dailysudoku.com

[ravel]

This puzzle was posted at the player's forum some days ago:

[Asellus]

ravel,

In your first grid, I follow everything except that I don't see the "b" marking for the <1> in r6c8. Instead, I see that the <1> in r3c3 should be marked "b", consistent with the elimination of <1>s in r3c12, with which I agree. As you've marked it, the <1>s in r6c12 would be eliminated. However, I don't agree with that. Am I not understanding something?

I suspect that not everyone will see how this coloring was done (or how I did it, at least). It involves locked candidates in the left "tower" (B147) based on the coloring in B3 and the {17} locked pair in r7c12. If "a" is true, there is an X-Wing on <1> in r17c12 leaving the <1> in r6c3 as the only "a" <1> in c3 (because of the "a" <1> in r3c8). And, since this "a" <1> displaces one of the only 2 <7>s in c3, the other <7> in r2c3 must be "a". (A similar approach could be used for the "b" case with a <7> X-Wing, etc.)

[Asellus]

I, too, next extended the "b" implication and found a contradiction after involving almost the entire grid. (Awkward, indeed!) This allowed placement of all "a" values. But, I only needed an XYZ Wing after that to finish. Here's the grid I got:

[ravel]

[ravel]

This is my notation exercise (whats its name ?)
(2=7)r2c3-(7=5)r2c9-(5=1)r3c8-(1)r3c3=(1-7)r6c3=(7-2)r2c3
Then either r2c3=7 or r2c9=7 etc.

[nataraj]

[ravel]

Ok, thanks again, nataraj,

i think i understood enough now to be able to read it (also noticed that - like with an ALS with 2 extra candidates - its not an exclusive either/or). But - like with (classical) nice loops and others - i do not intend to use it myself. Such a closed loop is exactly the only sample, where i see an advantage for this notation.

The problems i have with all these notations (instead of basic implication chains, marked grids and everyday speech) are:
- they dont reflect the way i spot the things (this includes ALS)
- you need an explanation to be able to read them (and e.g. the nice loop explanations are deterrently difficult)
- there are always (relatively) simple deductions, that cannot be expressed at all or only in a very difficult way
- i cant see any need for them (for humans)

Whats the Eureka notation for this simple elimination ?

[nataraj]

ravel,
I had to edit my previous post - the continuous loop only allows eliminations that use an odd number of links in the loop. Which goes to show it is a terribly tricky subject and I am no expert at all.

This said, I think the value of the concept of AICs or nice loops for me lies in their simple and elegant basic structure. It does not make the patterns easier to find. It helps me to be sure, though. Write down the links. Make sure there is an alternating sequence. Use the ends for elimination.

I do not think it is the best formal language for all situations. Maybe I will, given some more time. Which still leaves the question: is it effective? As you pointed out, it only works when the message is understood by the recipient. So the answer is probably: depends. Depends on the situation (more complex situations tend to need more formal structuring, I think) and depends on the partners in the conversation. Most of the time, simple sentences and basic implications like r1c2=3 => r1c6=7 are certainly more effective means of communication.

[Asellus]

ravel,

The Eureka notation for your simple elimination (a short ALS Chain) is:

(1)r1c1-({12}=3)r1c24-(3=4)r3c4-(4=1)r3c1-(1)r1c1; r1c1<>1

While it looks mysterious to those who don't know it, it is really not difficult to understand. (I don't attempt to explain the notation here, though.) Every ALS contains a strong link. This is obvious in bivalue cells. In the 2-cell {123} ALS of r1c24, the <3> is strongly linked ("=") to the {12} locked pair. If the <1> in r1c1 is true, then the {12} pair is false (as a locked pair, not as two digits), the <3> true, etc. In any case, to me, this notation is no more complicated than the way you wrote out the implication. It has the virtue of showing that one is exploiting an ALS sequence in a consistent way rather than just forcing values true.

Obviously, such notation isn't necessary for eliminations that are simple to see and describe in ordinary language. I believe the notation has value in (at least) two situations: (1) communicating accurately and concisely to others; (2) keeping track of more complex AICs when trying to solve a difficult puzzle on paper.

I started learning it mostly so that I could understand it when others used it. After I did, I gradually found that it increased my solving ability and altered how I looked at puzzles. The discipline of the notation does make one see things differently, in my experience. But then, that may have just been my route to such insights. The nice loops lingo isn't necessary for constructing AICs or using Eureka. For instance, I didn't know that what I was doing was a "discontinuous loop" until nataraj started using the term. But, as with all such things, it no doubt adds some more value.

[ravel]

I knew, that it can be expressed as xyz-ALS, but this is an unneccessary complicated thing here. One simple step more and you need an ALS-chain.

Just can say that i did not make the experience. i really never saw a nice loop, which i wouldnt have found easier without thinking in the notation.

Worse, i noticed that people were not willing or able to understand solutions, which could have been described in simple words to them.

Another sample:
I dont even know, how to write this chain in Eureka notation (suppose there is a good way, but just to demonstrate, that there is a lot to learn to express - and probably understand - simple things):

[Asellus]

The Eureka for the second example is
(9-3)r1c1=(3)r1c4-(3=2)r4c4-(2=9)r4c4-(9)r1c1; r1c1<>9

It's exactly the same as what you wrote but just looks different.

I agree that it is unnecessarily complicated (not helpful) for casual communication and simple cases, and myself only post Eureka for complex situations intended for more advanced readers or in addition to a "plain language" explanation. I wouldn't have used it for either of your simple examples, for instance; so, I'm with you there. I would still encourage folks to learn it if they have any interest.

[ravel]

(9-3)r1c1=(3)r4c1-(3=2)r4c4-(2=9)r1c4-(9)r1c1; r1c1<>9

What was confusing me is, that this way you dont have the alternating links starting and ending with a strong one. So (without the weakly linked ends) i just see directly, that one of r1c1=3 and r1c4=9 must be true - which of course both imply r1c1<>9.

On the other hand the contradiction above is obviously at the first glance.
But i must admit, that when exploring strong links i would not start with r1c1=9, but use a similar, but a bit more general way as looking for xy-chains, that is better reflected by this Eureka chain:
Can i find a "way" from r1c1=3 to one of 456 in a cell that sees r4c1 or one from r4c1=3 to one of 129 in a cell that sees r1c1 ?

[Asellus]

I agree: we actually tend to work from the "pincers" (i.e., the strongly linked ends that kill the victim). The convention in Eureka notation, however, is to place the node of the discontinuity (i.e., the victim(s)) at the two ends of the chain. The weak links indicate that it is false (an elimination). One quickly learns to look past the two ends.

It is possible to have a discontinuity node that is strongly linked on both ends. In that case, the node is proved true.

In either case, the affected node is usually one or more instances of some candidate digit. However, it could be anything... a locked set, for instance or a wing of some sort, I suppose.

Another quick point: focussing on the weak link starting point enables one to see what wouldn't typically be considered a pincer, such as the companion <3> sharing the cell with the victim <9> in this example. There is something nicely unifying about the AIC way of seeing things.