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Recent Puzzles (*1*)

Puzzle HP#14 (overall #136) (7x7 Hidoku Puzzle; proposed August 31, 2026)

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

Hidoku Puzzle

Hint (Update 2: truly complex fifth move!)
  .---------------------------.
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)

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)
    
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 -> the path from 2 to 20 leaves no room to 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 no room for 38
 ||          \     /
 ||          (43)g3
 ||                \
 ||                 (3)e1!!,(4)d1!,(5)c2, (44)f4!, now path 35 -> 39 leaves no room 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 ?
    

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Created: February 12, 2024

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