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Recent Puzzles (1)

Puzzle HP#7 (overall #82) (9x9 Hidoku Puzzle; proposed Oct 26, 2025)

I propose the following (tough!) Hidoku puzzle to be solved manually.

Hidoku Puzzle

Hint (New update)

,----------------------------------,
|__  __  61  __  59  58  __  __  __| 9
|__  __  __  39  __  __  42  __  52| 8
|65  __  __  __  19  __  __  __  51| 7
|__  35  __  __  __  __  __  __  __| 6
|67  __  15  __  01  03  __  45  __| 5
|__  33  __  08  __  __  __  46  __| 4
|69  __  __  __  11  __  __  __  81| 3
|__  __  __  29  28  27  26  __  __| 2
|__  __  73  __  __  __  __  __  __| 1
'----------------------------------'
 a   b   c   d   e   f   g   h   i  JCO#5 (Hidoku)

Update (Oct 28, 2025)
    
Step 1: 5 immediate placements.

,-----------------------------------,
| __  __  61 *60  59  58  __  __  __| 9
| __  __  __  39 *40  __  42  __  52| 8
| 65  __  __  __  19  __  __  __  51| 7
|*66  35  __  __  __  __  __  __  __| 6
| 67 *34  15  __  01  03  __  45  __| 5
|*68  33  __  08  __  __  __  46  __| 4
| 69  __  __  __  11  __  __  __  81| 3
| __  __  __  29  28  27  26  __  __| 2
| __  __  73  __  __  __  __  __  __| 1
'-----------------------------------'
  a   b   c   d   e   f   g   h   i

Now, for the next number, further analysis
is required to make progress.

Update (Oct 29, 2025)
    
Step 2:

. We first notice that we can't have 
e3,d4 both used for the path (12-13-14) because
it would block any possible path from 01 to 08.
=> * 12 can't go to f3 or f4 *

Now, either (12)d3 or (12)e4 is true.
BUT (12) e4 blocks the path 01-08, because
from above, (12)e4 -> (13)d2, (14)c3

=> 6.(12)d3!! and several placements follow

,-----------------------------------,
| __  __  61 *60  59  58  __  __  __| 9
| __  __  __  39 *40  __  42  __  52| 8
| 65  __  __  __  19  __  __  __  51| 7
|*66  35  __  __  __  __  __  __  __| 6
| 67 *34  15  __  01  03  __  45  __| 5
|*68  33  __  08  __  __  __  46  __| 4
| 69  __  __ *12  11  __  __  __  81| 3
| __  __  __  29  28  27  26  __  __| 2
| __  __  73  __  __  __  __  __  __| 1
'-----------------------------------'
  a   b   c   d   e   f   g   h   i

Update (Oct 31, 2025)

7.(14)c3! 8.(13)c3 9.(32)b3 10.(30)c2
11.(31)b2, 12.(70)a2, 13.(71)a1, 14.(72)b1
15.(74)d1, 16.(75)e1, 17.(76)f1, 18.(77)g1
19.(07)d5, 20.(09)e4 and we reach the following

,-----------------------------------,
| __  __  61 *60  59  58  __  __  __| 9
| __  __  __  39 *40  __  42  __  52| 8
| 65  __  __  __  19  __  __  __  51| 7
|*66  35  __  __  __  __  __  __  __| 6
| 67 *34  15 *07  01  03  __  45  __| 5
|*68  33 *14  08 *09  __  __  46  __| 4
| 69 *32 *13 *12  11  __  __  __  81| 3
|*70 *31 *30  29  28  27  26  __  __| 2
|*71 *72  73 *74 *75 *76 *77  __  __| 1
'-----------------------------------'
  a   b   c   d   e   f   g   h   i

How to continue ?

Update (Nov 1, 2025)
    
Clearly, the sole passage e6 is the key, being
critical to the path 01-07. There are 9 numbers
confined into 10 cells and a key inference from
this observation basically solves the puzzle.

Past Puzzles (82)

Past proposed 9x9 CLASSIC SUDOKU PUZZLES (35) are HERE
Past proposed SLITHERLINK PUZZLES (15) are HERE
Past proposed 9x9 JIGSAW SUDOKU PUZZLES (6) are HERE
Past proposed 6x6 SUDOKU-X PUZZLES (8) are HERE
Past proposed LATIN SQUARES PUZZLES (6) are HERE
Past proposed HIDOKU PUZZLES (6) are HERE
Past proposed 6x6 CLASSIC SUDOKU PUZZLES (5) are HERE
Past proposed HASHI PUZZLES (1) are HERE

Problems

Slitherlink and Jigsaw Sudoku Layouts

Problem #1

Slitherlink

In the game called Slitherlink, can you show all the details

proving that the following configuration is impossible ?

Impossible pattern 222x

Hidden solution

Part 1

(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).

Part 2

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.

Part 3

Case 2:

.-------------------
| .   .   .   .   . 
|           2       
| .   .   .   .   . 
|       2           
| .   .   .   .   . 
| | 2               
| .___.   .   .   . 
| x                 
| .   .   .   .   .

The following is a forced move

.-------------------
| .   .   .   .   . 
|           2       
| .   .B  .   .   . 
| |     2           
| . x .A  .   .   . 
| | 2 x             
| .___.   .   .   . 
| x                 
| .   .   .   .   .

Part 3.1

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).

Part 3.2

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. □

(Using symmetry, the proven result establishes a well-known slitherlink pattern)