Upper right corner:
At this point: Rand answered so I stopped writing up my progress. I'll try to reconstruct:
Unraveling that contradiction, we have:
So we have:
Detailed deduction is as follows, with the final solution and illustrative GIF at the end.
Top left region:
Bottom left region:
Top right region:
Bottom right region:
So far we have:
Note that the big doughnut room
Visit length for the big room
If the big doughnut room has visit length
Should've known what I'd gotten myself into when starting, whew. Great puzzle! Really hard, but I hope I got everything right.
0th Step: Try to squeeze out everything we can by normal Sudoku first:
I believe the following is the answer:
(Update: Explanation is complete now!.)
Solving Balance Loop
Masyu and Tapa-Like Loop
Geradeweg, Simple Loop and Resolving Masyu
Simple Loop, Geradeweg and Maxi Loop
Room Haisu and Solving the Simple Loop
Geradeweg and Room Haisu
Solving Detour with Yajilin
Solving Country Road and Room ...
I used the exact same logic for each picture here:
With that in mind, some pictures, in order. I mostly completed two regions per picture.
Step 6 (and the solution):
Not hard but quite enjoyable.
Solution (click to see large version):
The first thing is to produce the following list:
I: 1234 6789
II: 23 78
III: 3 8
From that, standard Sudoku techniques apply. I'll just list some middle steps below.
This is a fantastic puzzle! Incredibly difficult, but with a really nice solution path. I have no idea how you managed to come up with this!
How to solve:
(This took me about 7 hours so my memory of early logic is fairly rusty, but I have explained as best I can)
And finally, cleaning up the right hand grid and entering ...
Unruly offers the same game principle with custom parameters
Size of grid in squares. (Note that the rules of the game require both the width and height to be even numbers.)
Controls the difficulty of the generated puzzle.
Unique rows and columns
If enabled, no two rows are permitted to have exactly the same pattern, and ...
0h h1 is just one example of a Takuzu puzzle, so searching for Takuzus will broaden your search. For example, here is a 16x16 Binary Puzzle, and here is a 20x20 Binairo. The rules are identical; the only difference is what is used to fill in the cells (red vs. blue, black vs white, 0 vs 1).
(Will try and put into excel and clean up the images when I have the time)
Starting off, we can make some quick and easy deductions:
Moving on, there are a lot of hidden singles throughout the grid
Even more hidden singles later...
And the solution:
Keeping the numbers and filling in the obvious cells gets us this starting point:...
I decided to post my answer on PSE because I think it's already been unanswered for a long time here :)
Please keep in mind that I'm not really good at explaining (same reason as why I'm not trying to be active here), but I'll try my best. Also, please tell me if we can resize the spoiler box.
Thanks for the puzzle! :)
Repeatedly iterating over the boxes (regions?) gave me:
Then, doing the same over the columns gave me:
All in all, this was a great puzzle! The gaps in the board made it a little tricky to keep track of how some numbers blocked certain spaces, but it was still very enjoyable. Looking forward to more of the series! :) This was a pretty straightforward solve,...
The first thing to note is that some standard sudoku principles apply.
For example for each row and column as well as each block can only contain a particular digit 3 times in each place.
I will use notation [row,column].
To start off we can notice that in the fifth row all 3 of the right zeros ( -0)
are filled in so entry [5,4] (2-) must be equal to 22 ...
I thought it was a shame such a nice puzzle didn't have an explanation of its solve path. So here's mine! Click through to get the (large) full-size images. "Connectivity deduction" means "I put a line here because if there isn't a line, a single connected loop is now impossible". Shaded pieces mean I've placed them, and shaded parts of ...
I think there are two slightly different possible solutions (the path can join at either end in the top right corner)
From here we can connect to the small part in the top right corner, either horizontally or vertically and both are valid solutions.