The New Sudoku Players' Forum

[rjamil]

Hi eleven and experts,

I have read elsewhere regarding subject.

My question is as follows:

Is impossible patterns are opposite to Pattern Overlay Method?

R. Jamil

[denis_berthier]

Is impossible patterns are opposite to Pattern Overlay Method?

"impossible patterns" can only appear in contradictory puzzles. In consistent puzzles, they must have "guardians", which may them be used to form ORk relations and enter ORk resolution rules.

The questions about the 630 impossible 3-digit patterns (the key here its "3-digit") should be:
- can they be proven contradictory by the template method (= POM)?
- at which template-depth?

I haven't studied these questions, but at first sight, as I've proven them contradictory in the restricted form of T&E(2) or T&E(3) which involve only candidates in the pattern, it shouldn't be too hard to show that the same proofs work with templates - as I've done in the "Templates as patterns" thread for the tridagon.
.

[eleven]

I don't see a relation between impossible 3-digit patterns and POM, which i thought is a 1-digit-method (i never used).

[rjamil]

Hi eleven,

I read about multi-digit (3+) POM here, here and here.

R. Jamil

Added as on 20241030: Third link.

[eleven]

ok, but Denis' remark, that POM can prove impossible patterns is all i can see as relationship.

[rjamil]

Hi,

Well, where there are impossible patterns, there are possible patterns. No matter, which one are few.

R. Jamil

[P.O.]

my view on impossible patterns:
an independent set is a set of pairwise disconnected cells or a single cell
a template is a maximal independent set
a puzzle is a partition of n cells into k independent sets
a puzzle is valid if it is a subset of a partition of the 81 cells of the sudoku grid into 9 templates
an impossible pattern is a set of cells whose constraint on k makes its partitioning impossible
eleven's impossible patterns have the constraint that k = 3
- either there are no independent sets of appropriate size
- or they cannot perform a partition of the cells

[rjamil]

Hi experts,

Here is a puzzle with P.O.'s POM move solution for testing the subject move.

After basics, the puzzle is solved for digit 134567, and remaining only three digit 289 unsolved.

R. Jamil

[rjamil]

Hi expert,

After long time waiting and searching for any relation between eleven's 630 impossible 3-digit patterns and 3-digit pattern overlay method, finally I have decided to ask AI for the same and here is my correspondence.

R. Jamil

[StrmCkr]

Naked N Digit impossible arrangements also have the opposite hidden 9-n impossible patterns accompanying it
It's the duality of the two sets that makes the puzzle have zero solutions.

They are disambugatable.

To answer the question the N Digit patterns are
anti Muti fish

Muti-Fish being (x) nxn+k where x is a collection of digits where the cells of base /cover +k covers
provoides x digits N times with N vertex. For a 1:1 ratio.

Anti fish one or more of the vertex is over covered N times so that it or them cannot provide all x vertex N times if they makes sense..

[eleven]

... I have decided to ask AI for the same ...

And you got the usual chatGPT blah blah as answer.
Still the only relation i can see is, that if you restrict the overlay method to the pattern cells, you will not find a valid 3-digit pattern.

[rjamil]

Hi eleven,

And you got the usual chatGPT blah blah as answer.
Still the only relation i can see is, that if you restrict the overlay method to the pattern cells, you will not find a valid 3-digit pattern.

Well, for ChatGPT, I think, its highly unreliable, outdated and based on pre-defined data.

For POM, I see your same reaction here.

However, I have already developed an exhaustive and robust optimization single digit POM routine and now thinking about to extend it for multi-digit POM search as proposed by Jason T. Linhart here.

May I request to solve the Puzzle289 with yours impossible 3-digit pattern OTP move, if possible.

R. Jamil

[eleven]

Of course any pattern with a solution candidate missing is impossible, but i can't see any interesting one in that puzzle.

[rjamil]

Hi eleven,

Of course any pattern with a solution candidate missing is impossible, but i can't see any interesting one in that puzzle.

True. In other words, any candidate not in a solution cell is impossible, and may be eliminated by multi-digit POM as a complementary of impossible pattern.

If I analyze the P.O.'s OTP move of Puzzle289, after singletons, digit 2 and 8 have 4 possible templates each; and digit 9 has 6 possible templates. Out of which only one of each digit template are the solution, means that, rest of the possible templates of each digit are, basically, impossible due either one or more cell(s) overlap with another digits' solution pattern.

Conclusion from yours above mentioned quoted statement and mine is that, the multi-digit POM move is treated as bifurcation between solution and impossible patterns at same time.

R. Jamil
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https://www.threads.net/@sarayusudha/post/DDLqSdbC1dT