The New Sudoku Players' Forum

[eleven]

I remember, that in the alternative views e.g. a bivalue cell represents a strong link (and a pair an x-wing), so that some things can be spotted easier.
But if for the boxes you have to remember the corresponding mini-row digits instead of seeing them surrounded by the box borders, it is clear for me, why the classical presentation is preferred.
And i don't know of someone, who would manually transform a puzzle, and then always update 2 or 3 puzzles in the hope to find a solution faster.
I also personally have no ambition to use a program to do it, and learn, how to switch in the brain between them. But i can't speak for others.

[SpAce]

I remember, that in the alternative views e.g. a bivalue cell represents a strong link (and a pair an x-wing), so that some things can be spotted easier.

Exactly. You can see the same thing as a naked subset, a hidden subset, or a fish depending on the space you're using (the same thing with ALS and finned fishes). Bivalue and bilocation links are similarly switched etc. The most obvious actual benefit for a manual solver is the ability to see larger fishes as subsets, and finned fishes as ALSs, which was pointed out by Arcilla. I'm not really sure if there are any other significant benefits.

But if for the boxes you have to remember the corresponding mini-row digits instead of seeing them surrounded by the box borders, it is clear for me, why the classical presentation is preferred.

The rc-space is of course much more intuitive, but it's not difficult at all to use boxes in the other spaces either. It's actually quite nice because all nine box constraints for a single digit are encoded within the single line (1 box per micro-line; 3 micro-lines in a mini-line; 3 mini-lines in a line), which makes box operations (including intersections etc) really easy if you're using 3x3 candidates. In that format there can be only one resolved digit in the same micro-line within a mini-row. Thus, if one cell resolved to a 4, for example, it would wipe out any candidate 4, 5, and 6 in the same mini-row (+ all 4s in the full row and column, of course). Pretty easy to remember and to use in practice (I've only solved a couple of puzzles in nr- and nc-spaces, so it's not like I needed a ton of practice to get used to it). Yesterday's example shown in that format:

Code: Select all

  r  1     2     3      4     5     6      7     8     9
n .-----------------..-----------------..-----------------.
1 | ... | ... | .2. || ... | ..3 | 1.. || ... | 1.. | 1.3 |
1 | ... | ..6 | ... || .5. | ... | ... || 4.. | ... | 4.. |
1 | .89 | ... | ... || ... | .8. | 7.. || 7.9 | .89 | .8. |
  '-----------------''-----------------''-----------------'


c(7=1)n1r6 - c(1=8|9)n1r8 => -c7 n1r7

Unless you know the micro/mini-line rule, it's not obvious why the latter end of the chain works. But if you do, then it's clear that if n1r8=(8|9) then n1r7<>(7|9) and n1r9<>8. It takes a (short) while to get used to, but it's actually much faster than scanning the 3x3 boxes in the rc-space, though clearly not as intuitive. In this case the whole chain uses just two cells in one row in the nr-space, which I think is pretty cool.

The box-mapping for the nr-space:

Code: Select all

  r  1     2     3      4     5     6      7     8     9
n .-----------------..-----------------..-----------------.
1 | b1  | b1  | b1  || b4  | b4  | b4  || b7  | b7  | b7  |
1 | b2  | b2  | b2  || b5  | b5  | b5  || b8  | b8  | b8  |
1 | b3  | b3  | b3  || b6  | b6  | b6  || b9  | b9  | b9  |
  '-----------------''-----------------''-----------------'

And i don't know of someone, who would manually transform a puzzle, and then always update 2 or 3 puzzles in the hope to find a solution faster.

Me neither. I've tried it a few times, and always concluded that it's a total waste of effort. It makes more sense to just pick one space and solve the whole thing in that. I'm conjecturing that the same patterns are available in all of the spaces, but they just look different, so it's not like using all of the spaces would somehow add new solving options (some just might be a bit easier to spot than others). For example, the above solution works just as well in nc-space:

Code: Select all

  c  1     2     3      4     5     6      7     8     9
n .-----------------..-----------------..-----------------.
1 | ... | ..3 | ... || ... | ... | .2. || ... | 1.. | 1.. |
1 | ..6 | ... | .5. || ... | 4.. | ... || ..6 | .5. | ... |
1 | .89 | ... | ..9 || 7.9 | ... | ... || 7.. | .89 | 78. |
  '-----------------''-----------------''-----------------'

(r6)n1c7 = (r6-r8)n1c1 = (r8)n1c89 => -r7 n1c7

The box-mapping is very natural for the nc-space:

Code: Select all

  c  1     2     3      4     5     6      7     8     9
n .-----------------..-----------------..-----------------.
1 | b1  | b1  | b1  || b2  | b2  | b2  || b3  | b3  | b3  |
1 | b4  | b4  | b4  || b5  | b5  | b5  || b6  | b6  | b6  |
1 | b7  | b7  | b7  || b8  | b8  | b8  || b9  | b9  | b9  |
  '-----------------''-----------------''-----------------'

I also personally have no ambition to use a program to do it, and learn, how to switch in the brain between them. But i can't speak for others.

I haven't tried a software option for this, but I think it would at least make much more sense than doing it manually. Still, probably not very useful. The only obvious benefit I can see is the ability to see Swordfishes and Jellyfishes as subsets -- and that would actually help me because I'm likely to miss them otherwise. Perhaps it would similarly help in using their almost-forms (finned fishes) in AICs because they'd be visible as ALSs.

Added: if someone's interested, this is how intersections work (row/col correspond with nc-space; switch for nr):

pointing (box\row): a micro-line has only one type of digit -> eliminate same digit from other mini-lines in the row
pointing (box\col): a micro-line has digits only in one cell -> eliminate other digits in the cell
claiming (row\box): a digit is locked into one micro-line -> eliminate other digits on the same micro-line
claiming (col\box): a cell has digits only in one micro-line -> eliminate other digits on the same micro-line

I've been wondering if any of this might help find complex fishes more easily or yield any speed-ups for software solving, but both topics are above my pay grade.

[SpAce]

@Cenoman. I partly rewrote my earlier reply to your post, because it was originally written in haste and seemed a bit too "straight-to-the-point" to my eye afterwards That was not the least bit intentional, so I hope you didn't interpret it as unfriendly.

[Cenoman]

@Cenoman. I partly rewrote my earlier reply to your post, because it was originally written in haste and seemed a bit too "straight-to-the-point" to my eye afterwards That was not the least bit intentional, so I hope you didn't interpret it as unfriendly.

...neither friendly nor unfriendly. Just a dialogue of the deaf.

[SpAce]

Just a dialogue of the deaf.

Maybe so. I get confused with blank statements like "boxes do not exist in n-c and n-r spaces" when there's at least two ways to interpret it. It needs a qualification before it makes sense. It's still unclear to me if the method of using boxes in nr and nc spaces I explained above was self-evident to everyone or not. In either case, I'm certainly not looking for credit because a) its usefulness is limited as these days almost no one uses those extra spaces (except maybe for fish hunting using Arcilla's method), and b) I'm quite certain that I can't be the first to discover it, because at some point in time those extra spaces were probably used (or at least tried) by many solvers and it's not rocket-science to see how the boxes are mapped in them. I just haven't seen it described anywhere, or any evidence that Denis himself saw it or at least advocated using the full potential of those spaces:

The general idea is that you can play as usual on the sandard part of this extended board and you can apply the rules of Latin Squares (Sudoku without block constraints) on the other two sub-boards. You maintain the consistency between the three sub-boards by asserting a value or eliminating a candidate on the three sub-boards at the same time. (source)

It's normal that you could not extend your idea to boxes. Only block-free rules can be transposed to the rn- and cn- spaces.
In these spaces, I proved that only Latin Squares rules are valid. (source)

Based on that (lack of) evidence I must still presume that his ideas about them were limited, for what little it matters. I also think that saying "only Latin Squares rules are valid" in them is a misleading statement without any qualifications, as is saying "boxes do not exist" in them. They're true statements only in the limited 2D point of view.