A revival of Broken Wings

Advanced methods and approaches for solving Sudoku puzzles

Re: A revival of Broken Wings

Postby tarek » Wed May 27, 2020 4:13 pm

denis_berthier wrote:Hi tarek,
Thanks for the explanations.
Did your idea of oddagons include the possibility of multi-digit ones ? If not, is it shocking to you that I call these oddagons also ? It seems to be to be a natural extension of the single-digit ones covered by POM.

That notion has always been a possibility because how would you explain some of the single digit eliminations that POM can't explain? The answer comes from other digits because POM looks only into a single digit pattern. The same would apply to fish as there could be multi digit fish that follow the logic of base/cover.

I used the term oddagon because somebody else used it before. They must have used logical pathways not dissimilar to you!
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Re: A revival of Broken Wings

Postby denis_berthier » Wed May 27, 2020 4:47 pm

Tarek,
Thanks, that makes it totally clear.
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Re: A revival of Broken Wings

Postby SpAce » Wed May 27, 2020 5:21 pm

Hi tarek,

tarek wrote:That notion has always been a possibility because how would you explain some of the single digit eliminations that POM can't explain? The answer comes from other digits because POM looks only into a single digit pattern.

What exactly do you mean that POM only looks at a single digit pattern? I'm no POM expert at all (since it's not a manually applicable technique in almost all relevant cases) but I've understood that any non-trivial implementation of it considers the patterns of the other digits too. I think it's part of the original spec as well, based on for example this:

Myth Jellies wrote:Now we will put POM labels on just the 5's and 7's in this grid. Since the 5's and the 7's appear exactly twice in each box, we know there can't be more than 2 potential solution patterns for each of them. They are the same patterns that you would get from simple coloring. So labeling them 'A' and 'B' for each, we get the following.
...
A pair of cells which contain all of the potential patterns for a number, I call a vulnerable pair. You can note by inspection that in r8c3 and r7c6, the 7B pattern occupies cells containing both of 5's patterns. This means that if 7B were true, then 5's could not possibly have a valid pattern. Thus we can eliminate 7B, which basicly solves the puzzle.

In such a simple case it actually sounds awful lot like multi-digit multi-coloring (e.g. full tagging) to me. Only in such simple situations POM is manually applicable (and actually quite nice here), but not exactly necessary because the same eliminations are probably available with normal chaining.

The patterns of multiple digits are considered in Andrew Stuart's implementation as well:

SudokuWiki wrote:Rule 2 looks at all the patterns for all numbers 1 to 9. Within in each number all patterns may want to occupy certain cells - like a bottleneck. If that is the case then those cells are not available for other patterns used by other numbers. This is more cumbersome for a human to calculate, admittedly, but it works very well for the solver and we get a lot of this type. Patterns are pruned down and then Rule 1 is executed to find the first X where cells not used by X. Only the first X is reported - there may be other eliminations from numbers higher than X but it would be too confusing to report the total overlap.

The same is true about Phil's implementation (which is based on Andrew's book). I presume it's done by Hodoku's templates as well, although it's not as explicitly said.

(Sorry if I misunderstood what you meant.)

PS. Phil explains here how he uses a variant of POM kind of like a jigsaw puzzle to get to the complete solution.
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Re: A revival of Broken Wings

Postby tarek » Wed May 27, 2020 7:55 pm

POM was expanded to look at several digit interactions I agree. I was referring to the single digit POM to explain the NoFish eliminations in the NoFish list!

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Re: A revival of Broken Wings

Postby SpAce » Wed May 27, 2020 8:08 pm

tarek wrote:POM was expanded to look at several digit interactions I agree. I was referring to the single digit POM to explain the NoFish eliminations in the NoFish list!

Ok! That's an important qualifier. Where can one find such a single-digit POM implementation, if all the public ones use multiple digits by default (as I presume)? I'd actually be more interested in that, because it should give a more realistic picture of the fish/oddagon potential. I don't think it makes any sense to call all template eliminations/placements "single-digit techniques" if patterns of other digits affect the results.
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Re: A revival of Broken Wings

Postby SpAce » Wed May 27, 2020 8:18 pm

A related question. Has anyone tried POM in other than rc-space? I'd think the same principle should work in nr- and nc-spaces as well. It would be interesting to know if they all yielded the same results, as I've conjectured that all of those spaces have exactly the same solving patterns available just through slightly different POVs (naked vs hidden, subsets vs fishes, etc). (Of course it requires understanding how the boxes are mapped in nr and nc, but it's trivial.)
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Re: A revival of Broken Wings

Postby StrmCkr » Wed May 27, 2020 10:15 pm

Has anyone tried POM in other than rc-space?
you do realize POM tests all 46,656 template {all 9 solved cells for a single digit} cell arrangement on a grid correct?

Swapping it to:
RN or CN or BN changes it to: 46,665 templates for A 9- positional arrangements for each of the {N}digits : which is exactly the same as above.
as it only converts the Cell{x,y} value to the corresponding map: Rx[{y}position], Cy[{x}position] B{xy}[position{top down, left to right} ]

these extra spaces makes no difference for how pom functions, they are great for other faster functions in technique building. {like hidden subsets/fish}

the spaces that are interesting are the non standard ones:

mini row in a box
mini Col in a box
mini Box Row in a col
mini Box col in a Row

which again has no real application for POM.

notes for solving techniques: things can be converted from one to the other in the same space via a tiddler function by looking for he opposite
N set.

given digits - [1..9]Digit = off digits

given cells
{convert to R,C,B } - [1..9] position = off positions.

naked and hidden are always balanced to each other
Last edited by StrmCkr on Wed May 27, 2020 10:51 pm, edited 2 times in total.
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Re: A revival of Broken Wings

Postby SpAce » Wed May 27, 2020 10:37 pm

StrmCkr wrote:these extra spaces makes no difference for how pom functions

Thanks for confirming that, StrmCkr. It's what I thought.
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