 5
| __ __ __ __ 29 __ *17 *59 *61 | 4
| __ __ __ __ __ 27 __ *18 *60 | 3
| __ __ 32 __ __ __ 24 21 *19 | 2
| __ 09 __ __ __ __ *23 22 *20 | 1
'------------------------------------'
a b c d e f g h i
The puzzle is locked! How to proceed from here ?
Update (Nov 7, 2025)
Analyze which of the two possibilities for placing 14 is false.
Notice that (14)d6 restricts a lot rows 3,4,5,6.
Update (Nov 8, 2025)
So, a careful analysis of the consequences of (14)d6 leads to
. Three numbers (41,43,45) locked into three cells (a6,b6,c6)
. Two numbers (40,44) locked into two cells (a5,b5)
. Four number (12,34,36,39) locked into four cells (a4,b4,c4,d4)
. Six numbers (03,11,28,33,37,38) locked into six cells (a3,b3,c3,d3,e3,g3)
Now, notice that there is no place for the number 30!
=> 29. (14)d5!!
,------------------------------------,
|*48 49 *53 69 *70 81 *80 *78 *76 | 9
| 47 *50 52 54 *68 *71 79 77 *75 | 8
|*46 *51 42 *55 56 67 *72 73 *74 | 7
| __ __ __ __ 15 *57 *66 65 64 | 6
| __ __ 35 *14 01 *16 *58 *63 62 | 5
| __ __ __ __ 29 __ *17 *59 *61 | 4
| __ __ __ __ __ 27 __ *18 *60 | 3
| __ __ 32 __ __ __ 24 21 *19 | 2
| __ 09 __ __ __ __ *23 22 *20 | 1
'------------------------------------'
a b c d e f g h i
This move does not give immediate placements,
but now one can ask: which numbers go to c6,d6 ?
Update (Nov 9, 2025)
. 41,43,45 are locked into row 6 [45 at a6/b6, 41,43 at b6/c6/d6]
. 40,44 must be located at row 5 or 6.
. The numbers at c6,d6,c7 must be consecutive to comply with the "corner" d6.
=> 30. (41)!!d6
[and 5 placements: 31.(40)c6, 32.(43)b6, 33. (45)a6, 34.(39)b5, 35.(44)a4 ]
,------------------------------------,
|*48 49 *53 69 *70 81 *80 *78 *76 | 9
| 47 *50 52 54 *68 *71 79 77 *75 | 8
|*46 *51 42 *55 56 67 *72 73 *74 | 7
|*45 *43 *40 *41 15 *57 *66 65 64 | 6
|*44 *39 35 *14 01 *16 *58 *63 62 | 5
| __ __ __ __ 29 __ *17 *59 *61 | 4
| __ __ __ __ __ 27 __ *18 *60 | 3
| __ __ 32 __ __ __ 24 21 *19 | 2
| __ 09 __ __ __ __ *23 22 *20 | 1
'------------------------------------'
a b c d e f g h i
Is the knot untied ?
Update (Nov 10, 2025)
,------------------------------------,
|*48 49 *53 69 *70 81 *80 *78 *76 | 9
| 47 *50 52 54 *68 *71 79 77 *75 | 8
|*46 *51 42 *55 56 67 *72 73 *74 | 7
|*45 *43 *40 *41 15 *57 *66 65 64 | 6
|*44 *39 35 *14 01 *16 *58 *63 62 | 5
| __ __ __ __ 29 __ *17 *59 *61 | 4 02,13,34,36,38 [locked!]
| __ __ __ __ __ 27 __ *18 *60 | 3 33,28,30
| __ __ 32 __ __ __ 24 21 *19 | 2
| __ 09 __ __ __ __ *23 22 *20 | 1
'------------------------------------'
a b c d e f g h i
(02,13,34,36,38) are locked into row 4 with (02)f4 forced,
and there are only two possible places for 28: e3, f4,
=> 36.(02)f4!, 37.(28)e3!, 38.(03)g3, 39.(04)f2, 40.(25)f1,
41.(30)d3! (since d4 is taken!) 42.(26)e2, 43.(05)e1
,------------------------------------,
|*48 49 *53 69 *70 81 *80 *78 *76 | 9
| 47 *50 52 54 *68 *71 79 77 *75 | 8
|*46 *51 42 *55 56 67 *72 73 *74 | 7
|*45 *43 *40 *41 15 *57 *66 65 64 | 6
|*44 *39 35 *14 01 *16 *58 *63 62 | 5
| __ __ __ __ 29 *02 *17 *59 *61 | 4 13,34,36,38 [locked!]
| __ __ __ *30 *28 27 *03 *18 *60 | 3 33
| __ __ 32 __ *26 *04 24 21 *19 | 2
| __ 09 __ __ *05 *25 *23 22 *20 | 1
'------------------------------------'
a b c d e f g h i
Now it is almost over! what would be a final move ?
Update Nov 11, 2025
,------------------------------------,
|*48 49 *53 69 *70 81 *80 *78 *76 | 9
| 47 *50 52 54 *68 *71 79 77 *75 | 8
|*46 *51 42 *55 56 67 *72 73 *74 | 7
|*45 *43 *40 *41 15 *57 *66 65 64 | 6
|*44 *39 35 *14 01 *16 *58 *63 62 | 5
| __ __ __ __ 29 *02 *17 *59 *61 | 4 13,34,36,38 [locked!]
| __ __ __ *30 *28 27 *03 *18 *60 | 3 12,33,37 [locked!]
| __ __ 32 __ *26 *04 24 21 *19 | 2 31 only place is d2
| __ 09 __ __ *05 *25 *23 22 *20 | 1
'------------------------------------'
a b c d e f g h i
44.(31)d2! (see comments at side of the grid) and now only singles remain.
48 49 53 69 70 81 80 78 76
47 50 52 54 68 71 79 77 75
46 51 42 55 56 67 72 73 74
45 43 40 41 15 57 66 65 64
44 39 35 14 1 16 58 63 62
38 36 13 34 29 2 17 59 61
37 12 33 30 28 27 3 18 60
11 8 32 31 26 4 24 21 19
10 9 7 6 5 25 23 22 20
I propose the following Sudoku-X puzzle.
I have solved it (manually) in TWO steps (krakenless).
(generated and displayed with Sudoku6Explainer)
Grid after basics
+-------------------+-------------------+
| 13 145 6 | 145 123 1234 | 6
| 1345 2 1345 | 13456 136 13456 | 5
+-------------------+-------------------+
| 146 3 14 | 156 126 125 | 4
| 1256 156 125 | 136 4 13 | 3
+-------------------+-------------------+
| 12346 146 1234 | 134 5 1346 | 2
| 13456 1456 135 | 2 136 146 | 1
+-------------------+-------------------+ Sudoku-X
a b c d e f
Update (Nov 10, 2025)
+-------------------+-------------------+
| 13 145 6 | 145 123 1234 | 6
| 1345 2 1345 | 13456 136 13456 | 5
+-------------------+-------------------+
| 146 3 4-1 | 156 126 125 | 4
| 1256 156 125 | 136 4 13 | 3
+-------------------+-------------------+
| 12346 146 1234 | 134 5 1346 | 2
| 13456 1456 135 | 2 136 146 | 1
+-------------------+-------------------+ Sudoku-X
a b c d e f
For the first move, how to eliminate (1)c4 ?
Update (Nov 11, 2025)
+-------------------+-------------------+
|*13 145 6 | 145 123 1234 | 6
| 1345 2 1345 | 13456 136 13456 | 5
+-------------------+-------------------+
|*146 3 *4-1 |*156 *126 125 | 4
| 1256 156 125 |*136 4 13 | 3
+-------------------+-------------------+
| 12346 146 1234 | 134 5 1346 | 2
| 13456 1456 135 | 2 136 146 | 1
+-------------------+-------------------+ Sudoku-X
a b c d e f
Move 1 uses the marked cells (power of diagonal!):
either (4)c4 or there the naked pair (13)a6.d3.
The elimination of (1)c4 leads to:
+-------------------+-------------------+
| 13 145 6 | 145 123 1234 | 6
| 1345 2 135 | 13456 136 13456 | 5
+-------------------+-------------------+
| 16 3 4 | 156 126 125 | 4
| 1256 156 125 | 136 4 13 | 3
+-------------------+-------------------+
| 1236 16 123 | 134 5 1346 | 2
| 13456 1456 135 | 2 136 16 | 1
+-------------------+-------------------+
a b c d e f
How to finish the puzzle ?
In the game called Slitherlink, can you show all the details
proving that the following configuration is impossible ?
(My solution has a trivial initial observation, an easy Case 1 and Case 2 divided in two sub-cases)
We analyze the possible outcomes from this configuration but can already discard
all configurations in which the lower "2"-cell has vertical lines, or horizontal lines,
in both edges.
Also, this configuration
.------------------- | . . . . . | 2 | . . . . . | 2 | .___. . . . | | 2 |A. . . . . | x | . . . . .
and this
.------------------- | . . . . . | 2 | . . . . . | 2 | . . . . . | 2 | |A.___. . . . | x | . . . . .
are clearly impossible,
(dead end at corner A).
Case 1:
.-------------------
| . . . . .
| 2
| . . . . .
| 2
| .___. . . .
| 2 |
| . . . . .
| x
| . . . . .
Now the following is forced
.-------------------
| . .___.___. .
| x 2 |
| . .___. x . .
| | x 2 |
| .___. x . . .
| 2 |
| . . . . .
| x
| . . . . .
and this leads to an impossibility in the cell at the corner, reached by three lines.
.------------------- | . . . . . | 2 | . . . . . | 2 | . . . . . | | 2 | .___. . . . | x | . . . . .
The following is a forced move
.------------------- | . . . . . | 2 | . .B . . . | | 2 | . x .A . . . | | 2 x | .___. . . . | x | . . . . .
Case 2.1: If a vertical line exists at AB, it forces
.------------------- | . . . . . | | 2 | .C . . . . | | | 2 | . x .___.D . . | | 2 x | .___. . . . | x | . . . . .
and any continuation for the line meeting corner C will create a loop (impossible).
Case 2.2: the other possibility is to have the edge AB blocked, and then the bottom edge AD
of the "2"-cell in the middle needs to be blocked too, forcing the following configuration to be reached.
.------------------- | . .___.___. . | x 2 | | . .___. x . . | | x 2 | | . x . x . . . | | 2 x | .___. . . . | x | . . . . .
Now, we have an impossible situation in the cell at the corner, reached by three lines. □
The following Jigsaw Sudoku Layout is invalid. Why ?
(image created using SudokuExplainer)
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com