The New Sudoku Players' Forum

[SteveG48]

To me, the issue here is the final node: r1c5,r3c4. Once we eliminate the 1, then we have the node locked with 3 and 5.
Usually, that's the end of the story. Unfortunatel in this puzzle, we don't know how those digits are arranged, and it's
critical that we know where the 3 is. I chose to write it the way that I did because it explicitly excludes a 3 in r1c5, solving
the problem. At least, that's the way it works for me.

[SpAce]

To me, the issue here is the final node: r1c5,r3c4. Once we eliminate the 1, then we have the node locked with 3 and 5.
Usually, that's the end of the story. Unfortunatel in this puzzle, we don't know how those digits are arranged, and it's
critical that we know where the 3 is.

Exactly. That's why the normal (53) locked set (unordered) node wouldn't work if one wants to write it as an unsplit node. It needs a (5,3) locked tuple (ordered), but unfortunately I still haven't found a reference to prove my faint memory that such a notation exists in standard Eureka (doesn't stop me from using it anyway, because it's useful).

I chose to write it the way that I did because it explicitly excludes a 3 in r1c5, solving
the problem. At least, that's the way it works for me.

Yeah, I might have to concede that there's no practical difference between our notations. What bothers my eyes with yours is that the unsplit cells in the last node don't have an explicit relationship (except membership in the split node), which makes it a bit harder to see the necessary weak link between 5r1c5 and 5r3c4, i.e. why (1|5=3)r3c4 happens implicitly. I've seen (and used) split nodes with members in totally different sectors where the cells aren't linked at all, and that's why the existence of such a link here is not self-evident. It's there, of course, but requires looking at the cell addresses and noticing that they're in the same box -- which is a bit harder because of the rNcN addresses that need to be mapped to the box.

On the other hand, in a normal unsplit LS node the cells are by default in the same sector and thus the digits have an automatic weak link with the same kind. That's what I tried to express with the unsplit node approach. It has its own problems, though, one being the (possibly) non-standard tuple notation. It's also not a water-tight indication that the cells are linked, as it's not uncommon to see split-node chains with some unsplit nodes having unlinked cells. However, that's why I used the box/position notation which makes it explicit that they share a sector.