This seems to fit:
The initial step was to replace all 1's (red) with a 2 (black) and all 9's with an 8:
Then, whenever a red number was +/- 1 of a black number which was on the same row, column or box, the red number was changed to its other possible value. E.g. if a red 6 was on the same row as a black 5, the red 6 was changed to a black 7 as it couldn't ...
I have been asked by a couple of people to show the creation process for this puzzle, so here we go:
Also if people want to see more of these strange, Sudoku mash ups then I'll be more than happy to combine some new types :)
Wrap-up: The Making Of This Samurai Pseudoku
This is not a solution to the puzzle, but provides notes from its poster. This type of ...
A naked single occurs when
Basically, there will be numbers that rule out 8 of 9 possibilities. So for the 7 bottom right:
As all the others are ruled out in various ways, it must be a 7.
The strategy would be to look at a cell and go through 1-9 and see what is ruled out. If all but one number is ruled out, it must be that number!
Hope this helps!
I am officially an idiot.
I spent several hours figuring out brilliant deductions and got really good progress with many actual numbers on the grid, and even though I got stuck at places, there was always some clever bit that got me just that much forward.
In the end, I was just about to fill the grid in two different ways to show that the puzzle must be ...
Let's start with:
However, the basic rule of any sudoku says:
However, this is not a normal sudoku. So:
Now, the things get harder. But let's see that:
We have a:
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.
Completed grid (cube?):
There were a LOT of deductions to make here. I'm not going to give step-by-step, but I will show several milestones along the way. I'll explain some of my favorite (read: head-bangy complicated) deductions and some common deduction types I used a lot. Unfortunately, my pictures and my favorite deductions do not always ...
Now Complete Answer
The first thing to notice is:
To represent the solution:
The first steps:
At this point:
Using the funky square:
Some more funky square logic:
Some perspective after sleep:
One final logical step:
As others have seen, the 9 sudokus are generally unsolvable because they have numbers which repeat in rows and/or columns. However, there is one exception, which is the central sudoku. It turns out it is solvable and with a unique solution:
There is something striking about the solution, namely that the central 3x3 square has a very nice ordering of its ...
From the SO answer to the essentially same question (test cases for Sudoku solver):
You can find some large datasets for Sudoku benchmarking and testing
in this project: https://github.com/t-dillon/tdoku
See data.zip for the puzzles.
for descriptions of the datasets, their sources, and ...
The Solved Grid
A general observation:
The first deduction we can make is in:
Working in row 6 from the top:
Continuing in this row:
Some small deductions from here:
Now let's try to place the 9's:
Let's tackle the upper-left box:
Notice two important properties of these solutions:
Some more ...
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:
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 ...
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.
R6C5 doesn't have anything ruling out it being a 6... but R4C5 could only be a 6. There are no other options for R4C5: placing a 1, 2, 3, 4, 5, 7, 8, or 9 would break the rules. You know you have to fill a box with some number, and that is the only one left.
This is one of two basic Sudoku techniques, the "naked single" -- when a cell only has one ...