Welcome!
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).
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)
The following 5x5 Latin Squares Puzzle (generated with SudokuExplainer)
is rated SER = 8.3, and can be solved (manually) in four main steps.
(image created using SudokuExplainer)
First write all candidates in each cell.
+-------------------------+
| 23 13 5 123 4 | 5
| 1 345 24 235 23 | 4
| 34 2 14 13 5 | 3
| 245 145 3 125 12 | 2
| 235 135 12 4 123 | 1
+-------------------------+
a b c d e Latin squares
+-------------------------+
| 23 13 5 123 4 | 5
| 1 345 24 25-3 23 | 4
| 34 2 14 13 5 | 3
| 245 145 3 125 12 | 2
| 235 135 12 4 123 | 1
+-------------------------+
a b c d e Latin squares
Step 1: We can eliminate (3)d4 using a sequence of bivalued cells.
Step 2: the harder part! (the reason for that SE rating).
,---------------------,
| 23 13 5 123 4 | 5
| 1 345 24 5-2 23 | 4
| 34 2 14 13 5 | 3
| 245 145 3 125 12 | 2
| 235 135 12 4 123 | 1
'---------------------'
a b c d e Latin squares
The suggestion is to study carefully the grid (above)
and try to find a way to show that 2 is false at that same cell d4.
If Step 2 is done, the puzzle can be solved in two more moves.
For step 3, the configuration is:
,-------------------------,
| 23 13 5 123 4 | 5
| 1 34 24 5 23 | 4
| 34 2 14 13 5 | 3
| 45 45 3 2-1 12 | 2
| 235 135 12 4 123 | 1
'-------------------------'
a b c d e Latin squares
One can eliminate (1) d2, using a simple chain wih 4 strong links.
For the last move, there is a pretty, simple idea! (see configuration below)
,---------------------,
| 2 13 5 13 4 |5
| 1 34 24 5 23 |4
| 34 2 14 13 5 |3
| 45 45 3 2 1 |2
| 35 135 12 4 23 |1 Latin squares
'---------------------'
a b c d e
Write a detailed solution to the following hard Hidoku puzzle:
(Found recently 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.
The following puzzle is my first Hashi puzzle.
,-----------------------------------,
| 2 4 1 | 9
| |
| 2 1 2 2 | 8
| |
| 3 3 | 7
| |
| | 6
| |
| 2 4 3 | 5
| |
| 4 4 4 2 | 4
| |
| | 3
| |
| 1 2 3 2 | 2
| |
| 2 3 | 1 JCO#1 (9x9 Hashi)
'-----------------------------------'
a b c d e f g h i
(3)i1,(3)b7,(4)a4 are good places to start.
The sequence of inferences follow without obstruction,
leading quickly to
,-----------------------------------,
| *2*=====*4*---------*1* | 9
| | |
|*2*---------*1* | *2*---------*2*| 8
| | | | | |
| | *3*=========*3* | | | 7
| | | | | |
| | | | | | 6
| | | | | |
| | 2*-------------*4*=====*3* | | 5
| | | | |
|*4*=====*4*-----*4*=====*2* | | | 4
| | | | | | |
| | | | | | | 3
| | | | | | |
|*1* *2*-----*3*---------*2* | | 2
| | |
| *2*=========================*3*| 1
'-----------------------------------'
a b c d e f g h i
This interesting Classic Sudoku (6x6) puzzle can be solved in three steps.
(puzzle found with Sukaku 6x6Explainer)
After basics, the configuration is as follows.
,-----------------------------------,
6 | 2 *16 3 | 156 15 4 |
5 |*16 4 5 | 2 3 *16 |
|----------------+------------------|
4 | 1456 2 146 | 1456 145 3 |
3 | 3 *(5)16 146 | 1456 1245 *(2)16 |
|----------------+------------------|
2 | 14 3 2 | 14 6 5 |
1 | 1456 156 146 | 3 124 12 |
'-----------------------------------'
a b c d e f
As usual, many ways are possible.
The strong link (5)b3=(2)f3 is nice
(internal guardians of the bivalued oddagon *(16))
and leads to placements: +5 b3, +5 a1 (how ?)
Move 2 is a simple skyscraper and move 3 is similar (same idea) to move 1.
I propose the following 6x6 Classic Sudoku puzzle.
(puzzle found with Sukaku 6x6Explainer)
After no basics, the configuration is as follows.
+----------------+----------------+
| 26 3 24 | 2456 2456 1 | 6
| 5 126 124 | 3 246 46 | 5
+----------------+----------------+
| 23 25 6 | 45 1 345 | 4
| 13 4 15 | 56 356 2 | 3
+----------------+----------------+
| 126 1256 3 | 2456 2456 456 | 2
| 4 256 25 | 1 2356 356 | 1
+----------------+----------------+
a b c d e f
Update (March 18, 2025)
+----------------+----------------+
| 26 3 24 | 2456 2456 1 | 6
| 5 126 124 | 3 246 46 | 5
+----------------+----------------+
| 23 25 6 | 45 1 345 | 4
| 13 4 15 | 56 356 2 | 3
+----------------+----------------+
| 16-2 1256 3 | 2456 2456 456 | 2
| 4 256 25 | 1 2356 356 | 1
+----------------+----------------+
a b c d e f
For step 1: (2)a2 is easily shown to be false, using (1)a2=(1)a3.
For step 2: there is an almost turbot fish on 6 using cells f2,f5,b5,a6
that eliminates (6)a2, solving the puzzle.
I propose the following (interesting!) 6x6 Latin Squares Puzzle
that can be solved (manually) in five main steps.
(puzzle and image generated with SudokuExplainer)
After no basics, the configuration is as follows.
+-------------------------------------+
| 24 124 6 134 5 13 | 6
| 25 125 235 13 6 4 | 5
| 456 456 1 2 34 356 | 4
| 46 146 34 5 134 2 | 3
| 3 12456 245 146 124 156 | 2
| 1 3 245 46 24 56 | 1
+-------------------------------------+ LS
a b c d e f
Update (March 18, 2025)
+-------------------------------------+
| 24 124 6 134 5 13 | 6
| 25 125 235 13 6 4 | 5
| 456 456 1 2 34 356 | 4
| 46 146 34 5 134 2 | 3
| 3 12456 245 46-1 124 156 | 2
| 1 3 245 46 24 56 | 1
+-------------------------------------+ LS
a b c d e f
For Step 1, there is an M-wing that eliminates (1)d2,
that creates a Naked Pair (46)d1.d2, that gives another
NP(13)d6.f6.
---
+-------------------------------------+
| 24 24 6 13 5 13 | 6
| 25 125 235 13 6 4 | 5
| 456 456 1 2 34 356 | 4
| 46 146 34 5 13-4 2 | 3
| 3 12456 245 46 124 156 | 2
| 1 3 245 46 24 56 | 1
+-------------------------------------+ LS
a b c d e f
For Step 2, a five strong linked chain shows that (4)e3 is false.
The ALS (124)e1.e2 has a role in this chain.
---
+-------------------------------------+
| 24 24 6 13 5 13 | 6
| 25 125 235 13 6 4 | 5
| 456* 456* 1 2 34 36-5 | 4
| 46* 146* 34 5 13 2 | 3
| 3 12456 245 46 124 156 | 2
| 1 3 245 46 24 56 | 1
+-------------------------------------+ LS
a b c d e f
Step 3 is nice and simple: a chain using the guardians of the
UR(46)a3,a4,b3,b4 proves that (5)f4 is false.
---
+-------------------------------------+
| 24 24 6 13 5 13 | 6
| 25 125 235 13 6 4 | 5
| 456 456 1 2 34 36 | 4
| 46 146 34 5 13 2 | 3
| 3 12456 245 46 124 156 | 2
| 1 3 245 46 24 56 | 1
+-------------------------------------+ LS
a b c d e f
How to proceed from here ?
Update (March 21, 2025)
For Step 4, we can remove (6)a4 using and AHS M-wing or an ALS W-wing.
This gives only one placement (+6) a3, but now b3 is a bivalued cell, and
we can finish the puzzle with a pretty Y-wing with transport,
eliminating (4)b4, (4)b6, and solving the puzzle with singles.
This 6x6 Latin Squares Puzzle ("spiral") is solvable in just one step. Can you find it ?
(puzzle and image generated with SudokuExplainer)
After basics (3 placements), the configuration is as follows.
+------------------------------+
| 46-2 26 5 24 3 1 | 6
| 5 236 234 1 46 36 | 5
| 36 4 1 35 56 2 | 4
| 1 356 34 345 2 356| 3
| 23 235 6 35-2 1 4 | 2
| 234 1 234 6 45 35 | 1
+------------------------------+
a b c d e f
The key is to remove (2)d2. Using a chain in 'spiral' (hence the name), we
actually get -2 a6, -2 d2, leaving only singles to the end.
("small space crowded with birds!")
I propose the following (tough!) Latin Squares Puzzle (SE = 8.3)
solvable in a couple steps (after basics).
(generated with SudokuExplainer)
After basics moves, one should get the following configuration:
+-------------------------------+
| 16 4 5 136 236 1236 | 6
| 156 12 3 156 4 126 | 5
| 2 13 4 1356 356 136 | 4
| 3 5 6 2 1 4 | 3
| 4 23 1 36 236 5 | 2
| 15 6 2 4 35 13 | 1
+-------------------------------+
a b c d e f
Update 1: Jun 1, 2025
The first step was the hardest for me.
It took some time staring at the board to find
a (pretty) almost W-wing that eliminates (6)f6.
+-------------------------------+
| 16 4 5 136 236 123-6| 6
| 156 12 3 156 4 126 | 5
| 2 13 4 1356 356 136 | 4
| 3 5 6 2 1 4 | 3
| 4 23 1 36 236 5 | 2
| 15 6 2 4 35 13 | 1
+-------------------------------+
a b c d e f
Update 2: Jun 03, 2025
The almost w-wing already mentioned has main cells at
a6, a1,f1,f4 with (3)f4 as the spoiler.
The elimination of (6)f6 creates the strong link (6)f4=(6)f6
+-------------------------------+
| 16 4 5 136 236 123 | 6
| 156 12 3 156 4 (6)12 | 5
| 2 13 4 1356 356 (6)3-1| 4
| 3 5 6 2 1 4 | 3
| 4 23 1 36 236 5 | 2
| 15 6 2 4 35 13 | 1
+-------------------------------+
a b c d e f
that can be used to eliminate (1)f4 [using an L3-wing].
Final Update: Jun 4, 2025
From the second move, we have the bivalue cell (36)f4 that
can be used for a W-wing. There is another wing for move 4,
that eliminates (6)e4 giving the first placement: +6 f4.
This leads to
+----------------------------+
| 16 4 5 136 26 123 | 6
| 56 12 3 56 4 12 | 5
| 2 13 4 135 35 6 | 4
| 3 5 6 2 1 4 | 3
| 4 23 1 36 26 5 | 2
| 15 6 2 4 35 13 | 1
+----------------------------+
a b c d e f
Now, one has to find one last wing to finish this puzzle with singles.
I propose the following (also tough!) Latin Squares Puzzle (SE = 8.3)
solvable in few more challenging steps (after basics).
(generated with SudokuExplainer)
After a naked pair elimination, one should get the following configuration:
+-------------------------------+
| 13 13 4 25 25 6 | 6
| 36 2 35 4 56 1 | 5
| 1346 5 123 126 246 234 | 4
| 346 346 235 256 1 2345 | 3
| 2 14 6 15 3 45 | 2
| 5 146 12 3 246 24 | 1
+-------------------------------+
a b c d e f
Quite different solving experience in comparison to puzzle #51!
(no sequence of wings and harder first step).
Update (June 6, 2025)
I have solved this puzzle twice and in both solutions the
first step is complex !
Solution 1 has only 2 steps and explores the BV cells (13)a6, (13)b6,
and the strong links (1)a4=(1)a6, (3)b3=(3)b6 to show that (1)a4 is false.
After that elimination (involving a very complex move), we get two placements and
+-------------------------------+
| 1 3 4 25 25 6 | 6
| 36 2 35 4 56 1 | 5
| 346 5 123 126 246 234 | 4
| 346 46 235 256 1 2345 | 3
| 2 14 6 15 3 45 | 2
| 5 146 12 3 246 24 | 1
+-------------------------------+
a b c d e f
Now, there is a way finish this puzzle in one step.
Update (Jun 7, 2025)
The finishing move eliminates (3)a3 with a nice chain starting at
(4)a3 = (4)a4 - (4)e4 etc.
A second way to solve this puzzle starts with the idea of
exploring the weakness in the second row to get the elimination
(-5)d2 [and 3 placements] using a move still complex, but easier
the in solution 1.
After that, one gets the following configuration
+--------------------------------+
| 13 13 4 25 25 6 | 6
| 36 2 35 4 56 1 | 5
| 1346 5 123 26 246 234 | 4
| 346 36 235 256 1 234 | 3
| 2 4 6 1 3 5 | 2
| 5 16 12 3 246 24 | 1
+--------------------------------+
a b c d e f
Now, the puzzle can be solved at least with two simple chains.
Final Update (Jun 8, 2025)
For solution 1, one can see the first move as
+---------------------------------+
|(13) 13 4 25 25 6 | 6
|(3)6 2 (3)5 4 56 1 | 5
| 346-1 5 (13)2 [12]6 246 234 | 4
| 346 346 235 256 1 2345 | 3
| 2 14 6 15 3 45 | 2
| 5 146 12 3 246 24 | 1
+---------------------------------+
a b c d e f
'almost' W-wing (1=3)c4 - (3)c5 = (3)a5 - (3=1)a6
but there is the spoiler (2)c4, that we need to address.
If there is no (6)d4, then (2)c4 - (2=1)d4 also eliminates (1)a4.
So, the spoiler now is (6)d4. We can go down (to d3):
(6)d4 - (6)d3 = (6-4)a3 = (4)a4
that also eliminates (1)a4.
but we have the third spoiler (6)b3 and this is the
last one: (6)b3 - (3)b3 = (3)b6 - (3=1)a6
So, this is the very complex move that shows that (1)a4
can be removed. It all started with that 'almost' W-wing.
The configuration after this is:
+--------------------------------+
| 1 3 4 25 25 6 | 6
|(3)6 2 (35) 4 56 1 | 5
|(4)36 5 123 126 (4)26 234 | 4
|(4)6-3 46 (5)23 256 1 (5)234| 3
| 2 (14) 6 15 3 (45) | 2
| 5 (146) 12 3 (46)2 24 | 1
+--------------------------------+
a b c d e f
Now (4)a4 = a5 - e5 = (46-1)e1.b1 = (14-5)b2.f2 = (5)f3 - c3 = (5-3)c5 = (3)a5
eliminates (3) a3, producing a naked pair (46)a3.b3 that eliminates (6) d3.
After this the puzzle is solved easily with singles. ///
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
I have solved today the following Latin Squares Puzzle (SE = 7.1).
My solution has two steps (after basics).
(generated with SudokuExplainer)
After basics
+-------------------------------+
| 2 3 456 456 56 1 |
| 3 24 45 1 25 6 |
| 1456 46 1456 3 156 2 |
| 56 1 2 56 3 4 |
| 146 246 3 46 126 5 |
| 16 5 16 2 4 3 |
+-------------------------------+LS
Update (Sept 21, 2025)
+-------------------------------+
| 2 3 456 456 56 1 | 6
| 3 24 5-4 1 25 6 | 5
| 1456 46 1456 3 156 2 | 4
| 56 1 2 56 3 4 | 3
| 146 246 3 46 126 5 | 2
| 16 5 16 2 4 3 | 1
+-------------------------------+LS
a b c d e f
A chain with 7 strong links implies that (4)c5 is false.
This elimination allows simplifications:
+-------------------------+
| 2 3 46 456 56 1 |
| 3 4 5 1 2 6 |
| 145 6 14 3 15 2 |
| 56 1 2 56 3 4 |
| 146 2 3 46 16 5 |
| 16 5 16 2 4 3 |
+-------------------------+LS
How to finish this puzzle ?
** Hint on a tough Slitherlink Puzzle SL#3 with a very late update! (Sept 20, 2025) **
Created: February 12, 2024
Contact: sudo.jco.br@gmail.com