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Write a detailed solution to the following hard Hidoku puzzle:
(Found by Albert.Lang)
I found an interesting reasonably simple and short (manual) solution to this puzzle
and for this reason I decided to propose it here.
(the restrictive rule of including the first and last digits in the givens is waived)
This pattern has the smallest number of clues for a 5x5 Hidoku with unique solution.
.-----------------------. |. . . 6 . |5 | | |. . *7 . 13 |4 | | |. *8 x . . |3 | | |9 . . . . |2 | | |. . . . . |1 '-----------------------' a b c d e
After the forced start, the possible values for x are very limited. For instance, for x=11, we must have
a1=25,b1=24 and the connection of 13 to 24 demands 10 cells, but placing 12 will destroy any possible way.
I propose the following Hidoku puzzle (my first Hidoku puzzle).
Fill the grid so that consecutive numbers must be neighbours horizontally, vertically, or diagonally.
Update 1 (Jul 12, 2025)
Remark: the initial grid below is correct.
,----------------------------,
| __ __ __ __ _4 __ 20 |7
| __ __ 16 __ __ 19 22 |6
| _8 __ __ __ __ __ __ |5
| __ __ __ _1 25 29 __ |4
| __ __ __ __ __ __ __ |3
| __ __ 32 __ 39 __ __ |2
| 49 __ __ 38 __ __ 41 |1
'----------------------------'
a b c d e f g JCO#1 (7x7 Hidoku)
The previous version of the edited image (.png) of the puzzle had two errors:
(16)b6 instead of the correct (16)c6, and (8)a5 was missing.
So, the image of the puzzle and the hint below only makes sense as of today (July 12).
I enjoyed greatly the task of creating this puzzle. For those willing to solve it
without guessing and willing to justify carefully each step, this is a tough puzzle.
There are two easy numbers at the start:
1.(21)f7 2.(30)e3
,----------------------------,
| __ __ __ __ 04 *21 20 |7
| __ __ 16 __ __ 19 22 |6
| 08 __ __ __ __ __ __ |5
| __ __ __ 01 25 29 __ |4
| __ __ __ __ *30 __ __ |3
| __ __ 32 __ 39 __ __ |2
| 49 __ __ 38 __ __ 41 |1
'----------------------------'
a b c d e f g JCO#1 (7x7 Hidoku)
(numbers with * are deduced and numbers without * were given)
We cannot link (4)e7 to (8)a5 using the route (5)d6-(4)c5. Why ?
This observation gives six more placements.
Update 2 (Jul 13, 2025)
After the moves
3.(6)c7! 4.(7)b6 5.(15)b7! 6.(14)a7 7.(13)a6 8.(12)b5
we reach the grid
,----------------------------,
|*14 *15 *06 __ 04 *21 20 |7
|*13 *07 16 __ __ 19 22 |6
| 08 *12 __ __ __ __ __ |5
| __ __ __ 01 25 29 __ |4
| __ __ __ __ *30 __ __ |3
| __ __ 32 __ 39 __ __ |2
| 49 __ __ 38 __ __ 41 |1
'----------------------------'
a b c d e f g JCO#1 (7x7 Hidoku)
(! means that a small deduction is involved)
How to proceed ?
Update (Jul 14, 2025)
We reached the first key configuration for this puzzle. Now,
. The route from (16)c6 to (19)f6 cannot go through d7/d6,e6 (Why ?)
. We cannot have both (17)d5, (18)e5 (why ?)
. (17)d6 and (18)d7 lead to an empty cell! (how ?)
Using these observations we arrive at
9.(17)d5!! 10.(18)d6! 11.(3)d6! 12.(5)d7 13.(31)d3! 14.(26)f3!
[!! means that the move is justified by more involved deduction]
We reach this configuration
,----------------------------,
|*14 *15 *_6 *_5 _4 *21 20 |7
|*13 *_7 16 *_3 *18 19 22 |6
| _8 *12 __ *17 __ __ __ |5
| __ __ __ _1 25 29 __ |4
| __ __ __ *31 *30 *26 __ |3
| __ __ 32 __ 39 __ __ |2
| 49 __ __ 38 __ __ 41 |1
'----------------------------'
a b c d e f g JCO#1 (7x7 Hidoku)
How to proceed ?
Update (July 16, 2025)
Now, to connect (49)a1 to (41)g1 we cannot take the path
that includes c1-d2-e1 (why ?). So,
15.(37)c1!
,----------------------------,
|*14 *15 *_6 *_5 _4 *21 20 |7
|*13 *_7 16 *_3 *18 19 22 |6
| _8 *12 __ *17 __ __ __ |5
| __ __ __ _1 25 29 __ |4
| __ __ __ *31 *30 *26 __ |3
| __ __ 32 __ 39 __ __ |2
| 49 __ *37 38 __ __ 41 |1
'----------------------------'
a b c d e f g JCO#1 (7x7 Hidoku)
How to proceed ? This is the second key situation in this puzzle.
A careful analysis of the left-side [EDIT (Jul 20): correct is right-side]
of the puzzle will produce the final deduction that solves the puzzle
with simple moves afterwards.
Update (Jul 20, 2025) The only two possible places for number 2 and the narrow passage at e1,d2,c3 can be used to solve this puzzle. The starting point is to study the consequences of (2)e5. This has an immediate effect on the right side that propagates through that narrow passage into certain q numbers being locked into q cells, leading to a contradiction. So, 16.(2)c5!! breaks the last resistance at solving this puzzle with easy placements. Btw, as always, I may be missing a much simpler way to solve the puzzle. This is the risk one must accept when decides to solve puzzles manually. To conclude: this puzzle involves reasonings with conflicting paths, narrow passages and locked sets (term borrowed from sudoku). 14 15 6 5 4 21 20 13 7 16 3 18 19 22 8 12 2 17 24 23 28 9 10 11 1 25 29 27 34 33 47 31 30 26 43 35 48 32 46 39 44 42 49 36 37 38 45 40 41
I propose the following Hidoku puzzle (my second Hidoku puzzle).
Update 1 (July 12, 2025)
This second puzzle is certainly easier than the first. One can get
many numbers making small deductions (like the basics in sudoku).
For reference, the initial grid is
,----------------------------,
| 38 __ __ __ __ __ 29 |7
| __ 37 36 __ 32 31 __ |6
| __ 41 __ __ 8 27 __ |5
| __ 5 __ __ __ 10 __ |4
| __ __ __ 17 12 __ __ |3
| __ 46 __ __ __ 21 __ |2
| __ __ 49 1 19 __ __ |1
'----------------------------'
a b c d e f g JCO#2 (7x7 Hidoku)
The basics in my solving has 16 moves.
The four first moves are 1.(9)e4 2.(11)f3 3.(28)g6 4.(30)f7
Update (Jul 13/14, 2025)
After the moves
1.(9)e4 2.(11)f3 3.(28)g6 4.(30)f7 5.(26)g5!
6.(25)g4 7.(24)g3 8.(23)g2 9.(22)g1 10.(39)b7!
11.(40)a6 12.(20)f1! 13.(18)e2 14.(33)e7!
15.(34)d7 16.(35)c7
we reach the configuration
,----------------------------,
| 38 *39 *35 *34 *33 *30 29 |7
|*40 37 36 __ 32 31 *28 |6
| __ 41 __ __ 8 27 *26 |5
| __ 5 __ __ *9 10 *25 |4
| __ __ __ 17 12 *11 *24 |3
| __ 46 __ __ *18 21 *23 |2
| __ __ 49 1 19 *20 *22 |1
'----------------------------'
a b c d e f g JCO#2 (7x7 Hidoku)
How to proceed ?
Update (Jul 18, 2025)
This position is interesting. We have two possibilities for 13.
In the case of (13)d2, we get a sequence of forced moves resulting
in 6,7,15,16 locked at the cells c4,c5,d4,d5,d6 and either 42 xor
4 must be there. But in either case we arrive at a disconnection
between consecutive numbers. So,
17.(13)d4!! and the remaining moves are easy.
38 39 35 34 33 30 29
40 37 36 7 32 31 28
42 41 6 14 8 27 26
43 5 15 13 9 10 25
44 4 16 17 12 11 24
45 46 3 2 18 21 23
47 48 49 1 19 20 22
I propose the following Hidoku puzzle (my third Hidoku puzzle).
This is the last Hidoku puzzle (for now), being roughly at the same level as #60.
Grid with Givens
,----------------------------------,
|__ 75 __ __ __ __ __ __ __| 9
|__ 74 __ __ 33 36 __ __ __| 8
|__ __ __ 44 __ __ __ 30 __| 7
|__ 72 __ 45 __ 21 __ 19 __| 6
|__ __ 71 __ __ __ 18 __ __| 5
|64 62 __ __ 81 __ __ 17 15| 4
|63 56 __ __ 01 __ __ 12 11| 3
|__ 55 __ __ 02 __ __ 08 __| 2
|__ __ __ 52 __ 05 __ __ __| 1
'----------------------------------'
a b c d e f g h i JCO#3 (Hidoku)
(Jul 15, 2025 - revised Jul 28, 2025)
EDIT: I revised the whole solution. The initial
move 1. (20)g6 of the previous version was found
a lot later [paper and pencil solution].
The first moves are (indicated with * in the grid):
1.(80)d5 2.(79)c6 3.(78)b7 4.(77)a8 5.(76)a9
5.(14)h5 7.(13)g4 8.(10)i2 9.(9)i1 10.(7)h1
11.(16)i5 12.(29)i6 13.(28)i7
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
| __ *78 __ 44 __ __ __ 30 *28| 7
| __ 72 *79 45 __ 21 __ 19 *29| 6
| __ __ 71 *80 __ __ 18 *14 *16| 5
| 64 62 __ __ 81 __ *13 17 15| 4
| 63 56 __ __ 01 __ __ 12 11| 3
| __ 55 __ __ 02 __ __ 08 *10| 2
| __ __ __ 52 __ 05 __ *07 *09| 1
'-----------------------------------'
a b c d e f g h i
How to proceed ?
Update (Jul 18, 2025 - revised Jul 28, 2025)
14.(73)a7! (why ?)
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
|*73 *78 __ 44 __ __ __ 30 *28| 7
| __ 72 *79 45 __ 21 __ 19 *29| 6
| __ __ 71 *80 __ __ 18 *14 *16| 5
| 64 62 __ __ 81 __ *13 17 15| 4
| 63 56 __ __ 01 __ __ 12 11| 3
| __ 55 __ __ 02 __ __ 08 *10| 2
| __ __ __ 52 __ 05 __ *07 *09| 1
'-----------------------------------'
a b c d e f g h i
What would be a good next move ?
Update (Jul 21, 2025 - revised Jul 28, 2025)
15.(65)a5! 16.(66)a6 17.(67)b5 18.(68)c4
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
|*73 *78 __ 44 __ __ __ 30 *28| 7
|*66 72 *79 45 __ 21 __ 19 *29| 6
|*65 *67 71 *80 __ __ 18 *14 *16| 5
| 64 62 *68 __ 81 __ *13 17 15| 4
| 63 56 __ __ 01 __ __ 12 11| 3
| __ 55 __ __ 02 __ __ 08 *10| 2
| __ __ __ 52 __ 05 __ *07 *09| 1
'-----------------------------------'
a b c d e f g h i
19.(70)d4 20.(61)c3 21.(69)d3
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
|*73 *78 __ 44 __ __ __ 30 *28| 7
|*66 72 *79 45 __ 21 __ 19 *29| 6
|*65 *67 71 *80 __ __ 18 *14 *16| 5
| 64 62 *68 *70 81 __ *13 17 15| 4
| 63 56 *61 *69 01 __ __ 12 11| 3
| __ 55 __ __ 02 __ __ 08 *10| 2
| __ __ __ 52 __ 05 __ *07 *09| 1
'-----------------------------------'
a b c d e f g h i
We have reached a key position. How to continue ?
Update (Jul 28, 2025)
7 numbers 60,59,58,57,54,53,51 locked
at 7 cells: a1,a2,b1,c1,c2,d2,e1
22.(51)e1 23.(53)d2 24.(60)c2 25.(57)a2
26.(58)a1 27.(59)b1 28.(54)c1 29.(50)f2
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
|*73 *78 __ 44 __ __ __ 30 *28| 7
|*66 72 *79 45 __ 21 __ 19 *29| 6
|*65 *67 71 *80 __ __ 18 *14 *16| 5
| 64 62 *68 *70 81 __ *13 17 15| 4
| 63 56 *61 *69 01 __ __ 12 11| 3
|*57 55 *60 *53 02 *50 __ 08 *10| 2
|*58 *59 *54 52 *51 05 __ *07 *09| 1
'-----------------------------------'
a b c d e f g h i
30.(3)f3 31.(04)g2 32.(6)g1 33.(49)g3
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
|*73 *78 __ 44 __ __ __ 30 *28| 7
|*66 72 *79 45 __ 21 __ 19 *29| 6
|*65 *67 71 *80 __ __ 18 *14 *16| 5
| 64 62 *68 *70 81 ___*13 17 15| 4
| 63 56 *61 *69 01 *03 *49 12 11| 3
|*57 55 *60 *53 02 *50 *04 08 *10| 2
|*58 *59 *54 52 *51 05 *06 *07 *09| 1
'-----------------------------------'
a b c d e f g h i
34.(48)f4
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
|*73 *78 __ 44 __ __ __ 30 *28| 7
|*66 72 *79 45 __ 21 __ 19 *29| 6
|*65 *67 71 *80 __ __ 18 *14 *16| 5
| 64 62 *68 *70 81 *48 *13 17 15| 4
| 63 56 *61 *69 01 *03 *49 12 11| 3
|*57 55 *60 *53 02 *50 *04 08 *10| 2
|*58 *59 *54 52 *51 05 *06 *07 *09| 1
'-----------------------------------'
a b c d e f g h i
How to finish the puzzle ?
Update (July 30, 2025)
35.(47)f5!
[(47)e5 is not possible: (46)e6 creates a problem to fill f5
with 22,23 and link them to (28)i7 since (20),(31)block the path]
36.(46)e5
,-----------------------------------,
|*76 75 __ __ __ __ __ __ __| 9
|*77 74 __ __ 33 36 __ __ __| 8
|*73 *78 __ 44 __ __ __ 30 *28| 7
|*66 72 *79 45 __ 21 __ 19 *29| 6
|*65 *67 71 *80 *46 *47 18 *14 *16| 5
| 64 62 *68 *70 81 *48 *13 17 15| 4
| 63 56 *61 *69 01 *03 *49 12 11| 3
|*57 55 *60 *53 02 *50 *04 08 *10| 2
|*58 *59 *54 52 *51 05 *06 *07 *09| 1
'-----------------------------------'
a b c d e f g h i
Now, we need a last major deduction to remove the last hurdle.
The hint is to study the correct place for 32.
Update (Jul 31, 2025)
37.(32)f7 would force 38.(20)g6 39.(22)g7! 40.(31)g8 making
impossible to connect 22 to 28.
So, 37.(32)f9! 38.(31)g8 and now there is only one way to
fill out the right-hand side of the puzzle. The remaining
moves are easy. The unique solution is
76 75 41 34 35 32 24 25 26
77 74 42 40 33 36 31 23 27
73 78 43 44 39 37 22 30 28
66 72 79 45 38 21 20 19 29
65 67 71 80 46 47 18 14 16
64 62 68 70 81 48 13 17 15
63 56 61 69 01 03 49 12 11
57 55 60 53 02 50 04 08 10
58 59 54 52 51 05 06 07 09
I could not resist proposing this nice puzzle by Evert).
(king's walk problem with initial and final positions not given).
,----------------------------------,
|__ 22 20 __ __ __ __ 80 __| 9
|__ __ __ __ __ __ 73 __ __| 8
|__ __ __ 69 __ __ __ __ 77| 7
|35 __ 66 __ 64 05 __ __ __| 6
|__ __ 27 __ __ __ __ __ __| 5
|__ 39 __ 03 __ __ __ __ 58| 4
|__ 40 __ 02 30 __ __ __ 12| 3
|__ 43 __ __ __ __ __ __ __| 2
|__ __ __ __ 47 __ 10 __ 52| 1
'----------------------------------'
a b c d e f g h i Evert
Update (July 22, 2025)
1.(11)h2 2.(4)e5 3.(28)d5 4.(29)e4 5.(65)d6
,----------------------------------,
|__ 22 20 __ __ __ __ 80 __| 9
|__ __ __ __ __ __ 73 __ __| 8
|__ __ __ 69 __ __ __ __ 77| 7
|35 __ 66 *65 64 05 __ __ __| 6
|__ __ 27 *28 *04 __ __ __ __| 5
|__ 39 __ 03 *29 __ __ __ 58| 4
|__ 40 __ 02 30 __ __ __ 12| 3
|__ 43 __ __ __ __ __ *11 __| 2
|__ __ __ __ 47 __ 10 __ 52| 1
'----------------------------------'
a b c d e f g h i
6.(34)b5! 7.(33)c4 8.(32)c3 9.(31)d2 10.(26)b6
,----------------------------------,
|__ 22 20 __ __ __ __ 80 __| 9
|__ __ __ __ __ __ 73 __ __| 8
|__ __ __ 69 __ __ __ __ 77| 7
|35 *26 66 *65 64 05 __ __ __| 6
|__ *34 27 *28 *04 __ __ __ __| 5
|__ 39 *33 03 *29 __ __ __ 58| 4
|__ 40 *32 02 30 __ __ __ 12| 3
|__ 43 __ *31 __ __ __ *11 __| 2
|__ __ __ __ 47 __ 10 __ 52| 1
'----------------------------------'
a b c d e f g h i
11.(36)a5! 12.(37)a4 13.(38)a3
,-----------------------------------,
| __ 22 20 __ __ __ __ 80 __| 9
| __ __ __ __ __ __ 73 __ __| 8
| __ __ __ 69 __ __ __ __ 77| 7
| 35 *26 66 *65 64 05 __ __ __| 6
|*36 *34 27 *28 *04 __ __ __ __| 5
|*37 39 *33 03 *29 __ __ __ 58| 4
|*38 40 *32 02 30 __ __ __ 12| 3
|*41 43 *01 *31 __ __ __ *11 __| 2
|*42 *44 *45 *46 47 __ 10 __ 52| 1
'-----------------------------------'
a b c d e f g h i
14.(41)a2! 15.(42)a1 16.(44)b1!
17.(46)d1 18.(01)c2! 19.(45)c1
How to proceed ?
Update (Jul 23, 2025)
20.(13)h4!
(h3 can't have 13 because of problems at h1,i2;
i2 can't have 13: it looses connection to 20)
,-----------------------------------,
| __ 22 20 __ __ __ __ 80 __| 9
| __ __ __ __ __ __ 73 __ __| 8
| __ __ __ 69 __ __ __ __ 77| 7
| 35 *26 66 *65 64 05 __ __ __| 6
|*36 *34 27 *28 *04 __ __ __ __| 5
|*37 39 *33 03 *29 __ __ *13 58| 4
|*38 40 *32 02 30 __ __ __ 12| 3
|*41 43 01 *31 __ __ __ *11 __| 2
|*42 *44 *45 *46 47 __ 10 __ 52| 1
'-----------------------------------'
a b c d e f g h i
Now there is only on viable place for 51,
giving 14 more placements and reaching
the last key position of this puzzle.
(Update Jul 24, 2025)
After all placements, we get
,-----------------------------------,
| __ 22 20 __ __ __ __ 80 __| 9
| __ __ __ __ __ __ 73 __ __| 8
| __ __ __ 69 __ __ __ __ 77| 7
| 35 *26 66 *65 64 05 __ __ __| 6
|*36 *34 27 *28 *04 *06 *14 *57 *59| 5
|*37 39 *33 03 *29 *07 *56 *13 58| 4
|*38 40 *32 02 30 *08 *55 *54 12| 3
|*41 43 01 *31 *48 *09 *50 *11 *53| 2
|*42 *44 *45 *46 47 *49 10 *51 52| 1
'-----------------------------------'
a b c d e f g h i
Now, looking carefully at the grid, certain
quantity q of numbers are locked into q places.
This observation basically solves the puzzle.
Update (Jul 26, 2025)
,-----------------------------------,
| x_ 22 20 __ __ __ __ 80 __| 9
| x_ x_ x_ __ __ __ 73 __ __| 8
| x_ x_ x_ 69 __ __ __ __ 77| 7
| 35 *26 66 *65 64 05 __ __ __| 6
|*36 *34 27 *28 *04 *06 *14 *57 *59| 5
|*37 39 *33 03 *29 *07 *56 *13 58| 4
|*38 40 *32 02 30 *08 *55 *54 12| 3
|*41 43 01 *31 *48 *09 *50 *11 *53| 2
|*42 *44 *45 *46 47 *49 10 *51 52| 1
'-----------------------------------'
a b c d e f g h i
Numbers 25,24,23,21,19,67,68 are locked into
the region with locations a7,a8,a9,b7,b8,c7,c8
(marked with x above) and their places are easy
to see:
26.(19)c8 27.(68)c7 28.(21)b8 29.(67)b7
30.(23)a9 31.(24)a8 31.(25)a7
,-----------------------------------,
|*23 22 20 __ __ __ __ 80 __| 9
|*24 *21 *19 __ __ __ 73 __ __| 8
|*25 *67 *68 69 __ __ __ __ 77| 7
| 35 *26 66 *65 64 05 __ __ __| 6
|*36 *34 27 *28 *04 *06 *14 *57 *59| 5
|*37 39 *33 03 *29 *07 *56 *13 58| 4
|*38 40 *32 02 30 *08 *55 *54 12| 3
|*41 43 01 *31 *48 *09 *50 *11 *53| 2
|*42 *44 *45 *46 47 *49 10 *51 52| 1
'-----------------------------------'
a b c d e f g h i
32.(15)g6! and easy singles to the end.
23 22 20 18 71 72 81 80 79
24 21 19 70 17 62 73 74 78
25 67 68 69 63 16 61 75 77
35 26 66 65 64 5 15 60 76
36 34 27 28 4 6 14 57 59
37 39 33 3 29 7 56 13 58
38 40 32 2 30 8 55 54 12
41 43 1 31 48 9 50 11 53
42 44 45 46 47 49 10 51 52