dailysudoku.com

[storm_norm]

[ravel]

[Asellus]

Well, I didn't read the other thread. (Didn't want to spoil the fun.) Because the initial grid didn't offer any of the usual approaches, I went for my extended Medusa:

[storm_norm]

for the casual observer, these two approaches by Ravel and Asellus might be latin or greek. BUT...

one of the best reasons to get hooked on sudoku, in my mind, is because THERE IS a different approach to a "harder" puzzle.

and the best question to ask is , why this approach over that approach. that might be the best way to hear about new techniques.

[Asellus]

storm_norm,

I agree that it's fun and interesting to discover new techniques. And, others prefer to stay with a few methods with which they are comfortable and so are not interested in the more difficult puzzles.

I don't believe it is possible to provide a logically based (as opposed to guesswork) solution to a puzzle as difficult as the one above that does not involve advanced techniques that some would find bewildering or even off-putting. But there will always be a few out there who find that such examples provide something they are ready to absorb and learn. In any case, that's how I've advanced over the 7 months since I joined this forum (at which time I knew about the basic "wings" and a bit of coloring, but had never heard of ERs or Skyscrapers or many other such things).


As to your question: why use something such as the extended Medusa coloring? Since I started using it in the past week or two, I've found that it is very powerful. I've been able to solve a dozen or two "extreme" "fiendish" "nightmare" type puzzles using only this coloring approach. Sometimes, a different approach might be a bit more efficient in reaching the solution. But then, with these real toughies, one must usually unearth hard-to-spot things such as finned swordfish or sashimi jellyfish or complex deadly pattern implications or subtle AICs. With the coloring, it's just a matter of marking and extending the coloring and then watching for traps and wraps. It is a semi-mechanical process that finds those underlying implications without having to detect them explicitly.

Notice, for instance, how the coloring quickly revealed that crucial {37} UR. And, notice that it did so in a way "backwards" from a UR solution. When exploiting a UR, one locates the potential UR and then draws inferences from it. With the coloring, I proceeded until the UR was revealed and caused a color contradiction (or "wrap"). I never had to figure explicitly the implications that result from the UR.

The trickiest part of this extended Medusa is learning how to do the inferred (extended) coloring. There are various ways of doing so, most of them straightforward. Where an inferred coloring is not so obvious, I try to make a point of writing out the explanation. I figure this can help those trying to learn what it is I am doing.

By the way, in my solution above, I did not actually need to use those ERs (nor that XYZ Wing). The entire puzzle can be solved using only the extended Medusa. However, in your original post, you mentioned that it was a nice puzzle for ER lovers. So, I stopped and used ERs whenever I noticed them. (The XYZ Wing just happened to jump out at me.)

[storm_norm]

I love the explanations. it has helped me understand. in order to teach myself medusa coloring, I have actually taken a few of the random extremes on vanhegan's site and solved them with medusa only, after basics of course.

once i get going with medusa, I don't want to stop.

most recently for my learning curve has been the medusa trap ( color trap). A.K.A. AIC finder. I can find the eliminations just fine between the two medusa clusters. however, putting them down in the Eureka notation is another story.

and consequently, I would rather medusa color than look for xy-chains.

[Asellus]

I've always liked Medusa, but didn't always find it to produce useful results. And, there was the problem of "Where do I start?" However, since I've started the "extended" approach that I demonstrate above (and in the Techniques section), I've found it to be so widely useful that I, too, have been tempted to "give up" the other approaches and just go with Medusa. The extended approach is so powerful that it almost (but not quite) doesn't matter where one starts.

Learning Eureka notation has value, in my experience, for learning to see and understand the variety of logical implications that can be found in these puzzles. But, I can see that it's not for everyone. For those who choose to pursue it, it is very helpful to study the AIC examples (in Eureka notation) that experienced solvers post as part of that learning experience. I can attest that it can expand ones ability to see solution paths.

On the other hand, the nice thing about Medusa is that it uncovers implications without having to find them explicitly. I've written elsewhere here that there are many implications that Medusa does not reveal. I now need to modify that: using the "extended" approach to Medusa, a great many more underlying implications are revealed. Only the more complex G.E.M. is more powerful, as far as I am aware.

A note on terminology, normal Medusa involves only a single color cluster (for example, "red-green"). Two or more clusters (such as "red-green" and "blue-orange") are involved in Medusa multi-coloring, something I haven't generally found to be useful enough to justify the added complexity. (The "extended" Medusa I advocate is definitely easier in practice than Medusa multi-coloring.)

[storm_norm]

I totally get your point on the AIC argument. finding the AIC chain in eureka notation is definitely useful, but probably not necessary for the player that just wants to solve the puzzle because writing it out in notation isn't necessary. so I definitely agree that if eureka notation isn't for you then medusa is definitely the way to go.

your point on the two medusa coloring clusters is also interesting because when you start to color, in the first place, on one candidate, you most likely will learn that two chains can make important eliminations between the two. so the fact that you like the extended medusa rather than the medusa trap is very interesting.

so I have to ask... when you look at one candidate and color the various chains, did you just naturally look for the implications made by the chains?

the reason I ask is because its interesting that you didn't go with coloring two medusa clusters and bridging them, like you would when you brigde two (single candidate) chains. because, instead, you moved to extended medusa.

or... do you bridge medusa clusters and just didn't say it?

[Asellus]

storm_norm,

Before I can answer your interesting, and important, question, I need to clear up some more terminology.

"Extended" Medusa and Medusa "traps" are not mutually exclusive. The first is a way of coloring; the second is a method of eliminating candidates.

In all coloring, regardless of the technique (single digit vs. Medusa; single cluster vs. multi-cluster), eliminations can occur in one of two ways: "traps" or "wraps".

A "trap" occurs when a digit is trapped by two opposing (strongly linked) color polarities. A <5> that sees both a red <5> and a green <5> is thus trapped and eliminated. The same occurs with a <5> that shares a cell with a green <8> and sees a red <5>.

A "wrap" occurs when a color can "see itself" within a house or a cell. This is a contradiction and means that that color must be false and the other true. Two red <5>s in a row, or a red <8> and a red <3> in the same cell are examples of "wraps."

So, I suspect you might be saying "Medusa trap" above when you mean "Medusa multi-coloring," which is also sometimes called a "Medusa Wing" (and probably has other names, too!).

Now, to your question...

First, I agree that multi-cluster coloring can be very useful in the case of single-digit coloring. One would expect there to be a similarly beneficial enhancement in the case of Medusa. But, in actual experience, I haven't found that to be so. I suspect that this is because it is difficult to locate such useful pairs of Medusa clusters and figure out the effective "bridge" link point. Combine this with the added need to keep track of which of the bridged colors are strongly linked and which are not and, frankly, I find this to be a much more difficult challenge than constructing those AICs using Eureka notation!

In my "extended Medusa" examples, there are no such bridges: it remains a single color cluster. However, I have to use 4 color symbols because not all of the reds and greens are equal. In all my postings of this approach, I use "R" and "G" for the standard Medusa coloring of conjugate pairs. Then, the resulting Medusa cluster is extended by assuming in turn that one and then the other of the colors is true. When I assume "R" to be true, the resulting determinations are colored "r". When I assume "G" to be true, the results are colored "g". (It is understandable that someone seeing the 4 symbols might assume that it is multi-cluster coloring. It is not.)

This approach is much easier to use than Medusa multi-coloring since "red" and "green" remain strongly linked without regard to that upper case-lower case distinction I've used. "Traps" occur with R-G, R-g, r-G and r-g. "Wraps" occur with R-R, R-r, r-r, G-G, G-g, and g-g.

The only difference is that in the case of a "wrap" only the upper case colored candidates are determined to be false. For instance, if we find two conflicting "reds" in a cell or house, then all "R" values are false and all "G" and "g" values are true. But, we know nothing about the "r" values; they are not necessarily false because their coloring depended upon the assumption that "R" was true.

Often in a puzzle, a conventional Medusa cluster does not extend far enough to be useful. With this method of extending the cluster, I find that it more frequently leads to eliminations. And while some judgment about the most fruitful appearing place to start coloring is still advisable, more possible initial choices become fruitful because of the extensions.

[Edit for typo.]

[Asellus]

I suddenly realize that there is a comment I could add that might help:

In the Medusa marking, one contructs an "R" and "G" "chain" by alternate coloring of conjugate links.

However, the extended "r" and "g" coloring doesn't work in this way at all. Rather, one constructs a chain of "r" values alone. Separately, one constructs a chain of "g" values. There is no alternating of "r" and "g" along a "chain" in the way in which the standard coloring is done. When coloring "r", you must ignore all green values... as if you are colorblind and cannot see green!

If you mark a "g" because it is strongly linked with an "r", you have made an invalid mark and you risk making invalid eliminations. (You have to break any coloring habit you might have to do such a thing.)

Maybe that helps to explain it.

[storm_norm]

thank you asellus for the responses.

I totally understand the differences between the lower case letters and the upper case letters.

my nine lives of cat curiousity boil over not only when I learn something new about the solving process, but when I learn something about one's solving preferences. fascinating stuff