The New Sudoku Players' Forum

[SpAce]

No, I think you have put it the other way around. My assumption is that: (4) is the solution in r1c1, but, the chain shows 4 is in r3c1, so it cannot be in r1c1 as assumed.

Sorry, Clement, you're right. I missed the fact that your chain started with a weak link. Not good on my part, particularly considering that I used to use that form frequently myself.

Well, the bottom line should be that starting with a weak link is in almost all cases totally unnecessary and confusing. Here too. It's not the reader's fault when someone deliberately uses practices that are not expected and don't make sense. With AICs the common idiom is to have a strong link at both ends, and there's zero reason to deviate from that here. (Something like eleven's solution is a bit different, but even in that case I rather add the 'DP' to the start to have a strong link at both ends. That way the interpretation of every AIC is exactly the same: one or the other end point must be true. Since a DP can't be true the other must be.)

(4)r1c1 - (4=5*6)r1c47 - (6=3)r2c8 - (35*=1)r2c6 - r2c5 = r7c5 - (5*1=3)r7c4 - (3=64)r3c41 => - 4r1c1; stte

Mostly good, except for the starting weak link and a couple of usual (minor) problems. Here's how I'd have written it:

(4=5*6)r1c47 - (6=3)r2c8 - (3|*5=1)r2c6 - r2c5 = r7c5 - (1|*5=3)r7c4 - (3=64)r3c41 => -4 r1c1,r3c8; stte

...or with just one memory operation:

(4=6)r1c7 - (6=35*)r2c8,r1c4 - (3|5=1)r2c6 - r2c5 = r7c5 - (1|*5=3)r7c4 - (3=64)r3c41 => -4 r1c1,r3c8; stte

That said, nice solution otherwise. (Btw, the grid shows a wrong elimination.)

[Cenoman]

The reason for the complexity can be seen in the matrix. At least I can't write it with anything simpler than a BTM:

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6x6 BTM:
 6r3c4 3r3c4
       3r2c6 5r2c6 1r2c6
 6r2c1       5r2c1
                   1r4c6 3r4c6
                         3r5c5 6r5c5
       3r2c5       1r2c5       6r2c5
------------------------------------
-6r2c5,r3c1

(Hope Cenoman will correct that matrix if it has problems.)

Well, I'd just suggest to write it as a TM, exchanging rows 2,3:

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 6r3c4 3r3c4
 6r2c1       5r2c1
       3r2c6 5r2c6 1r2c6
                   1r4c6 3r4c6
                         3r5c5 6r5c5
       3r2c5       1r2c5       6r2c5
------------------------------------
-6r2c5,r3c1

That said, it hides as well the complexity of the move (double kraken) and reveals the beauty of eleven's move.
IMHO, this 6x6 TM is the best presentation for such a solution: it is compact, avoids any repetition and displays clearly all natice links used. But that's not more than my own preference.

[SpAce]

Well, I'd just suggest to write it as a TM, exchanging rows 2,3:

Lol, how did I not see that? I naturally tried to write it as a TM but missed the simple fix that would have achieved it. Like I said, I was running on limited brain cycles. Thanks, Cenoman! I knew I could trust you to see what I couldn't!

IMHO, this 6x6 TM is the best presentation for such a solution: it is compact, avoids any repetition and displays clearly all natice links used.

I agree, except for the fact that it doesn't capture the compact elegance of the original logic by itself. I love matrices, thanks to you, but in general I think a move presented only as a matrix is a bit raw. It does show the internal details of the logic better than anything, but it doesn't necessarily reflect how the player saw it. It doesn't leave much room for creativity either, as there's usually only one good way to write it (like you just demonstrated).

Yet for the same reasons it's perfect raw material to find other, possibly more interesting and creative, presentations. If I hadn't written the matrix first, I'm sure I wouldn't have seen the dual-almost-Y-Wing, for example. Even though it's quite far from eleven's presented logic in this case, it is somewhat similar to what we've seen from him in the past. It's conceivable that a good player could have seen the move like that. It's also the only AIC representation I've personally liked so far, besides the compact DP-variant that's essentially the same as the original.

[SteveG48]

Well, the bottom line should be that starting with a weak link is in almost all cases totally unnecessary and confusing. Here too.

Yes, and that's the reason that I stopped using that form almost completely. You can almost always simply eliminate the first term, as is the case here.

[SpAce]

Yes, and that's the reason that I stopped using that form almost completely. You can almost always simply eliminate the first term, as is the case here.

Indeed. Yet if someone really really wants to use that style (I don't know why), they should at least do it consistently so others can learn to expect it. While I have learned to expect it from Clement every now and then, I haven't figured out any pattern in it. Seems totally random to me, as most of the time he writes normal AICs. Since it's clearly not an accident (unlike I thought the first time I saw it), there must be a reason for it. I'm curious what it is.

[Ajò Dimonios]

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Ngisa wrote:
(4)r1c1 - (4=5*6)r1c47 - (6=3)r2c8 - (35*=1)r2c6 - r2c5 = r7c5 - (5*1=3)r7c4 - (3=64)r3c41 => - 4r1c1;

I don't see irregularities in the Ngisa chain because the first weak inference 4r1c1- (4 = 5 * 6) r1c47 is equivalent to the strong inference 4r3c1 = 4r3c8- (4 = 5 * 6) r1c47. The only problem of orthodoxy is simply linked to the memory that is preserved of previous inferences (however valid) such as the weak inference 3r2c8-35r2c6 which is valid if we take into account the previous strong inference (4 = 5 * 6) r1c47 or the weak inference 1r7c5-5 * 1r7c4 which is correct if the previous strong inference (4 = 5 * 6) r1c47 is always taken into account.

Paolo

[SpAce]

I don't see irregularities in the Ngisa chain because the first weak inference 4r1c1- (4 = 5 * 6) r1c47 is equivalent to the strong inference 4r3c1 = 4r3c8- (4 = 5 * 6) r1c47.

What? I have no idea what you're saying, nor why you're mixing in cells that aren't even part of the chain. It doesn't make any sense to say a weak inference is equivalent to a strong inference anyway. They can't be equal because they're totally different concepts. One is OR and the other is NAND, in terms of logic gates.

Besides, no one said Clement's style was incorrect. It's just inefficient and unidiomatic (thus confusing and hard to read). It's actually two things that AICs are not natively (though they can mimic them): a contradiction chain and an implication chain. Neither makes it incorrect per se, but both make it extremely unidiomatic. The best way to fix that is simply to remove the first node, which would make it an idiomatic AIC. The second best fix is to add a weak link to the end too (with a duplicated start node), which would make it a Discontinuous Nice Loop (DNL). The way it's now written is a mongrel between the the DNL and the AIC styles, which is the worst possibility. The idiomatic way to write something like that would be to use the implication chain notation (A -> B) instead of Eureka. That would be the third best option.

Both the AIC and the DNL styles are easy to read because they have the same link type at both ends. It tells at a glance that the end nodes have either an OR relationship (AICs) or a NAND relationship (DNL). The conclusions are easy to made in both cases. The mongrel style is not so easy at all, because it basically requires one to mentally convert the chain into an implication chain (which AICs are not natively). The relationship between the end nodes is (A -> B) and (-B -> -A) which is asymmetric and equivalent to (~A | B). Asymmetry and any hint of directionality are unidiomatic for AICs (unlike for implication chains). Also, to see the concluded elimination (only one possible, unlike AICs), one has to also see that the end nodes are contradictory (A NAND B): thus A can't be true since it implies B while both can't be true.

Thus, that style is much more complicated than either the AIC or the DNL logic, especially for those who've used to seeing AICs as boolean logic constructs (which they are natively, instead of implication chains). I can see how it might feel more comfortable for those who've come from implication and contradiction chain backgrounds, but it just tells that they haven't internalized the true nature of AICs. The fact that Eureka can more or less mimic those other paradigms too doesn't mean that it's a good idea to use it for them.

The only problem of orthodoxy is simply linked to the memory that is preserved of previous inferences (however valid) such as the weak inference 3r2c8-35r2c6 which is valid if we take into account the previous strong inference (4 = 5 * 6) r1c47 or the weak inference 1r7c5-5 * 1r7c4 which is correct if the previous strong inference (4 = 5 * 6) r1c47 is always taken into account.

There's no problem or confusion there. Clement's chain is a memory chain and correctly marked as such (though not exactly how I'd place the marks, but that's less relevant). Thus it's not a valid AIC (which can only use inferences from adjacent nodes) but neither does it claim to be. All is well in that regard.

[StrmCkr]

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+----------------+-------------------+----------------+
| 456   1   3    | 5(6)     7    8   | (46)  2      9 |
| 56    9   2    | 4        136  135 | 8     36     7 |
| (46)  7   8    | 3(6)     9    2   | 1     36(4)  5 |
+----------------+-------------------+----------------+
| 9     36  47   | -13(67)  2    13  | 346   5      8 |
| 1     36  5    | 8        36   4   | 9     7      2 |
| 8     2   (47) | 3(67)    5    9   | 36-4  (46)   1 |
+----------------+-------------------+----------------+
| 7     4   9    | 135      13   135 | 2     8      6 |
| 3     5   1    | 2        8    6   | 7     9      4 |
| 2     8   6    | 9        4    7   | 5     1      3 |
+----------------+-------------------+----------------+


simplified elevens further:
[my chain writing skills suck]:
when R3C8 = 4 => [R1C7,R3C1,R6C8 = 6] =>[ R4C4 = 6] & [ R6C3 = 4 ]
when R3C8 <> 4, => [R1C7,R3C1,R6C8 = 4] =>[ R6C3 = 7 ]& [ R4C4 = 7]
=> R4C4 <> 1,3 & R6C7 <> 4

[Ajò Dimonios]

Hi Space.

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 Space wrote:
What? I have no idea what you're saying, nor why you're mixing in cells that aren't even part of the chain. It doesn't make any sense to say a weak inference is equivalent to a strong inference anyway. They can't be equal because they're totally different concepts. One is OR and the other is NAND, in terms of logic gates.

I'm sorry but I don't agree with you at all. Between 4 in r1c1 and 4 in r3c1 there is a strong inference. Any weak inference that starts at 4r1c1 can be written equivalently with a strong inference that starts at 4r3c1. To put it in terms of tracks, track P (4r1c1) is equivalent to track P '(4r3c1). This means that 4r3c1 = 4r1c1- (4 = 5 * 6) r1c47 produces the exact same chain start as 4r1c1- (4 = 5 * 6) r1c47. The end of the chain -4r1c1 is interpreted in one case as the elimination of an AIC with memory or in the other case as the elimination of a discontinuous nice loop (with memory). It is evident that two identical chains are given different names. The question I ask myself now is this, since there is always a conjugated anti-track for every track defined, can any chain of contradiction be transformed into an AIC with memory? In practice it is possible to address the contradiction of the chain, choosing artfully the useful inferences that lead to contradict the initial hypothesis of the chain?

Paolo

[SpAce]

I'm sorry but I don't agree with you at all.

By all means. All I can say to that is to quote a good friend of mine:

"You could think I'm wrong, but that's no reason to stop thinking."

[Ajò Dimonios]

Hi Space.

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Gregory House, M.D. wrote:
"You could think I'm wrong, but that's no reason to stop thinking."

On this I fully agree with you. The important thing in a discussion, when you are convinced of what you think, to convince the interlocutor when he is wrong.

Paolo

[eleven]

The question I ask myself now is this, since there is always a conjugated anti-track for every track defined, can any chain of contradiction be transformed into an AIC with memory?

It can be transformed into a net. If it is possible to write it as AIC with memory depends on the definition of, what a chain and an AIC is.

[Ajò Dimonios]

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Eleven wrote:
It can be transformed into a net. If it is possible to write it as AIC with memory depends on the definition of, what a chain and an AIC is.

I agree that an AIC must be well defined.
If for an AiC we mean the classic one without considering the memory of a previous inference in the chain, the field is very narrow and the chains of contradiction that can be transformed into a valid AIC are not many, only those in which the contradiction is reached after a few steps. If, on the other hand, we also consider memory, many chains of contradiction, transforming into a net, can be transformed into an AIC.

Paolo

[SpAce]

The important thing in a discussion, when you are convinced of what you think, to convince the interlocutor when he is wrong.

Dear Paolo, rest assured -- my vague memories of our past discussions make me seriously doubt that I could ever convince you that you're wrong about anything. Besides, I don't really feel like arguing about notational issues with someone who doesn't even spell my handle correctly and uses 'code' when 'quote' is needed. Makes me think that either your eye for such things is not exactly sharp, or otherwise you simply prefer sloppiness and ugliness. Either way, it's unlikely that we'd find common ground, so I'm quite happy to let you keep your opinions.

[Ajò Dimonios]

Space wrote:
Dear Paolo, rest assured -- my vague memories of our past discussions make me seriously doubt that I could ever convince you that you're wrong about anything. Besides, I don't really feel like arguing about notational issues with someone who doesn't even spell my handle correctly and uses 'code' when 'quote' is needed. Makes me think that either your eye for such things is not exactly sharp, or otherwise you simply prefer sloppiness and ugliness. Either way, it's unlikely that we'd find common ground, so I'm quite happy to let you keep your opinions.

Dear Space, I am sorry that you are so aggressive perhaps it is related to your character or perhaps because you have no valid arguments to reply. However I also don't like, being very crude and not very lucid, to discuss these matters with you.


Paolo