New Elimination for 3D Medusa(?) with an ALS

Advanced methods and approaches for solving Sudoku puzzles

Re: New Elimination for 3D Medusa(?) with an ALS

Postby David P Bird » Sun Mar 17, 2013 1:32 pm

JasonLion wrote:Medusa coloring is equivalent to AIC in my book, but it is hardly ever used these days and not everyone agrees on that.

I think that wording is misleading as it implies that it should be possible to freely translate one form into the other, and that just isn't so. While all conjugate chains can be expressed as AICs, only some AICs can be expressed as conjugate chains.
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Re: New Elimination for 3D Medusa(?) with an ALS

Postby JasonLion » Sun Mar 17, 2013 2:19 pm

Hum, I seem to have internalized multi-colors as part of 3D Medusa, yet several of the common reference works, and particularly the earliest descriptions, are not written that way. Looking around, there are some people/sites mentioning medusa coloring as a multi-digit extension of multi-coloring and/or advanced coloring, but they are in the minority and all more recent than the earliest references.

I've always taken medusa as an extension of multi-coloring, which I believe does give you symmetric equivalence to AIC, while basing it on simple coloring does not give you symmetric equivalence to AIC. This is why I said that "not everyone agrees on that". I suppose that it is more correct to say that medusa coloring is not symmetrically equivalent to AIC, but that common extensions to medusa coloring are. This discussion has also been using other extensions to medusa coloring, not described in the original descriptions, like grouped links.

Regardless, any simple coloring based medusa coloring net can be expressed as an AIC, which allows us to use Myth's 2006 post as "prior art" for the purpose of the question that started this topic.
Last edited by JasonLion on Mon Mar 18, 2013 2:15 am, edited 1 time in total.
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Re: New Elimination for 3D Medusa(?) with an ALS

Postby mturner » Sun Mar 17, 2013 10:43 pm

David P Bird,
Take a look here for a quick tutorial about nodes in AICs.

Choosing arbitrary colors:
in my example,
(3)r9c5 Blue
(3)r8c6 Green
(3)r8c2 Blue
(8)r8c2 Green
(8)r8c5 Blue
(8)r9c45 Green

In Myth Jellies's:
(6)r6c8 Blue
(6)r6c4 Green
(5)r6c4 Blue
(5)r45c5, (5)r23c4 Green
(12)r23c4, (34)r45c5 Blue
(1234)r1c5 Green
(7)r1c5 Blue
(7)r1c8 Green

JasonLion,
Could you give a brief history (or appropriate links) of the ER technique?

As a holder of two patents, I am quite familiar with the ideas of prior art and obviousness. Certainly MythJellies's 2006 posting is prior art of a similar type of elimination. Obviousness is always a bit tricky. Quite often, once someone shows you something, it becomes obvious. Ask Dr Watson about how he felt after Mr Holmes explained something to him. But if it were indeed obvious, it would have been explained at the time as a claim.

Do you know of any other postings that show the same reasoning as I have shown in the initial posting?
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Re: New Elimination for 3D Medusa(?) with an ALS

Postby David P Bird » Mon Mar 18, 2013 1:28 am

mturner Thanks for the description and I now know precisely how you're extending your 3D Medusa colouring. But using group nodes isn't described in either the < Scanraid > or the < Sudopedia > description of the method. This is the reason I baulked at your use of the term "Medusa chains". The problem with colouring group nodes in Medusa is that there can be colour clashes on some candidates when several pairs of colours are being used.

Code: Select all
     *--------------------------------------------------------------------*
     | .      .      .      | .     D12347  .      | .     A37     .      |
     | .      .      .      |C125    .      .      | .      .      .      |
     | .      .      .      |C125    .      .      | .      .      .      |
     +----------------------+----------------------+----------------------+
     | .      .      .      | .     C345    .      | .      .      .      |
     | .      .      .      | .     C345    .      | .      .      .      |
     | .      .      .      |B56     .      .      | .     A367    .      |
     +----------------------+----------------------+----------------------+
     | .      .      .      | .      .      .      | .      .      .      |
     | .      .      .      | .      .      .      | .      .      .      |
     | .      .      .      | .      .      .      | .      .      .      |
     *--------------------------------------------------------------------*

In your own example every node you're colouring is conjugate, but that's not so in Myths example above where the dot cells can hold any combination of candidates. Colouring only conjugate nodes you could colour the cells in columns 4 & 5 green and blue but not those in column 8 because the links for 7 in r1 and 6 in r6 are weak (but 3 & 7 r8c1 could be coloured red and yellow). Without the aid of that colouring the discovery could take quite a bit of effort to find considering how many nodes get coloured in a typical Medusa grid with several colour pairs.
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Re: New Elimination for 3D Medusa(?) with an ALS

Postby JasonLion » Mon Mar 18, 2013 3:23 am

mturner,

Empty rectangle goes back a ways, and the oldest mentions I know of are from the Eureka forum which no longer exists. I wasn't in the Sudoku community back then. I'm basing my ER mention on my memory of posts I read on the Eureka forum before it went away. So I'm not sure I can give you as much detail as would be preferred. There may well be someone else around who participated in the original discussions who remembers it more accurately/differently than I do.

The earliest mention I can find at the moment is from Jan 2006, here, where ER is named in a list of techniques that can form one of the kinds of nodes that can occur in Grouped Nice Loops. A relatively complete definition occurs in Feb 2006 here, in the context of Turbot Fish, where chains doesn't really enter into it. But both of these come after mentions from 2005 on the Eureka forum which no longer exist.

A good overview of ER occurs here. It is from slightly later, and the links don't work, but it mentions ERs use both stand alone and as part of Grouped Coloring. Another interesting post is a topic from 2008 where grouped coloring and ER again come up, here.

Another thing to keep in mind is that chains have been around for a very long time, but originally there were lots of different kinds of chains which maintained their separate identities for some time. The modern view is that a chain is a chain, and it's links can be made in a variety of ways and subsume a variety of techniques. See for example here, where a w-wing is used as a link in a chain. There is often debate about the correct notation for these chains, but just about everyone appears to accept the validity of the chains themselves.

I don't claim that Myth Jellie's 2006 post made your technique clear. That post is the first example I can find of something with the same essential character, even if it is lacking in full generality. What is interesting is that we can get fairly close to your technique back in 2006, even if it wasn't really generalized back then.

A lot has happened since then, for example ALS Chains (also discussed here), and then there is this example which pretty much nails it, as does this one, both from much more recently.

Even so, there is still room for confusion/debate, as my references use terms like AIC, Nice Loops, etc, while you talk about medusa coloring (with extensions). I've certainly never seen ALS used with medusa coloring specifically, rather I have seen ALS used with various kinds of chains. Now personally I take medusa coloring as being a cool notational device for locating chains, but as you have seen in this topic it is very easy to become mired in questions of terminology. Neither of us are using the term medusa coloring in the traditional way and how medusa coloring corresponds to chains rather depends on which extensions you accept and which you don't and even then it is still a completely different way of looking at the situation which some would distinguish as a distinct technique regardless of the parallels.

There is also the possibility that I haven't fully grasped your description of your technique, and simply assumed it is describing a technique I already know, filling in the blanks/contradictions as needed. I will leave it to you to read some of these more recent references and tell me if any of them capture the idea.
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Re: New Elimination for 3D Medusa(?) with an ALS

Postby daj95376 » Mon Mar 18, 2013 6:39 am

You might consider this post as well on Empty Rectangle.

There are two thing to note in the post:

* Empty Rectangle is described as a pattern in a box

* ERLs and ERI are described and should be remembered

In addition, under "And now for the use of this thing", the technique described is also called an Empty Rectangle. This has caused confusion numerous times!
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