The New Sudoku Players' Forum

[ArkieTech]

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 *-----------*
 |..5|.21|..6|
 |..4|...|3..|
 |2..|.4.|8..|
 |---+---+---|
 |4..|...|7..|
 |.8.|.1.|.9.|
 |..6|...|..8|
 |---+---+---|
 |..1|.6.|..3|
 |..8|...|2..|
 |5..|83.|6..|
 *-----------*


Play/Print this puzzle online

[SpAce]

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.-----------------.-----------------.--------------------.
|  8     79    5  | 3     2    1    |   49   47    6     |
|  1     679   4  | 5679  579  8    |   3    2     579   |
|  2     679   3  | 5679  4    5679 |   8    157   1579  |
:-----------------+-----------------+--------------------:
|  4     1    a29 | 59    8    3    |   7    6    a2[5]  |
|  3     8     27 | 567   1    567  |   4-5  9     245   |
|  79    5     6  | 24    79   24   |   1    3     8     |
:-----------------+-----------------+--------------------:
| c7(9)  24    1  | 24    6    579  | c(5)9  8     3     |
|  6     3     8  | 1     579  4579 |   2    457   479-5 |
|  5     24   b79 | 8     3    2479 |   6    147   1479  |
'-----------------'-----------------'--------------------'

(5=29)r4c93 - r9c3 = (95)r7c17 => -5 r5c7,r8c9; stte

3D-Medusa Multi-Coloring: Show

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.-------------------.--------------------.------------------------.
| 8    +7B-9b  5    | 3     2     1      | +9B-4b  +4B-7b  6      |
| 1     69-7   4    | 5679  579   8      |  3       2      57-9   |
| 2     69-7   3    | 5679  4     5679   |  8       157    157-9  |
:-------------------+--------------------+------------------------:
| 4     1      2A9a | 5a9A  8     3      |  7       6      2a5A   |
| 3     8      2a7A | 567   1     56-7   | +4B-5b   9      2A5-4b |
| 7a9A  5      6    | 24    7A9a  24     |  1       3      8      |
:-------------------+--------------------+------------------------:
| 7A9a  24     1    | 24    6     7a9-5b | +5B-9b   8      3      |
| 6     3      8    | 1     59-7  4579   |  2       57-4   479-5  |
| 5     24     7a9A | 8     3     2479   |  6       17-4   1479   |
'-------------------'--------------------'------------------------'

Two medusa-clusters: aA and bB

3D-Multi-Coloring Wrap: 'b' sees both parities of 'aA' (r7c6,5b6) => 'b'=false, 'B'=true
=> 5 B-placements; stte

also:

Simple Coloring Traps (sub-cluster 7aA): -7 r5c6,r8c5

(total: 16 immediate coloring eliminations)

[Sudtyro2]

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                                     b
+----------------+----------------+-----------------+
|  8   79   5    | 3    2   1     | a49# 47   6     |
|  1   679  4    | 5679 579 8     |  3   2    579   |
|  2   679  3    | 5679 4   5679  |  8   157  1579  |
+----------------+----------------+-----------------+
|  4   1    29   | 59   8   3     |  7   6    25    |
|  3   8   d27   | 567  1   567   | b45  9  e25-4   | c
|  79  5    6    | 24   79  24    |  1   3    8     |
+----------------+----------------+-----------------+
| c79  24   1    | 24   6   579   | b59  8    3     |
|  6   3    8    | 1    579 4579  |  2   457  4579  |
|  5   24  d79   | 8    3   2479  |  6   147  1479  |
+----------------+----------------+-----------------+

Kraken 1-Fish (4)c7\r5 + rfr1c7.
4r1c7 - (45=9)r57c7 - r7c1 = (97-2)r59c3 = 2r5c9 => - 4r5c9; stte

SteveC

[Cenoman]

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 +------------------+----------------------+--------------------+
 |  8    79    5    |  3      2     1      |  49   47    6      |
 |  1    679   4    |  5679   579   8      |  3    2     579    |
 |  2    679   3    |  5679   4     5679   |  8    157   1579   |
 +------------------+----------------------+--------------------+
 |  4    1     29   |  59     8     3      |  7    6     25     |
 |  3    8    c27   | d567    1    d567    |  4-5  9     245    |
 |  79   5     6    |  24*    79    24*    |  1    3     8      |
 +------------------+----------------------+--------------------+
 |  79   24*   1    |  24*    6     579    | D59   8     3      |
 |  6    3     8    |  1     B579  B4579   |  2    457  C4579   |
 |  5    24*  b79   |  8      3   Aa2479*  |  6    147   1479   |
 +------------------+----------------------+--------------------+

DP(24)r79c2, b8p19, r6c46 using internals
(7)r9c6 - r9c3 = r5c3 - (76=5)r5c46
(9)r9c6 - r8c56 = r8c9 - (9=5)r7c7
=> -5 r5c7; ste
...hopefully no missing guardian today !

[SpAce]

Hi Steve!

Kraken 1-Fish (4)c7\r5 + rfr1c7.
4r1c7 - (45=9)r57c7 - r7c1 = (97-2)r59c3 = 2r5c9 => - 4r5c9; stte

Why not start the chain with: (4)c7\r5 = r1c7 ... ? That would make the logic explicit and put it in a single place where it belongs. That strong link is what a finned fish is all about: either the fish is true or at least one of the fins is. It would also combine the UFG and AIC notations nicely, which is what I've been trying to advocate lately. Since you're fluent in both and like to use those Cyclopsfishes for kicks anyway, why not join the movement?

Similarly, if there were more remote fins with different chains, I'd write it as a full kraken with the fish body as a member. Otherwise the fin-chains just hang in the air without a real connection to the fish, which hides part of the logic and makes them look like DP guardian chains. The distinction is important, because the fins form a SIS with each other AND the fish, unlike DP guardians which form a SIS with each other only (and not the DP pattern). To make matters worse, there are deadly fishes too which are in fact DPs, i.e. at least one of the fins must be true, so they're not even totally separate contexts.

Btw, I forgot to mention that you had a real beauty here!

[SpAce]

...hopefully no missing guardian today !

Can't see any However, as a punishment for missing one yesterday, I have a question for you! As far as I know, you're an expert in full tagging (among other things). I've never studied that in detail, nor have immediate plans to do so, but I'd like to have a better high-level grasp of the concept. Am I on the right track if I think my Medusa Multi-Coloring (hidden above) might somewhat resemble its initial stages?

[Ngisa]

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+-----------------+---------------------+--------------------+
| 8     79     5  | 3       2      1    |a49     47     6    |
| 1     679    4  | 5679    579    8    | 3      2      579  |
| 2     679    3  | 5679    4      5679 | 8      157    1579 |
+-----------------+---------------------+--------------------+
| 4     1     b29 | 59      8      3    | 7      6     b25   |
| 3     8      27 | 567     1      567  |a45     9      245  |
|c79    5      6  | 24      79     24   | 1      3      8    |
+-----------------+---------------------+--------------------+
|d79    24     1  | 24      6      24   | 5-9    8      3    |
| 6     3      8  | 1       579    4579 | 2      457    4579 |
| 5     24     79 | 8       3      2479 | 6      147    1479 |
+-----------------+---------------------+--------------------+


(9=45)r15c7 - (5=29)r4c39 - (9)r6c1 = (9)r7c1 => - 9r7c7; stte

Clement

[Sudtyro2]

Kraken 1-Fish (4)c7\r5 + rfr1c7.
4r1c7 - (45=9)r57c7 - r7c1 = (97-2)r59c3 = 2r5c9 => - 4r5c9; stte

Why not start the chain with: (4)c7\r5 = r1c7 ... ? That would make the logic explicit and put it in a single place where it belongs. That strong link is what a finned fish is all about: either the fish is true or at least one of the fins is. It would also combine the UFG and AIC notations nicely, which is what I've been trying to advocate lately.

JC Van Hay once pointed out (a very LONG time back) that the standard Fish=Fin strong-link rule is not always valid because the (unfinned) Fish itself can sometimes be false. I never really understood that statement, but he did provide an example. I'll try to dig out my old notes on that issue.

SteveC

[SpAce]

JC Van Hay once pointed out (a very LONG time back) that the standard Fish=Fin strong-link rule is not always valid because the (unfinned) Fish itself can sometimes be false. I never really understood that statement, but he did provide an example. I'll try to dig out my old notes on that issue.

I bet he was talking about "headless fishes", just like I was here:

To make matters worse, there are deadly fishes too which are in fact DPs, i.e. at least one of the fins must be true, so they're not even totally separate contexts.

That poorly understood variant remained a mystery to me for a long while. Then we had a good discussion about those with tarek et al, and I think I got it. I fully agree with tarek's final conclusion on the matter:

When candidates are mapped on a n/n base/cover fish construct: If the fish body is false then the creature is not a fish

As far as I know, that's the most current opinion of the main UFG authority, given after careful consideration. Thus, we don't really need to worry about the false body case, because it's not a fish in the first place! If the fish body is known to be false (as an invalid pattern), it's a DP ("illegal fish") and the "fins" are actually guardians (and shouldn't be called fins at all to avoid confusion). The concept applies to any unviable pattern in a valid grid, like three cells with just two digits (a DP type that at least I and Cenoman have used a couple of times).

Like I already said in my previous post, the "deadly fish" variant should be written as a normal DP (with only the guardians forming the SIS) and not confused with real finned fishes (where the fish body is an active part of the SIS, capable of weak-linking on its own). Therefore, there's absolutely no reason not to write normal fish situations with the strong link between the fish body and the fins, because it applies to every valid fish and is an integral part of the logic (and differentiates it clearly from the DP case). Invalid fishes are no longer considered fishes at all, so you can safely drop that reason to reject my suggestion.

Furthermore, the strong link is actually valid for dead fishes too -- as long as it's clearly indicated that the fish body is dead, because "false OR something" <-> "something". If the fish body is known to be false at least one of the fins must be true (in a valid puzzle), and no logical rule has been broken by strong-linking "dead_fish = fins" (it's only wrong if you notate a valid fish type for the body). It's just not useful in a verity chain (e.g. normal AIC or kraken) because you can't weak-link the dead fish (or any known false) to anything. It's a no-solution contradiction, just like Oddagon+0, so the only way to use it as a node is as an end-point of a contradiction chain. Normally we prefer verity chains and then the only relevant SIS is between the guardians ("fins") of a dead fish, and the false fish body only provides the catalyst that strong-links the guardians with each other -- just like any other DP.

Btw, it would be better to talk about "invalid" instead of "false" fish bodies if the DP variant is meant. Of course the fish body can end up being false in a valid finned fish too, but we don't know that just by looking at the pattern (i.e. the unfinned pattern is a valid fish until further solving breaks it). That's why we need the strong link to the fins in the first place.

[Cenoman]

However, as a punishment for missing one yesterday, I have a question for you! As far as I know, you're an expert in full tagging (among other things). I've never studied that in detail, nor have immediate plans to do so, but I'd like to have a better high-level grasp of the concept. Am I on the right track if I think my Medusa Multi-Coloring (hidden above) might somewhat resemble its initial stages?

...a punishment for missing one yesterday

I don't agree that my senior moment on July 20 was worth any punishment ! Being upset was enough !

Anyhow, as I am pleased to make some ads for full tagging, responding your question will not be a punishment.
First of all, I know nothing about 3D Medusa. Never practised it, never read detailed documentation.
So my comment will be terse.

Your Medusa Multi-coloring PM is very similar to my tagged PM. The inference process for 'b' elimination is the same as in tagging, i.e. finding two "conflicts" a-b and A-b.

I can't do anything else better than copy-paste full tagging master's (champagne's) presentation here in 2008-2009

"Full tagging" belongs to the multi-colouring family.

The process is highly progressive, and can be divided (up to now) in three levels.

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level 1 : more or less equivalent to MEDUSA 3D. Major differences are :
 - No use of forcing chains,
 - extended to groups,
 - intensive use of Alternate Chains.


level 2
- expanding strong links and weak links thru ALS and their counterpart which I call "Almost Cells".
- looking for multi-chains starting from an Almost Cell and killing candidates

level 3 (looping process as long as you can expand)
- expanding weak links thru multi-chains starting from an Almost Cell

Now, in the past 10 years, 3D Medusa must have evolved, as well as full tagging.

[SpAce]

I don't agree that my senior moment on July 20 was worth any punishment ! Being upset was enough ! Anyhow, as I am pleased to make some ads for full tagging, responding your question will not be a punishment.

Thanks!

First of all, I know nothing about 3D Medusa. Never practised it, never read detailed documentation.

Based on what you said below, I think you must already know everything about 3D Medusa without knowing it!

Your Medusa Multi-coloring PM is very similar to my tagged PM. The inference process for 'b' elimination is the same as in tagging, i.e. finding two "conflicts" a-b and A-b.

Ok, good to know! Since you confirm that they're similar (with this very simple example), then I would make the assumption that Multi-Colored 3D Medusa is in fact a small subset of full tagging (comprising most of champagne's level 1). On the other hand, basic 3D Medusa (the usual variant) is a much smaller and weaker subset, as it has a single coloring cluster (i.e. tag pair) and only works if inferences can be found without crossing weak-only links (i.e. "conflicts" between clusters). However, it's probably how you would start full tagging with the first tag pair (just like I started mine above, first coloring the 'aA'-cluster), so basic Medusa is also implicitly included in full tagging (and so is Simple Coloring because it's a subset of basic Medusa). Both versions of Medusa only use the most basic links (bilocals and bivalues), which keeps them in level 1 of full tagging.

The multi-colored extension I used here (for the second time ever) is rarely used with 3D Medusa these days (or so I presume), so most people probably think of the basic version when the term is used. In any case, since everything about both versions (and any possible extension I can think of) seems to be included in full tagging, you do know what Medusa is (and now you know you know!). On the other hand, a typical Medusa user doesn't probably know much about full tagging (or even multi-colored Medusa).

Some comments about champagne's old definitions and comparisons (which have probably evolved):

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level 1 : more or less equivalent to MEDUSA 3D.

So it seems -- but only if the (uncommon) multi-colored Medusa is used. The difference is much more striking against the basic Medusa. Not sure what the common definition was back then, though.

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 Major differences are :
 - extended to groups,

This is a fairly easy extension to both Medusa and Simple Coloring, at least in a limited form, so it's not necessarily a major difference.

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 - No use of forcing chains,
 - intensive use of Alternate Chains.

I don't really know what champagne meant here. If the inference process is roughly the same, as you said above, then I don't see any difference. AICs and forcing chains are just two (not very different) ways to express coloring inferences as chains, but I don't see them as part of the coloring process or philosophy per se -- or at least as a differentiating factor between full tagging and Medusa specifically. Both chain types can be produced either way (and converted to each other at will), just like with GEM.

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level 2
- expanding strong links and weak links thru ALS and their counterpart which I call "Almost Cells".
- looking for multi-chains starting from an Almost Cell and killing candidates

level 3 (looping process as long as you can expand)
- expanding weak links thru multi-chains starting from an Almost Cell

These extensions aren't part of any form of 3D Medusa that I'm aware of. They're part of GEM, though, if I understand the terms correctly (Almost Cell <-> AHS?). However, GEM is otherwise quite different, as it's not based on multi-coloring.

Now, in the past 10 years, 3D Medusa must have evolved, as well as full tagging.

Obviously I don't know about the evolution of full tagging, but I'm pretty sure any (public) evolution of 3D Medusa has been only backwards (with the exception of GEM if it's seen as a non-multi-colored extension to it). It seems that only the basic form of Medusa has really survived under that name. I hadn't even seen an example of a multi-colored Medusa until I recently produced one (and then this other) as a proof of concept, but I'm sure those could be found in old discussions. From what I understand (mostly heard from StrmCkr), there were plans and experiments to make other multi-coloring methods approach the capabilities of full tagging, but at some point those extensions seem to have vanished.

Anyway, thanks for helping me out! I think I have a slightly better idea of full tagging now. It seems like an elegant way to find inferences, and at the very least quite applicable for a software solving engine (based on your and champagne's impressive results). What I still don't understand is how it could be used manually, except in very simple cases like my example. With anything more complex the number of coloring clusters (tag pairs) grows fast beyond practically usable (real) colors and human inferencing capability. It seems to me that the only way to even attempt to use it then would be actual letter-based tagging of pm grids, but that seems really tedious and hard to read. Does anyone actually use it for manual solving? Do you? If so, how?

Btw, it would be really interesting to see a comparison of the solving power between full tagging and GEM. I wonder if anyone has ever attempted to investigate that? Logically I would presume they should be about the same if both are taken to the extremes, but I have no idea if that's true. For manual solving the choice seems easy anyway, unless I learn how full tagging/multi-coloring can be used for that in any practical way (I would like that as it would be a whole new world).