The New Sudoku Players' Forum

by **eleven** » Sun Nov 03, 2019 9:47 pm

Code: Select all: +-------+-------+-------+ | . . 3 | . . . | . . 9 | | . . . | . 8 . | 1 . . | | 7 . . | . . . | . . . | +-------+-------+-------+ | . . . | . . 3 | . . 6 | | . 6 . | . . . | 4 . . | | . 8 . | . . 5 | . . . | +-------+-------+-------+ | . 1 . | . 6 . | . . . | | . . . | . . . | . 5 . | | . . 2 | . 9 . | . 3 7 | +-------+-------+-------+

by **SpAce** » Mon Nov 04, 2019 2:21 pm

original: Show

Code: Select all: .-------------------.-----------------.----------------------------. | f18 2 3 | 14 5 46 | 7 468 9 | | 46 5 46 | 79 8 79 | 1 2 3 | | 7 9 e18 | 124 3 246 | i{58} 468 458 | :-------------------+-----------------+----------------------------: | 2 7 gh1459 | 489 14 3 | hi{58}9 189 6 | | 3 6 159 | 2789 127 2789 | 4 1789 58 | | f149 8 g149 | 6 147 5 | 3 g179 2 | :-------------------+-----------------+----------------------------: | 5 1 d79#8 | 3 6 278 | A29[#8] A49[#8] A4[#8] | | 68+9 3 d79#68 | 2478 247 2478 | c68+29 5 1 | | 68+ 4 2 | 5 9 1 | b(6)-8+ 3 7 | '-------------------'-----------------'----------------------------'

UR(68)r89c17 using externals:

(8)r7c789 = [(6)r9c7 = r8c7 - (6==8)r87c3 - r3c3 = (81-4|9)r16c1 = (94)r64c3|(9)r6c8 - (5,9)r4c37 = (58)r34c7] => -8 r9c7; stte

--
Edit. Added a slightly simplified version.

by **Cenoman** » Mon Nov 04, 2019 3:43 pm

Code: Select all: +--------------------+----------------------+----------------------+ | 1-8 2 3 | 14 5 46 | 7 468 9 | | 46 5 46 | 79 8 79 | 1 2 3 | | 7 9 b18 | 124 3 246 | D58x 468 458 | +--------------------+----------------------+----------------------+ | 2 7 1459 | 489w 14 3 | C589x 189 6 | | 3 6 Aa159u | 2789v 127 2789v | 4 1789 B58 | | 149 8 149 | 6 147 5 | 3 179 2 | +--------------------+----------------------+----------------------+ | 5 1 79-8 | 3 6 278 | 289 489 48 | | 689 3 679-8 | 2478 247 2478 | 2689 5 1 | | F68z 4 2 | 5 9 1 | E68y 3 7 | +--------------------+----------------------+----------------------+

Kraken cell (159)r5c3
(1)r5c3 - (1=8)r3c3
(5)r5c3 - r5c9 = r4c7 - (5=8)r3c7 - r9c7 = (8)r9c1
(9)r5c3 - r5c46 = r4c4 - (9=58)r34c7 - r9c7 = (8)r9c1
=> -8 r1c1, r78c3; ste

by **SteveG48** » Mon Nov 04, 2019 3:44 pm

Code: Select all: *--------------------------------------------------------------* | 1-8 2 3 | 14 5 46 | 7 468 9 | | b46 5 46 | 79 8 79 | 1 2 3 | | 7 9 18 | 124 3 246 | g58 468 458 | *---------------------+-------------------+--------------------| | 2 7 f1459 |e489 e14 3 | f589 189 6 | | 3 6 159 | 2789 127 2789 | 4 1789 58 | | c149 8 149 | 6 d147 5 | 3 c179 2 | *---------------------+-------------------+--------------------| | 5 1 79-8 | 3 6 278 | 289 b489 b48 | | ab689 3 679-8 | 2478 247 2478 | 2689 5 1 | |abh68 4 2 | 5 9 1 |bg68 3 7 | *--------------------------------------------------------------*

8r89c1 = (649)r289c1&(489)b9p237 - (4|9=17)r6c18 - (1|7=4)r6c5 - r4c45 = (45)r4c37 - (5=86)r39c7 - (6=8)r9c1 => =8 r1c1,r78c3 ; stte

by **Ngisa** » Mon Nov 04, 2019 4:38 pm

Code: Select all: +-------------------+--------------------+---------------------+ | 1468 2 3 | 14 5 46 | 7 468 9 | | 46 5 46 | 79 8 79 | 1 2 3 | | 7 9 g18 | 124 3 246 |e58 468 f458 | +-------------------+--------------------+---------------------+ | 2 7 e145*9|i48(9) 14 3 |d589* c189 6 | | 3 6 h159* |i278(9) 127 i278(9)| 4 c1789 58 | | 149 8 149 | 6 147 5 | 3 c179 2 | +-------------------+--------------------+---------------------+ | 5 1 789 | 3 6 278 | 289 b489 b4*8 | | 689 3 6789 | 2478 247 2478 | 2689 5 1 | | a8-6 4 2 | 5 9 1 |b68 3 7 | +-------------------+--------------------+---------------------+

Nishio:
(6)r9c1 - (6=84*9)b9p732 - (9)456c8 = (9*-5)r4c7 = (5*)r4c3&r3c7 -(4*5=8)r3c9 - (8=1)r3c3 - (15*=9)r5c3 - (9)b5p146(box5 devoid of 9) => - 6r9c1; stte

Clement

by **eleven** » Mon Nov 04, 2019 9:53 pm

Wow, 4 different ste solutions.

Code: Select all: *----------------------------------------------------------------* | b18 2 3 | 14 5 46 | 7 468 9 | | 46 5 46 | 79 8 79 | 1 2 3 | | 7 9 18 | 124 3 246 | a58 468 458 | |------------------+----------------------+----------------------| | 2 7 1459 | #489 #14 3 | a589 #189 6 | | 3 6 159 | 2789 127 2789 | 4 1789 58 | | 49-1 8 149 | 6 #147 5 | 3 #179 2 | |------------------+----------------------+----------------------| | 5 1 789 | 3 6 278 | 289 489 48 | | 689 3 6789 | 2478 247 2478 | 2689 5 1 | | b68 4 2 | 5 9 1 | a68 3 7 | *----------------------------------------------------------------*

5 digits 14789 in the 5 #-marked cells r4c458,r6c58, 478 are locked in a unit.
If 1 is not twice (like in an x-wing), there must be a 9.
1r46c5&8 == 9r4c48,r6c8 - (9=586)r349c7 - (6=81)r91c1 => -1r6c1, stte

by **SpAce** » Mon Nov 04, 2019 10:05 pm

eleven wrote:5 digits 14789 in the 5 #-marked cells r4c458,r6c58, 478 are locked in a unit.
If 1 is not twice (like in an x-wing), there must be a 9.
1r46c5&8 == 9r4c48,r6c8 - (9=586)r349c7 - (6=81)r91c1 => -1r6c1, stte

Very nice!

by **Cenoman** » Tue Nov 05, 2019 10:11 am

eleven wrote:5 digits 14789 in the 5 #-marked cells r4c458,r6c58, 478 are locked in a unit.
If 1 is not twice (like in an x-wing), there must be a 9.
1r46c5&8 == 9r4c48,r6c8 - (9=586)r349c7 - (6=81)r91c1 => -1r6c1, stte

Speechless as usual in front of such a beautiful solution !

The presentation in English is clear and meaningful. What follows is just a way for me to catch it. I try to translate into "classical" sudoku techniques.
I will use (9r4c7==1r1c1) as a shortcut for the ALS chain (9=586)r349c7-(6=81)r19c1
First as a triangular matrix:

Hidden Text: Show

The matrix shows the specific role of the group 1r6c58
The whole could be considered as an almost ALS chain:
(1)r6c58 = [(918=4)r4c458 - (4*=79)]r6c58] - (9=586)r349c7-(6=81)r19c1 => -1 r6c1; ste

by **SpAce** » Tue Nov 05, 2019 11:55 am

Hi Cenoman,

Cenoman wrote:The presentation in English is clear and meaningful. What follows is just a way for me to catch it. I try to translate into "classical" sudoku techniques.
First as a triangular matrix:

Nice matrix! It might have taken a while for me to come up with that, as it has surprising complexity. Here's the same as a net diagram:

net diagram: Show

(1)r6c58 = [(918=4)r4c458 - (4*=79)]r6c58] - (9=586)r349c7-(6=81)r19c1 => -1 r6c1; ste

I think that's a very elegant way to write the chain, using the ALS-XZ node!

On a different note -- and I hope you take this as a very friendly and constructive concern -- I still don't like your use of the '*' in nested chains (and also subchains with a different meaning). I think it takes away some of the beauty of that nice chain

I can't help that it always looks like a memory chain to me when I first see it, and I don't know why you'd voluntarily give such a first impression (a memory chain being clearly a less elegant option). I know you have a good intention of making your chain clearer with it, being a champion of clarity in general, but I think its overall effect is negative in that regard.

There are plenty of symbols available that wouldn't have such a misleading effect. That said, personally I don't think any symbol is usually necessary for this purpose, especially with such a short nested chain. Here I think the best clarity would result from its reversal (putting the strongly linked spoiler next to where it's missing):

(1)r6c58 = [(97=4)r6c58 - (4=819)r4c458] - (9=...)

--
Btw, here's a straight-forward but inelegant and uninteresting option for a "classical" chain (with the '*' in its more common meaning):

(18)r19c1 = (859*)r934c7 - (9=184)r4c845 - (4|*9=71)r6c58 => -1 r6c1

The same without memory:

(18)r19c1 = (85)r93c7 - (8|5)r4c7 = (9,184)r4c7845 - (9|4=71)r6c85 => -1 r6c1

by **SpAce** » Wed Nov 06, 2019 7:31 am

I'm interested in a way to write eleven's original logic (which seems to be recurring quite a bit) formally without twisting it too much. I'm thinking it must fall into one or more of the families of multi-digit fishes, MSLS, DDS, and so forth types of things.

So, here's one attempt:

Kraken Alien 5-Fish (Almost-MSNS ?):

{4N458 6N58 \ 18r4 7r6 4b5 [1r6]} = (9)r4c48,r6c8 - (958)r349c7 = (81)r91c1 => -1 r6c1; stte

The fish on the left side is a Rank 0 structure, which means that every link (cover set) must be occupied, including 1r6. I think (but am not sure) that it could be called a multi-sector naked set (MSNS) because the truths (base sets) are all cells. It's not a Distributed Disjoint Subset (DDS) in this case, because its definition would require all occurrences of the same digit to share a sector (and the 1s don't). I think some of eleven's earlier examples might have been almost-DDSs as well, however.

That Rank 0 fish is extracted from the full Rank 2 structure where both 1s and 9s have two cover sets (i.e. if all instances of 1 or 9 are removed, two cover sets are also removed, which decrements the rank by 2 -> 0):

Alien 5x7-Fish: {4N458 6N58 \ 189r4 17r6 4b5 9b6}

The logic used by eleven can be directly read from that too, because Rank 2 means that at most two cover sets can be without a base candidate. Thus it's impossible that all of 1r6, 9r4, and 9b6 are unoccupied; in other words we have: [{1r6 == 9r4|9b6} -> 1r1c1] => -1 r6c1.

Not really relevant, but here's the whole logic as an Alien ObiFish (Rank 2):

Alien 13x15-ObiFish: {8R99 1N11 34N77 4N458 6N58 \ 189r4 7r6 8c11 58c77 4b5 9b6 [1r6 1c11]} => -1 r6c1

by **Cenoman** » Wed Nov 06, 2019 3:31 pm

Hi SpAce,

SpAce wrote:Nice matrix!
...
I think that's a very elegant way to write the chain, using the ALS-XZ node!

Thanks !

SpAce wrote:I still don't like your use of the '*' in nested chains (and also subchains with a different meaning). I can't help that it always looks like a memory chain to me.

I am aware. You already complained several times about it! I dislike memory chain so strongly that I never write one (and quite never read posted ones) So, making a chain look like a memory chain is out of my concerns

.

I don't think any symbol is usually necessary for this purpose,
...
the best clarity would result from its reversal (putting the strongly linked spoiler next to where it's missing)

I agree with both your proposals, knowing that the second one may be unavailable (whenever the strongly linked spoiler is missing a middle term)

Now the "*" symbol is one of the easiest to use (at least on French azerty keyboards). I consider that writers of memory chains are so minority that I do not agree with leaving them exclusively use the "*" symbol. Let them find another one ! (Not sure they were the first users...)

You propose alternative AICs:

(18)r19c1 = (859*)r934c7 - (9=184)r4c845 - (4|*9=71)r6c58 => -1 r6c1

(18)r19c1 = (85)r93c7 - (8|5)r4c7 = (9,184)r4c7845 - (9|4=71)r6c85 => -1 r6c1

No further comment about the first one !

I would not qualify the second one "classical". To me, nodes with "|"symbols and split nodes as (9,184)r4c7845 are practiced by rather advanced sudoku players. But the "classical" quality is so vague and undefined that we can have an endless discussion about "classical" solution writing. (If so, without me

)

You had the courage to draw the quadruple kraken net! So good
I was missing time when I posted the matrix, but I felt that a net had to be joined.
Here one that sticks to both the matrix and the chain. In the light of your comments, I guess it is unambiguous and provides good clarity.

Kraken AALS r6c58
(1)r6c58
(4)r6c5 - (4=189)r4c458 - (9)r4c7 == (1)r1c1
(79)r6c58 - (9)r4c7 == (1)r1c1
=> -1 r6c1

(PS Your post doesn't appear as having been edited. I'd not have answered the first version...

)

by **SpAce** » Thu Nov 07, 2019 7:40 am

Cenoman wrote:
SpAce wrote:I still don't like your use of the '*' in nested chains (and also subchains with a different meaning). I can't help that it always looks like a memory chain to me.

I am aware. You already complained several times about it!

I know, but this is the first time you responded

Thanks for that. I won't bug you about it after this. (I still wish you'd respond to the question about fish notation. In both cases I'm perfectly fine if you stick to your old ways, but I'm just interested in your reasons. That's all.)

I dislike memory chain so strongly that I never write one (and quite never read posted ones)

I know. That's why it's obvious that your use of the '*' is not related to memory chains, but it's only obvious to those who've been around long enough to know that. You might remember that I had to ask when I first saw you use it for a nested chain, because the only association I'd seen before was with memory chains. So, I would claim that it's not intuitively understandable.

So, making a chain look like a memory chain is out of my concerns .

I'd presume just the opposite! If I really dislike something I usually go out of my way to avoid any apparent association that could make someone think otherwise.

Now the "*" symbol is one of the easiest to use (at least on French azerty keyboards).

Understandable.

I consider that writers of memory chains are so minority that I do not agree with leaving them exclusively use the "*" symbol. Let them find another one !

Are they a minority? Of the current or recent regulars I've seen memory chains used at least by myself, Clement, SteveG, and Phil. I'd rather guess that nested chains and their users are probably a rarer variety, as it's a more advanced technique. (And of the nested chain users I think you're the only one here who uses the '*' for that purpose, while all the memory chain writers use it as the primary memory marker without exception. So at least in this context your usage is in the clear minority.)

I tend to avoid memory chains just because they're not very interesting to write, but I have no problem writing or reading them either. Sometimes one is the best option, because it's often the cheapest way to write a simple net. It's straight-forward to write and to understand, and it usually takes up the least amount of effort and space compared to split-nodes, nested chains, net diagrams, and krakens. There's absolutely no difference in functionality or reversibility (if correctly written and interpreted), so why not? Their biggest fault is that they're not valid AICs, but as long as everyone knows that, it's not a practical problem.

(Not sure they were the first users...)

I wouldn't know about that. Either way I think it's more relevant how most people interpret it now.

Anyway, like I said, I'm satisfied with your response. I won't bring this up again!

You propose alternative AICs:
(18)r19c1 = (859*)r934c7 - (9=184)r4c845 - (4|*9=71)r6c58 => -1 r6c1

(18)r19c1 = (85)r93c7 - (8|5)r4c7 = (9,184)r4c7845 - (9|4=71)r6c85 => -1 r6c1

No further comment about the first one !

Well, it's the least elegant for sure, but it's also probably the shortest way to arrive at the conclusion. It's quite simple too, and I would imagine that even a relative beginner could write and read that. So, I don't think it's totally without merit.

Personally I welcome a large variety of logic and notations, as long as they're correct and understandable. There's something to learn from them all, and any artificial restriction denies that opportunity. For example, I thought it was refreshing that Clement used an honest Nishio recently (though I wouldn't want to see it very often).

I would not qualify the second one "classical". To me, nodes with "|"symbols and split nodes as (9,184)r4c7845 are practiced by rather advanced sudoku players.

Of course. Yet I'd put a nested chain even higher up in the food chain. While the notation within the nested chain might be simpler, the overall logic is more complex -- at least from some point of view. It's a bit like recursion vs looping in programming. One is more elegant, the other is usually simpler to understand.

Here one that sticks to both the matrix and the chain. In the light of your comments, I guess it is unambiguous and provides good clarity.

Indeed! Very nice. Krakens are often the most readable variants, but they're not without faults either. They take up space and are the hardest to mark (and read) on the grid because of the discontinuous and complex lettering schemes. The latter especially is one reason why I avoid them, or at least don't always bother with elaborate grid markings with them.

(PS Your post doesn't appear as having been edited. I'd not have answered the first version... )

I wrote the first version in a hurry, so I rewrote it the way it was supposed to be. The whole point of the original was to show that there was (imho) a relatively simple way to see the logic without nested chains and matrices. It wasn't meant as a criticism against your more elegant way at all, but I realized it could have seemed that way.

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