Nishio vs AICs. When is it considered cheating?

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Re: Nishio vs AICs. When is it considered cheating?

Postby David P Bird » Sat Dec 23, 2017 3:43 pm

btw When Eleven says
To get the AIC "(6)r9c13 = (6-2)r7c2 = r9c3 - r9c9 = (2-6)r8c9 = (6)r8c45 => -6 r9c4" SpAce had to make the assumption, that 6r7c2 is true. So it is just nonsense to claim "That is an unassumptive pattern-based elimination".

he deliberately ignores that the chain would have been started from a strong link (perhaps (6)r9c13 = (6)r7c2) and grew from there, with no assumption being made about which one was true.

Btw when David says, he uses a method to show all bifurcations, that is called "brute force" (there can be really much).


I also have a 'brute force' method for distinguishing apples from oranges.
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Re: Nishio vs AICs. When is it considered cheating?

Postby eleven » Sat Dec 23, 2017 4:47 pm

David,

can you explain the difference between "starting from a strong link (perhaps (6)r9c13 = (6)r7c2) and growing from there" and "assuming r7c2=6 (or r9c13 not 6) and building a chain from this assumption" ?
And what, if you grow into a contradiction ? Don' t tell anyone ?
Don't tell me, that these are no religious aspects, far away from a logical perspective.
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Re: Nishio vs AICs. When is it considered cheating?

Postby SpAce » Sat Dec 23, 2017 5:17 pm

eleven wrote:Andrew Stuarts Nishio consists of 2 multidigit forcing chains showing a contradiction.
What they have in common is, that they start with a single digit, setting it one time true and one time false.


Actually, I think in Stuart's solver that's a Digit Forcing Chain. His Nishio only uses a true assumption but forms two branches with that.

In both cases i cannot see any reason, why they stop their chains somewhere in the grid (where their contradiction arises), instead of continuing, until they get a contradition in the starting cell.


Me neither. Well, I can really only agree about Stuart's case, because I don't know anything about the Explainer's implementation (but I trust you).

Once again let me say that AIC's ARE NO PATTERNS, but an ASSUMPTIVE TRIAL & ERROR technique.


That's quite assumptive itself :)

A pattern is something, which has a structure, you can optically recognize in a grid. Examples are the patterns, which show you the hidden singles, many fish and wings, unique rectangles, deadly patterns and so forth. But no one can identify any non trivial AIC optically without following the chain.


I don't claim that I do - yet - but I don't consider it impossible. If you have a system that visualizes most kinds of strong links clearly, and your brain is very used to interpreting those visuals, I bet you start seeing full or at least partial chains without having to follow every link one at a time. I know I'm improving in that all the time, and many chain patterns are starting to stand out from the grid. It's like learning to read. At first you can process only one letter at a time, then a syllable, then a word, then a sentence, then a paragraph, and I guess some can even process a whole page with one glance. At first it's a strictly linear process, but with enough experience it starts happening so quickly that it appears almost parallel (or maybe it is, who knows how the brain really work).

And to follow it, you have to make the assumption, that a digit is true or false, just as you do with the nishios above.


No. To see the chain doesn't require following it, because it's built from recognizable parts -- strong links at both ends which are connected by alternating links. It's like connecting components that have well-defined interfaces. If you have a correctly built chain, you don't have to follow it to know what an assumption at one end produces in the other. Of course, it would be quite risky not to test your chain with an assumption, but it's not strictly necessary when building it in your mind. It just requires a paradigm shift in thinking and looking at things. I'm not quite there yet but I don't think it's impossible.

(Talking about paradigm shifts --I think this is very similar to why long-time procedural programmers often have a hard time learning object-oriented programming. It also requires a different way of looking at things, and incidentally quite similar to this.)

To get the AIC "(6)r9c13 = (6-2)r7c2 = r9c3 - r9c9 = (2-6)r8c9 = (6)r8c45 => -6 r9c4" SpAce had to make the assumption, that 6r7c2 is true. So it is just nonsense to claim "That is an unassumptive pattern-based elimination".


No. See what David said about that. I never had to make any assumption about the eventual elimination. It's not part of the chain.

This is my last attempt to make that clear here. If people don't want to accept the truth, it makes no sense, trying to explain it. At the end you are just lying to yourselves.


I'm not a big fan of lying to myself, and I gratefully accept wake-up calls if someone catches me doing it. I'm not yet convinced that I need to wake up from this. I usually agree with you, but I think you may be looking at this from a bit narrow window.
Last edited by SpAce on Sat Dec 23, 2017 5:34 pm, edited 1 time in total.
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Re: Nishio vs AICs. When is it considered cheating?

Postby eleven » Sat Dec 23, 2017 5:27 pm

SpAce, you did not catch the point.
I read about a shephard, who with one glance could say, if one of the 500 sheeps is missing.
If with one glance you can see the AIC, then you also can see the candidates to eliminate with one glance. You don't need the AIC at all then.
But if you need AIC's, you need assumptions and chains following from then.
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Re: Nishio vs AICs. When is it considered cheating?

Postby SpAce » Sat Dec 23, 2017 5:48 pm

eleven wrote:SpAce, you did not catch the point.
I read about a shephard, who with one glance could say, if one of the 500 sheeps is missing.
If with one glance you can see the AIC, then you also can see the candidates to eliminate with one glance. You don't need the AIC at all then.


But where's the fun in that? Building the AIC is the fun part to me. I used a comparison with programming paradigms above, partly because I see AICs as simple programs that take input (the assumption) and produce output. Input and output are not part of the program itself, though. Even though AICs run procedurally, like almost all programs, you don't have to build them thinking procedurally. You can also think in terms of interfaces and connected components.
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Re: Nishio vs AICs. When is it considered cheating?

Postby eleven » Sat Dec 23, 2017 6:02 pm

Yes, all i say is, that you can have the same fun not using AIC's, but just assuming candidates in an educated way - and AIC is an assumptive trial&error method as well.
(for me AIC's have exactly one advantage: it's a bit easier to verify other's loop eliminations)

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Re: Nishio vs AICs. When is it considered cheating?

Postby StrmCkr » Sat Dec 23, 2017 10:23 pm

happy festivities to you eleven
and every one else
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Re: Nishio vs AICs. When is it considered cheating?

Postby SpAce » Sat Dec 23, 2017 11:09 pm

eleven wrote:Yes, all i say is, that you can have the same fun not using AIC's, but just assuming candidates in an educated way


Sure. I'm not saying anything to the contrary. Why not have double the fun and learn to see it both ways? I'm personally more into cherry-picking than choosing religious sides.

- and AIC is an assumptive trial&error method as well.


I think I said the same in my very first post in this thread, and I haven't changed my mind. I'm just saying it's not the only way to see and use AICs. I'm still probably using the assumptive mode more, but I'm starting to feel comfortable with the other paradigm too. Being able to see the same thing from multiple perspectives gives you more possibilities to actually find what you're looking for. I don't really care if what I'm doing is assumptive or not, as long as it works and is mentally stimulating.

Happy holidays, everyone!
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Re: Nishio vs AICs. When is it considered cheating?

Postby coloin » Sun Dec 24, 2017 11:31 am

eleven wrote:And what, if you grow into a contradiction ? Don' t tell anyone ?

hmmm this makes more sense to me if you say "if you don't grow into a contradiction - dont tell anyone" !

but i understand you eleven that trail and error is perfectly acceptable to produce an elimination.
if there are 3 options in a cell and 2 are wrong then whats left is correct

the degree to which you have to go to to get a contradiction is proportional to some description of the difficulty.

So in any valid 21 clue puzzle
there will be 60 insertions that are correct
8 x 60 trial and error [error] moves
more than half of these 8 will be easy to show errors

i dont know of many puzzles which dont have one or more bivalue/bilocal cells.
So i think "sucking it and see" as my old chemistry master put it would be reasonable

Say you have 2 of these bivalue options - so you have 4 paired options
When/If you get a contradiction [ length/degree of difficulty to be ascertained] then 3 of the proposed pairs will be shown to be incorrect.

If you get it right the first [ of the 4 ]time it has been a guess
If you go back and prove that the other 3 options lead to a contradiction you will have proved your guess correct. And it is no longer a guess.

If two of the pairs dont lead to a contradiction - you either have gone wrong or have a multi-solution "puzzle"
If all of the pairs lead to a contradiction - you have either gone wrong or have a no-solution "puzzle"
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Re: Nishio vs AICs. When is it considered cheating?

Postby David P Bird » Sun Dec 24, 2017 12:40 pm

coloin, I think you start on the wrong track here.

Eleven was posing that question in respect to an AIC where no assumption is made about the truth of any term in the chain.

If all the weak and strong links in an AIC are sound, I can't see how you can reach a contradiction. As far as I'm concerned a contradiction can only arise if false assumption is made somewhere. When that contradiction is reached, it shows the assumption was wrong.

If I'm reading it correctly, the balance of your post then seems to cover ways to reduce the number of trial and error assumptions needed to reduce a puzzle, which is interesting, but not my cup of tea (just as assuming uniqueness is not yours).

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Re: Nishio vs AICs. When is it considered cheating?

Postby eleven » Mon Dec 25, 2017 11:36 pm

eleven wrote:And what, if you grow into a contradiction ? Don' t tell anyone ?

Should not have said that, sorry.
Just recently i wrote myself, that you can reuse a candidate in an AIC, as often you want (and i meant also true or false in the same cell) - as long as the links are correct, the chain is correct.
This way AIC's have no problem with contradictions. They just can be ignored. To give an example:

Code: Select all
  16 . . | 13 . .
  .  . . | .  . .
  .  . . | .  . .
 -----------------
  12 . . | 23  . .
  .  . . | .  . .
  .  . . | .  . .

xy-wing 123 => -1r1c1
If you try 1 in r1c1, you get 3r1c4, 2r4c4 and 1r4c1, a contradiction, r1c1<>1
If you start an AIC with (6=1)r1c1-(1=3)r1c4-(3=2)r4c4-(2=1)r4c1, you can skip the first term and get 1r1c4 or 1r4c1 => r1c1<>1
Now personally i first would recognize the contradiction than the possibility to skip the first term and see the elimination without it.

It is often easier and simpler to find eliminations by contradiction than without (especially including small but obvious nets).
That's the reason, why i don't like this holy "contradiction-free" postulate. You see the contradiction, but it is not accepted, before you formulate it without contradiction. Though everyone should know, that this is always possible (but often hard with the clumsy AIC construction rules).

[Added:]
@Coloin: yes, if the assumption turns out to be right, and you solve the puzzle with it, it is a guess, until you have proved, that with the assumption set false there would be a contradiction (or other solutions).
In practice you would hardly directly come from an assumption to the solution. There are many more moves from there. Also if these all would be singles, they build a complex net, which hardly can be solved in the head. So normally you would stop to follow it rather soon - and try something else, if you found no eliminations.
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Re: Nishio vs AICs. When is it considered cheating?

Postby SpAce » Wed Dec 27, 2017 4:44 am

While we're at it, I have some questions about net techniques. Why are they considered bad, except for the obvious reason that they're more complicated and harder to communicate? I personally think netting is quite acceptable as long as the logic is explainable and preferably worked out in one's head. That being said, I've only used it a couple of times when I couldn't find other ways to move forward, but I actually thought it was quite enjoyable to find such non-prepackaged solutions. It felt like actual problem solving instead of just looking for patterns invented by other people. It also resembled the thrill of parallel programming compared to the bore of most linear programs.

I just happened to run into a simple example at the beginning of one of Ruud's nightmares (Nov 18, 2007). I didn't actually use the net I found, because I wanted to keep my solve path clean and it wasn't hard to find alternatives, but it was still fun to see it. It would have shaved off one step had I used it (and not changed anything else).

Code: Select all
+--------------+--------------+----------------------+
| 78  39  78   | 49  1   24   |  25-3   6       2345 |
| 2   46  46   | 3   7   5    |  8      1       9    |
| 1   39  5    | 469 26  8    |  7     h2(3)    234  |
+--------------+--------------+----------------------+
| 456 1   3    | 8   259 24   |  2569   259     7    |
| 568 2   68   | 1  E359 7    | D3569   4       358  |
| 9   457 478  | 45 F235 6    |  1     g235    C2358 |
+--------------+--------------+----------------------+
| 457 457 9    | 2   58  1    | a45(3)  578-3   6    |
| 3   456 2    | 7   568 9    | a45     58      1    |
| 567 8   1    | 56  4   3    | b259    b2579  b25   |
+--------------+--------------+----------------------+


The chain [a-h] has two branches [C] and [D-F] that start at [b] and join at [g] (or I guess one could see just one subchain, [C], and [D-F] as part of the main chain). Now my next question is about the net notation. Is there any standard for that? I guess it's not officially supported by Eureka. I used this:

-3 r1c7, r7c8 <= [3r7c7 | 3r3c8] <= AIC-NET:
(3=45)r78c7 - (5=729)r9c789 [ [- (2)r6c9] & [- (9)r5c7 = (9-3)r5c5 = (3-2)r6c5] ] = (2)r6c8 - (2=3)r3c8

Edit: As expected, there were a few clear mistakes in the notation above. This would be more correct:
(3=45)r78c7 - (5=29)r9c79 - [ [(2)r6c9] | [(9)r5c7 = (9-3)r5c5 = (3-2)r6c5] ] = (2)r6c8 - (2=3)r3c8

Last question: how would you reverse that? [Edit: the corrected version above is bidirectional.] I can't see any obvious way to do it. Does it matter, however, except for reasons of principle and the possibly confusing abuse of Eureka?

The original puzzle:

000010060200305009100008700003800007020000040900006100009200006300709001080040000
Last edited by SpAce on Fri Dec 29, 2017 9:12 am, edited 1 time in total.
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Re: Nishio vs AICs. When is it considered cheating?

Postby eleven » Wed Dec 27, 2017 12:53 pm

In an AIC notation i would write it
(3=29)r78c7,r9c79 - (2r6c9 | [9r5c7=(9-3)r5c5=(3-2)r6c5]) = 2r6c8 - (2=3)r3c8 => -3r1c6,r7c8

Alternatively you could write the subchain seperately, e.g.
(*) -9r5c7=(9-3)r5c5=(3-2)r6c5
(3=29)r78c7,r9c79 - (2r6c9 | (*)2r6c5) = 2r6c8 - (2=3)r3c8

Otherwise i would write it as i see it
-3r78c7 -> 5r78c7 -> -5r9c79 -> 2r9c9 & (9r9c7 -> -9r7c5 -> 9r5c5 -> 3r6c5 -> -2r6c5) -> 2r7c8 -> 3r3c8 => -3r1c6,r7c8
or
-3r78c7,r9c79 -> 2r9c9 & (9r9c7 -> 9r5c5 -> 3r6c5) -> 2r7c8 -> 3r3c8 => -3r1c6,r7c8
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Re: Nishio vs AICs. When is it considered cheating?

Postby ghfick » Wed Dec 27, 2017 7:37 pm

One could use a fairly short bidirectional chain here to accomplish the same exclusions.

(3=2)r3c8 - r3c5 = r1c6 - (2=4)r4c6 - (4=5)r6c4 - (5=3)r36c8 - (3)r7c8 = r7c7 => -3 r1c7 r7c8

Or one could take the ER and the UR first and then there is a bidirectional chain without ALS nodes.

I do agree that it is interesting to see more elaborate methods accomplishing the same exclusions. Here, though, I would surmise that there are many nets in play. Maybe some variation as to how one should use Eureka here as well.
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Re: Nishio vs AICs. When is it considered cheating?

Postby SpAce » Wed Dec 27, 2017 10:35 pm

ghfick wrote:One could use a fairly short bidirectional chain here to accomplish the same exclusions.

(3=2)r3c8 - r3c5 = r1c6 - (2=4)r4c6 - (4=5)r6c4 - (5=3)r36c8 - (3)r7c8 = r7c7 => -3 r1c7 r7c8


You're right, thanks! I actually didn't see that. It's definitely preferable to use the simplest possible chain that achieves the same result.

Or one could take the ER and the UR first and then there is a bidirectional chain without ALS nodes.


Yeah, this is a relatively simple nightmare so there are many possibilities. For example, I never went for the 3s directly. I actually didn't use any ALSs or URs here, so every step is just a simple chain (only the ERs are even grouped). My solve path was pretty long, though (10 non-trivial steps; would be 9 with that net or your chain above). This is getting off-topic, but could someone show a shorter path (preferably without knowing the backdoors) to this? I used:

3 x AIC (Hodoku Type 1)
2 x AIC (Hodoku Type 2)
2 x X-Chain (Grouped, ER)
2 x XY-Wing
1 x XY-Chain

Full path:

Hidden Text: Show
Code: Select all
1)  -4 r8c2      <= [6r8c2 | 4r8c7]  <= AIC-2:    (6)r8c2 = r8c5 - (6=2)r3c5 - (2=3)r3c8 - r7c8 = (3-4)r7c7 = (4)r8c7

2)  -5 r9c1      <= [5r5c4 | 5r45c1] <= X-Chain:  (5)r9c4 = r6c4 - r6c2 = (5)r45c1

3)  -4 r6c2      <= [4r2c2 | 4r6c4]  <= AIC-1:    (4=6)r2c2 - r8c2 = r9c1 - (6=5)r9c4 - (5=4)r6c4

4)  -7 r7c2      <= [7r6c2 | 7r9c1]  <= XY-Wing:  (7=5)r6c2 - (5=6)r8c2 - (6=7)r9c1

5)  -5 r7c5      <= [5r7c2 | 5r9c4]  <= XY-Chain: (5=4)r7c2 - (4=7)r7c1 - (7=6)r9c1 - (6=5)r9c4

6)  -5 r7c7      <= [5r7c2 | 3r7c7]  <= AIC-2:    (5)r7c2 = (5-6)r8c2 = r8c5 - (6=2)r3c5 - (2=3)r3c8 - (r7c8) = (3)r7c7

7)  -5 r6c8      <= [5r6c4 | 5r7c8]  <= X-Chain:  (5)r6c4 = r9c4 - r9c789 = (5)r7c8

8)  -5 r4c5 r6c9 <= [5r6c4 | 5r4c8]  <= AIC-1:    (5=4)r6c4 - (4=8)r6c3 - r6c9 = (8-3)r5c9 = (3-9)r5c5 = r4c5 - (9=5)r4c8

9)  -5 r45c7     <= [5r1c7 | 5r4c8]  <= AIC-1:    (5=2)r1c7 - r1c6 = r4c6 - (2=9)r4c5 - (9=5)r4c8

10) -5 r4c1 r5c9 <= [5r5c1 | 5r4c8]  <= XY-Wing:  (5=6)r5c1 - (6=9)r5c7 - (9=5)r4c8; stte


The same using the conventional layout:

Hidden Text: Show
Code: Select all
1) AIC (Type 2): (6)r8c2 = r8c5 - (6=2)r3c5 - (2=3)r3c8 - r7c8 = (3-4)r7c7 = (4)r8c7 => -4 r8c2 

2) X-Chain (Grouped, ER): (5)r9c4 = r6c4 - r6c2 = (5)r45c1 => -5 r9c1

3) AIC (Type 1): (4=6)r2c2 - r8c2 = r9c1 - (6=5)r9c4 - (5=4)r6c4 => -4 r6c2 

4) XY-Wing: (7=5)r6c2 - (5=6)r8c2 - (6=7)r9c1 => -7 r7c2

5) XY-Chain: (5=4)r7c2 - (4=7)r7c1 - (7=6)r9c1 - (6=5)r9c4 => -5 r7c5

6) AIC (Type 2): (5)r7c2 = (5-6)r8c2 = r8c5 - (6=2)r3c5 - (2=3)r3c8 - (r7c8) = (3)r7c7 => -5 r7c7

7) X-Chain (Grouped, ER): (5)r6c4 = r9c4 - r9c789 = (5)r7c8 => -5 r6c8

8) AIC (Type 1): (5=4)r6c4 - (4=8)r6c3 - r6c9 = (8-3)r5c9 = (3-9)r5c5 = r4c5 - (9=5)r4c8 => -5 r4c5 r6c9

9) AIC (Type 1): (5=2)r1c7 - r1c6 = r4c6 - (2=9)r4c5 - (9=5)r4c8 => -5 r45c7

10) XY-Wing: (5=6)r5c1 - (6=9)r5c7 - (9=5)r4c8 => -5 r4c1 r5c9; stte
Last edited by SpAce on Thu Dec 28, 2017 12:43 am, edited 1 time in total.
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