Posted 10th Jan 2025 at 07:38
Last edited by winterer 10th Jan 2025 at 08:15It's interesting that in many Hitori, there is a specific cell that immediately forces the solution when set correctly.
Same here: a certain cell must be set white and the rest follows easily.
If only one could find that cell easily! :-)
Wondering if there is any research on this topic...

Posted 10th Jan 2025 at 08:55Definitely seems to be a correct observation. As soon as I filled in one particular square as white then the whole puzzle fell into place. Unfortunately, I too have no idea how to find it logically.

Posted 11th Jan 2025 at 00:25I try not to just fill out the puzzle and erase to test things out, but there's often some big indicators as to which cells are particularly powerful - I use powerful here to express how many other cells they force in some way or another. You'll notice the stratified diagonal patterns in many places on larger puzzles, there are a few spots I can now intuitively recognise on these as critical to the makeup of the puzzle. An easier but slightly less effective test is just using the tool that shows repeated digit, and testing a cell as black if it's surrounded by many of these underlined repeated digits, as it's more likely to create a scenario where there's a clash, and you can then put it as white if it does clash. If you can't find clashes, then there's a good chance you've found a very powerful correct cell:) Just 2 years ago I'd avoid the hitoris as they were a bit overwhelming and I was still getting to grips with a lot of the other puzzle types here that were new to me - it's lovely to look back and see how far I've progressed from being almost unable to get around the simplest ones!

Posted 11th Jan 2025 at 11:39Whilst I try to complete these, and all other puzzles, by using logic, this is often not the case. I then try with a digit in the middle of those which are duplicates and see whether this produces a possible outcome. Or, if there are two of the same digit I go for one of them and hope it doesn't work so it means it has to be the other digit. As you say sometimes one is lucky and finds everything falls into place but that doesn't always happen! Hitori is one of my favourite puzzles along with all the jigsaws.

Posted 12th Jan 2025 at 10:51I usually solve these by doing quick horizontal and vertical scans for the cells that need to be set white or black according to the rules, then scanning for areas that must be connected, etc. In the worst case, I scan for row&column singletons, which might give me a clues as to which cells must be black as otherwise nothing would force neighbouring singleton cells white.
Not caring for deeper structures, but not doing try/error tests either.

It's only on subsequent runs that I try to find these "nexus" cells that would force the _complete_ solution _immediately_ through simple application of the rules.

Here, it's one of four cells in the same row/column (no spoiler) with the same number, where the solution follows if the right one of these is colored white. I don't see any structure that would point to this cell being that important. That's why I'm wondering whether there is any graph theory on this topic - even if it would be to complex to apply manually when solving these puzzles.

Posted 13th Jan 2025 at 10:54That's pretty much how I do them too, Winterer. Systematically but no obvious shortcuts to finding "key" squares.

Posted Today at 19:10Curious by this discussion I just solved this puzzle, even though I'm way behind, solving late September right now, trying to catch up. Staying current was way easier when there were only four puzzles a day...

I solved this one using logic only, no try and error. I couldn't find one specific white cell that made the puzzle a run-through. Had to read the comments again - oh, it's one of several same numbers in one row, on of those have to be white, but not one that is obvious by direct logic - if I get you correctly, winterer, that cell is not necessarily between two cells with the same number (the only case where a white cell is immediately forced and might imply others. If you have a number that is not repeated in its row and its column, that one has to be white, but it doesn't imply more without context).

I usually look for cells that can't be black, because it whitens two neighbour-cells that lead directly to a clash because they imply two black cells to be directly next to each other.
This and the rather obvious case, when there are two of more numbers in the same row/cell that would shut off a region - so you know those "more" all have to be black, was enough for this puzzle.

I hope you get the idea...