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Marty R. · Posted: Sat Sep 20, 2008 9:23 pm Post subject: ERs--beyond the basics

I know the very basics of an ER (and make frequent use of them): eliminate a candidate that sees both the ERI and the second part of the strong link. Is there more that can be done with these that falls short of rocket science? Wink

wapati · Posted: Sun Sep 21, 2008 1:17 am Post subject:

You can use them to look for 2-string kites at the same time, if the vertex of the ER does NOT have the candidate.

X is the candidate, cells marked "-" are not X, @ is the vertex, which has not X as a candidate, # cannot be X.

keith · Posted: Sun Sep 21, 2008 3:58 am Post subject:

Marty,

I think of ER's (Empty Rectangles) as kites with "grouped" coloring. Let me try to explain.

Suppose you have this:

keith · Posted: Sun Sep 21, 2008 4:11 am Post subject:

Marty R. · Posted: Sun Sep 21, 2008 5:01 am Post subject:

Keith,

I think what Wapati calls a vertex and you call a hinge, I call an ERI. But I don't understand what you're saying. Despite the talk of kites, grouped coloring, etc., in each of the two grids you show, I see an ordinary ER. What am I missing?

Wapati,

Thank you. I'll wait for your response to Keith before commenting further.

wapati · Posted: Sun Sep 21, 2008 5:47 am Post subject:

daj95376 · Joined: 23 Aug 2008 Posts: 3854

Are we talking apples and oranges here?

Apples: wapati's diagram can be viewed as a grouped 2-String Kite. He uses a subset of the Empty Rectangle pattern to make it work -- vertex cell void of the candidate. (Personally, I wouldn't call this a 2-String Kite.)

Oranges: keith's Diagram 2 uses the ER pattern as the Empty Rectangle technique. In it, the vertex cell does not have to be void of the candidate.

Marty R. · Posted: Sun Sep 21, 2008 4:11 pm Post subject:

keith · Posted: Sun Sep 21, 2008 5:27 pm Post subject:

Marty,

You asked "Is there more that can be done with these ..."?

I replied, "I do not recall any explanation of ER's that talks about eliminating any candidate other than in the cell I have called @."

In other words, my answer to your question is no, not so far as I know.

It seems to me you could replace the strong link with a different inference. For example:

Marty R. · Posted: Sun Sep 21, 2008 5:39 pm Post subject:

daj95376 · Joined: 23 Aug 2008 Posts: 3854

In the Players' Forums, Havard introduced the Empty Rectangle pattern in this thread.

http://www.sudoku.com/boards/viewtopic.php?p=21366#21366

keith · Posted: Sun Sep 21, 2008 7:02 pm Post subject:

Marty R. · Posted: Sun Sep 21, 2008 9:24 pm Post subject:

Asellus · Posted: Sun Sep 21, 2008 9:40 pm Post subject:

To resolve (I hope) the confusion above, we need to look a little more closely at the grouped link involved in a hinge/ER. If the ERI cell contains candidate X, then the grouped link is a strong (only) inference link. It is possible for both sides of the link to be true... IF the ERI cell is true. (It is impossible for both sides to be false, hence the strong inference.)

However, if the ERI cell does NOT contain candidate X, it is now a conjugate link, which means that it can serve as either a strong link OR a weak link, according to the need.

When used in the standard way as an ER, it is being used as a strong link. So, it doesn't matter whether or not X occurs in the ERI.

In wapati's example, the ER-like grouped link is being used as the weak link pivot of a Kite (or Turbot Fish). Thus, candidate X must not occur in the ERI. The strong links occur in the row and column to the lone Xs (and thus pincers) that occur outside the "pivot box". These are also grouped links, of course.

By the way, I would (and do) call this a Kite. I can see no advantage in denying the name to to something that has exactly the same logic and requires only a modicum of additional sodoku knowledge (a comfort with grouped links) to recognize and use.

I hope that helps clarify things.