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