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Recent Puzzles (*1*)

Puzzle HP#15 (overall #137) (7x7 Hidoku Puzzle; proposed September 12, 2026)

I propose this newly created Hidoku puzzle (for a manual solution !)

Hidoku Puzzle

Hint (Update 3: move 2 solves the puzzle)
  .---------------------------.
7 | __  __  __  01  __  __  __|
6 | __  19  __  __  __  42  __|
5 | __  __  __  31  __  __  __|
4 | __  22  __  30  __  __  __|
3 | __  __  __  __  35  __  12|
2 | __  __  __  __  __  __  __|
1 | __  __  __  49  08  __  __|
  '---------------------------'
    a   b   c   d   e   f   g
    
Update 1 (Sept 13, 2026)

This puzzle has a very tough beginning, but after working
hard in the first move, placing a key number, only easy
deductions are needed afterwards ! 

Some hints for the key move 1:

. study important connections, like 01-08, 12-19, etc, and the
  possible paths for each connection.
. special attention to unique passages is very important, like
  f3, d3-f4, c4, and a few others.
. In summary: global view is better here than local considerations.
    
Update 2 (September 14, 2026)

  .---------------------------.
7 | __  __  __  01  __  __  __|
6 | __  19  __  __  __  42  __|
5 | __  __  __  31  __  __  __|
4 | __  22  __  30  __  __  __|
3 | __  __  __  __  35  __  12|
2 | __  __  __  __  __  __  __|
1 | __  __  __  49  08  __  __|
  '---------------------------'
    a   b   c   d   e   f   g
 
 For move 1 we consider the following possibilities:
 
                   I.1 42-49 takes d3,e4
                  /
 I. 01-08 takes c4 
                  \
                   I.2 42-49 takes e2,f3
 
                   II.1 42-49 passes by c4,e6, and disconnects 12-19!
                  /
II. 01-08 takes f3                        II.2.1 12-19 uses c4 [quick trouble!]
                  \                      /
                   II.2 42-49 takes e3,f4
                                         \
                                          II.2.2 12-19 uses c6 [quick trouble!]

                          III.1 42-49 takes c4,c6 -> disconnect 12-19!
                         /
III. 01-08(x) takes d3,e4
                         \
                          III.2 42-49(y) takes e2,f3 and also f4 or g4.
                                while 12-19(z) must use one of f4 or g4.
                                Then, 35-42(w) must go through d2, c4, e6,
                                disconnecting 12-19 [see below]
                             
                              .---------------------------.
                            7 | __  __  __  01  __  __  __|
                            6 | __  19  __  w_  __  42  __|
                            5 | __  __  __  31  __  __  __|
                            4 | __  22  w_  30  x_  yz  yz|
                            3 | __  __  __  x_  35  y_  12|
                            2 | __  __  __  w_  y_  __  __|
                            1 | __  __  __  49  08  __  __|
                              '---------------------------'
                                a   b   c   d   e   f   g

Apart from III.2 (shown above), we show the details of I.1 below:

42-49(y) takes d3,e4 then 12-19(z) must pass through d6,
         and through f4 or f5. But 31-35(w) must pass through f4 or f5.
         So f4,f5 is locked to those paths(zw). Also, one of 35-42(v),
         31-35(w) must use cell f3. This forces 42-49(y) to use cell 
         e5, and 31-35(w) must use e6. Now 12-19 is disconnected!

  .---------------------------.
7 | __  __  __  01  __  __  __|
6 | __  19  __  z_  w_  42  __|
5 | __  __  __  31  y_  zw  __|
4 | __  22  x_  30  y_ vzw  __|
3 | __  __  __  y_  35  vw  12|
2 | __  __  __  __  __  __  __|
1 | __  __  __  49  08  __  __|
  '---------------------------'
    a   b   c   d   e   f   g
 
From this long analysis, we conclude

1.(02)c6!!! with 12 additional placements

we get

  .---------------------------.
7 |*18 *17 *16  01  __  __  __|
6 |*20  19 *02 *15  __  42  __|
5 |*21 *03  __  31 *14  __  __|
4 |*04  22  __  30  __ *13  __|
3 | __ *05  __  __  35  __  12|
2 | __  __  __ *07  __  __  __|
1 | __  __  __  49  08  __  __|
  '---------------------------'
    a   b   c   d   e   f   g
 
How to continue ?
    
Update 3 (Sept 15, 2026)
    
Part 2: 35-42(x) and 42-49(y)
must use, each, one of the passages
[e4](XX), and [f3,g4](YY).
So 11, must be at Row 2 and

            06  
  .---------------------------.
7 |*18 *17 *16  01  __  __  __|
6 |*20  19 *02 *15  __  42  __|
5 |*21 *03  __  31 *14  __  __|
4 |*04  22  __  30  XX *13  YY|
3 | __ *05  __  __  35  YY  12|
2 | __  __  __ *07  __  __  __|11
1 | __  __  __  49  08  __  __|
  '---------------------------'
    a   b   c   d   e   f   g  

14.(32)c5!!

After this the remaining moves
are easily found.

The final configuration is

  .---------------------------.
7 |*18 *17 *16  01 *39 *40 *41|
6 |*20  19 *02 *15 *38  42 *43|
5 |*21 *03 *32  31 *14 *37 *44|
4 |*04  22 *33  30 *36 *13 *45|
3 |*23 *05 *29 *34  35 *46  12|
2 |*24 *28 *06 *07 *48 *47 *11|
1 |*25 *26 *27  49  08 *09 *10|
  '---------------------------'
    a   b   c   d   e   f   g
    

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