tarek wrote:daj95376 wrote:Obi-Wahn wrote:Construction Rule: We have a Fish pattern if we can construct two sets of sectors, a Base set and a Cover set, in such a way that every candidate of a given digit belongs to at least as many Cover sectors as it belongs to Base sectors.

So forgive me here for not following this. Does this mean that in the Nx(N+k) construction rules as described by Obi-Wahn do not have Fins??!!!

My interpretation of his ideas was (using what was mentioned before) is: any PEs will have C/B = k+1 & any EE will be a PE that sees ALL fins.

My understanding is that

finned NxN Fish have

fin cells that are covered with fewer cover sectors than base sectors.

Obi-Wahn eliminated fin cells in his "arithmetic" for

finned Nx(N+k) Fish by adding additional cover sectors until every candidate cell is as I quoted in his

Construction Rule above. He refers to these extra cover sectors as

fin sectors.

Obi-Wahn wrote:Number of fin sectors = Number of cover sectors - Number of base sectors

When talking of a

finned fish, the distinction is in the dimensionality of the base and cover sets. In a finned NxN fish, I only consider fin cells being present. In a finned Nx(N+k) fish, I only consider (extra) fin sectors being present.

As far as the mathematics goes for Nx(N+k) fish, each cover sector's contribution is independent of any other cover sector's contribution -- even if it's the same house/unit being repeated.

In finned NxN fish, eliminations are determined using peers of the fin cells and PEs from the unfinned fish. In finned Nx(N+k) fish, eliminations occur in candidate cells where

( cover_sector_count - base_sector_count ) > k.