dailysudoku.com

[Asellus]

storm_norm,

Personally, I usually don't consider ERs until after I believe I've exhausted the possible usual suspects, such as X-Wings and other fish (including finned) and XY(Z) Wings and Skyscrapers and such.

An ER is, essentially, a right-angle "mirror" that allows some Cell(s) to "see" some Cell(s) elsewhere that it/they wouldn't otherwise see. In the simple classic ER example, the mirror exposes a Cell to both ends of a strong link. Once this is mastered, one sees that these mirrors have other uses, such as "reflecting" fish fins to other locations, or reflecting an XY Wing/Chain Pincer elsewhere. Two or more of these mirrors can be lined up to reflect cells all over the place, including back onto themselves in a self-destructive way! They can have all sorts of uses. (That's what I meant in my comment that has been so flatteringly quoted above.)

The original term "Hinge" is easier to grasp. As Marty says, an ER is just a Box in which a candidate is limited to just two lines. He should have added: two perpendicular lines, one Row segment and one Column segment.

It is possible to use these mirrors without thinking about their internal workings. However, if you want to do so, then they can be seen as an example of grouped coloring strong links: the Row segment is strongly linked with the Column segment. If the cell at the Hinge intersection point contains the candidate of interest, then the link is strongly inferential (rather than conjugate). However, this doesn't matter since we use the mirror to reflect cells that have their effect if they are true. (If you don't understand these last remarks, don't worry. It is just inference logic stuff. If you do understand, then you will have some idea how an ER can be used in an AIC.)

In any case, welcome to sudoku life A.E.R. (After Empty Rectangles)!

[DennyOR]

Marty,

I don't see the W-Wing in boxes 1 and 2. Would you mind giving a more detailed explanation.

[Marty R.]

[DennyOR]

Thanks Marty. I was only looking for W-wings where the common number was in the third row or column in the two boxes with the common pair, like the original example on this site.

[storm_norm]

asellus,

ok, so if the ER is there, why not take it, right? if it sticks out like a sore thumb. it would take me a few more examples to really get a feel for looking for them. I totally understand its usefullness.

i am sure you have noticed that in the last year, the very hards have evolved. they use to be very hard if they needed a massive onslaught of naked pairs to complete it. in the last year or so it has moved into deeper waters, more fish.

I would love to start a topic about solving patterns. these very hards don't require an exclusive path to the end. i would argue that some solving paths are actually harder than others.

for example: I find an x-wing as my first move.
the next person finds an xy-wing as their first move.

now bear with me,

I would argue and theorize that the state of the puzzle ( the solved cells up to that point ), after the x-wing, is different than the state of the puzzle after the xy-wing.

therefore, depending on what move you make first, the puzzle after that move, actually changes rating.

As you fill in cells, the puzzle's rating fluctuates from move to move.

example:

lets say an x-wing leads to a series of singles before the next major move. the puzzle is definitely in an easier state after the x-wing, than before it. then at the point where you need the next major move, the puzzle now takes on a higher rating because at this point you need that harder move.

anybony who's done easy puzzle after easy puzzle knows what I am talking about. there is that one point in a puzzle where it goes from being easy, kind of easy to hard, then back to being easy.

I'd love to find out if anyone agrees or disagrees about this.

and I would love to find out if this "subjective feel" for a puzzle is called something.

norm

[nataraj]

[ravel]

[re'born]

[nataraj]