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by **tarek** » Mon Jan 06, 2020 1:37 am

Code: Select all: +-------+-------+-------+ | . . . | . . . | . . . | | . . 1 | 2 3 4 | 5 . . | | . 2 . | 6 . 5 | . 7 . | +-------+-------+-------+ | . 5 8 | . . . | 3 1 . | | . 6 . | . . . | . 5 . | | . 1 7 | . . . | 8 2 . | +-------+-------+-------+ | . 3 . | 7 . 2 | . 4 . | | . . 2 | 1 4 3 | 9 . . | | . . . | . . . | . . . | +-------+-------+-------+ ...........12345...2.6.5.7..58...31..6.....5..17...82..3.7.2.4...21439...........

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by **Leren** » Mon Jan 06, 2020 5:42 am

Code: Select all: *------------------------------------------------------------* | 345689 489 34569 | 89 1789 1789 | 1246 369 1234 | | 679 79 1 | 2 3 4 | 5 69 8 | | 3489 2 349 | 6 189 5 | 14 7 134 | |--------------------+-----------------+---------------------| | 249 5 8 | 49 2679 679 | 3 1 4679 | | 2349 6 349 | 3489 12789 1789 | 47 5 479 | | 349 1 7 | 3459 569 69 | 8 2 469 | |--------------------+-----------------+---------------------| | 5689-1 3 569 | 7 5689 2 |a16 4 e15 | |c56-78 78 2 | 1 4 3 | 9 b68 d57 | | 1456789 4789 4569 | 589 5689 689 | 27-16 38-6 237-15 | *------------------------------------------------------------*

(1=6) r7c7 - r8c8 = (6-5) r8c1 = r8c9 - (5=1) r7c9 loop => - 1 r7c1, - 78 r8c1, - 16 r9c7, - 6 r9c8, - 15 r9c9; stte

Leren

by **Cenoman** » Mon Jan 06, 2020 10:11 am

Another funny "square XY-loop" (yields bte finish only, so bad !)

Code: Select all: +---------------------------+------------------------+-----------------------+ | 345689 489 34569 | 89 1789 1789 | 1246 39-6 1234 | | 67-9 a79 1 | 2 3 4 | 5 d69 8 | | 3489 2 349 | 6 189 5 | 14 7 134 | +---------------------------+------------------------+-----------------------+ | 249 5 8 | 49 2679 679 | 3 1 4679 | | 2349 6 349 | 3489 12789 1789 | 47 5 479 | | 349 1 7 | 3459 569 69 | 8 2 469 | +---------------------------+------------------------+-----------------------+ | 15689 3 569 | 7 5689 2 | 16 4 15 | | 567-8 b78 2 | 1 4 3 | 9 c68 57 | | 1456789 *489-7 *4569 | *589 *5689 *689 | 1267 38-6 12357 | +---------------------------+------------------------+-----------------------+

(9=7)r2c2 - (7=8)r8c2 - (8=6)r8c8 - (6=9)r2c8@ => -8 r8c1, -9 r2c1, -6 r19c8, -7 r9c2; bte (5-Naked set 45689r9 =>+3r9c8; ste, or HT 127r9 => -3 r9c9...)

by **eleven** » Mon Jan 06, 2020 10:34 am

Almost hidden triple:

Code: Select all: *----------------------------------------------------------------------------* | 345689 489 34569 | 89 1789 1789 | 1246 369 1234 | | 679 c79 1 | 2 3 4 | 5 d69 8 | | 3489 2 349 | 6 189 5 | 14 7 134 | |---------------------------+------------------------+-----------------------| | 249 5 8 | 49 2679 679 | 3 1 4679 | | 2349 6 349 | 3489 12789 1789 | 47 5 479 | | 349 1 7 | 3459 569 69 | 8 2 469 | |---------------------------+------------------------+-----------------------| | 15689 3 569 | 7 5689 2 | 16 4 15 | | 5678 78 2 | 1 4 3 | 9 d68 57 | | a1456789 b4789 4569 | 589 5689 689 | a1267 d368 a1257-3 | *----------------------------------------------------------------------------*

127r9c179 = 7r9c2 - (7=9)r2c2 - (9=683)r289c8 => -3r9c9, stte

by **tarek** » Mon Jan 06, 2020 1:16 pm

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 34568-9 *489 3456-9 | 89 178-9 1789 | 1246 369 1234 | | 67-9 *79 1 | 2 3 4 | 5 69 8 | |*3489 2 *349 | 6 *189 5 | 14 7 134 | +-------------------------+-------------------------+-------------------------+ | 249 5 8 | 49 267-9 679 | 3 1 4679 | | 2349 6 349 | 3489 1278-9 1789 | 47 5 479 | | 349 1 7 | 3459 56-9 69 | 8 2 469 | +-------------------------+-------------------------+-------------------------+ |*15689 3 *569 | 7 *5689 2 | 16 4 15 | | 5678 78 2 | 1 4 3 | 9 68 57 | |145678-9 *4789 456-9 | 589 568-9 689 | 1267 368 12357 | +-------------------------+-------------------------+-------------------------+ Grouped L1-Ring r19c135,r2c1,r456c5<>9 or Mutant Swordfish 9r37c2\c5b17 btte (X-wing, Pair, intersections)

Or a more brutal equivalent:

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 34568-9 *489 3456-9 | 89 178-9 1789 | 1246 369 1234 | | 67-9 *79 1 | 2 3 4 | 5 69 8 | |*3489 2 *349 | 6 *189 5 | 14 7 134 | +-------------------------+-------------------------+-------------------------+ | 249 5 8 | 49 267-9 679 | 3 1 4679 | | 2349 6 349 | 3489 1278-9 1789 | 47 5 479 | | 349 1 7 | 3459 56-9 69 | 8 2 469 | +-------------------------+-------------------------+-------------------------+ | 15689 3 569 | 7 *5689 2 | 16 4 15 | | 5678 78 2 | 1 4 3 | 9 68 57 | |145678-9 *4789 456-9 |*589 *568-9 *689 | 1267 368 12357 | +-------------------------+-------------------------+-------------------------+ Grouped L1-Ring r19c135,r2c1,r456c5<>9 or Cannibalistic Mutant Swordfish 9r3c2b8\r9c5b1 btte (X-wing, Pair, intersections)

Spotting the grouped strong link in b8 with the cannibalistic elimination is as tough as it gets

by **Mauriès Robert** » Mon Jan 06, 2020 9:08 pm

Hi,
Congratulations to Eleven for his ultra fast resolution!
Another way to eliminate 3r9c9 for a stte is as follows:
P'(3r3c9) : -3r3c9-> --- -> 3r9c8 (see diagram)

Code: Select all: ->2r1c7->2r9c9->3r9c8 / -3r3c9->14r3c79-> \ ->6r1c7->1r7c7->4r3c7->7r5c7-> \ \ \ \ ->1r9c1-> \ \ \ \ ->9r2c8->7r2c2---->7r8c1-->7r9c9->3r9c8

by **SpAce** » Mon Jan 06, 2020 10:23 pm

Hi tarek,

tarek wrote:Grouped L1-Ring r19c135,r2c1,r456c5<>9
or Mutant Swordfish 9r37c2\c5b17
btte (X-wing, Pair, intersections)
...
Grouped L1-Ring r19c135,r2c1,r456c5<>9
or Cannibalistic Mutant Swordfish 9r3c2b8\r9c5b1
btte (X-wing, Pair, intersections)[/code]Spotting the grouped strong link in b8 with the cannibalistic elimination is as tough as it gets

Beautiful examples of L1-Rings! Also a very nice example of a cannibalistic elimination with a mixed rank (0/1) fish.

One minor point. It's not "btte" if you need an X-Wing (not a basic technique as per our definitions)

I guess it could be called "sstste" instead.

by **Wecoc** » Tue Jan 07, 2020 12:01 am

I'm late but couldn't resist that one. When I saw the puzzle I thought it was a donut, but now I get it... it's a Ring! :lol:

Anyway, I found you can also do this one from the very start (copied directly from HoDoKu):

Code: Select all: Franken Jellyfish: 9 r37b46 c1359 => r1c1359,r2c19,r4569c5,r9c13<>9

This badass fish eliminates 12 candidates at once...
Sadly you still need X-Wings later so it's still not a stte, but I thought it may be interesting to point that one out anyways :roll:

by **SpAce** » Tue Jan 07, 2020 2:14 am

Hi Wecoc,

Wecoc wrote:Anyway, I found you can also do this one from the very start (copied directly from HoDoKu):

Code: Select all
Franken Jellyfish: 9 r37b46 c1359 => r1c1359,r2c19,r4569c5,r9c13<>9

This badass fish eliminates 12 candidates at once...
Sadly you still need X-Wings later so it's still not a stte, but I thought it may be interesting to point that one out anyways

It's nice, but tarek's L1-Rings and Mutant Swordfishes get the same exact eliminations arguably more simply. This is a good example of the fact that there are usually several different fishes with the same effects. They can be converted into each other quite easily using Obi-Wahn's arithmetic.

For example, your fish (r37b46\c1359) converted into tarek's first fish (r37c2\c5b17):

Code: Select all: r37b46 \ c1359 +c2 r37c2b46 \ c12359 c123 -> b147 r37c2b46 \ c59b147 -b4 r37c2b6 \ c59b17 c9 -> b6 r37c2b6 \ c5b167 -b6 r37c2 \ c5b17

It means that those two fishes (among many others) are equal for all practical purposes. When you have such equal fishes, the smallest and simplest variants are usually preferred. In this case tarek's fish is smaller (3x3 vs 4x4) but yours is technically simpler (Franken vs Mutant). However, in practice tarek's fish is simpler both ways because it can be seen and written as a (relatively) simple loop.

That said, nothing wrong with yours. I just kind of doubt that many human solvers can spot such creatures easily. On the other hand, tarek's loops (which are also mutant fishes) are relatively easy to find, like chains in general, even though they're a bit hidden due to the heavy grouping. Because of that tendency I actually think mutant fishes are in many cases easier to spot and to understand than frankens, despite being technically more complicated.

by **tarek** » Tue Jan 07, 2020 8:50 am

Wecoc wrote:I thought it was a donut, but now I get it... it's a Ring!

Well spotted!!!

SpAce wrote:One minor point. It's not "btte" if you need an X-Wing (not a basic technique as per our definitions)

I think I may have read somebody's post that said that N-tuples + basic N-fishes are btte and that btte + wings is SSTS (simple sudoku techniques set). Thanks for clarification

SpAce wrote: I just kind of doubt that many human solvers can spot such creatures easily

with more vertices in that NxN fish filled, it will be more & more difficult to spot it as a loop with strong links … The example of grouped 2x2x2x2 Jellyfish of whatever shape could possibly be easier to spot than some 3x3x3 swordfishes. In Latin Square where we lose the boxes, unless the fish is 2x2x(… Size of fish), it will always be difficult to spot unless you rely on some clever observations (missing candidates, arrangement of clues)

tarek

by **SpAce** » Tue Jan 07, 2020 10:43 pm

tarek wrote:I think I may have read somebody's post that said that N-tuples + basic N-fishes are btte and that btte + wings is SSTS (simple sudoku techniques set). Thanks for clarification

No problem. There has been confusion about that before, though I'm pretty sure the convention has always been the same. I guess the previously standard term "lclste" was somewhat less ambiguous -- at least for those who could decipher what it meant. That said, there used to be similar confusion with that too, and in any case "btte" is much nicer to use and probably more intuitive to understand (if one knows what "stte" means). Problem is, it requires knowing what techniques are considered basic, but it seems that almost all conventions (including Hodoku, SudokuWiki, Robert's TDP, etc) limit them to singles, locked candidates, and disjoint subsets.

I understand the confusion, though, because it could be argued that basic fishes are logically equivalent to disjoint subsets, and in practice an X-Wing is often easier to spot than a quad or even a triple. So perhaps the convention is more or less arbitrary. I still think it probably makes the most sense all things considered, as most manual players are much more likely to spot a quad than a (non-minimal) Jellyfish. It can be expected that a decent manual player can relatively easily spot all singles, locked candidates, and disjoint subsets, but not necessarily all basic fishes without significantly more effort and a good technique.

with more vertices in that NxN fish filled, it will be more & more difficult to spot it as a loop with strong links … The example of grouped 2x2x2x2 Jellyfish of whatever shape could possibly be easier to spot than some 3x3x3 swordfishes.

My point exactly. At least for me, the 2x2x2x2 Jellyfish would almost certainly be easier to spot than a 3x3x3 Swordfish, because I'd find it as a loop. Anytime some vertices are spread into more than two boxes within a line, there's no longer even a grouped strong link available, and thus no (non-branching) loop possibility.

In Latin Square where we lose the boxes, unless the fish is 2x2x(… Size of fish), it will always be difficult to spot unless you rely on some clever observations (missing candidates, arrangement of clues)

Exactly. Without boxes there can be no group links at all, so the only easy fishes are simple X-Loops (2x2... types). Then again, chains are much easier to spot in general because all angles are 90 degrees and there's one fewer link type to consider. On the other hand, variants like X-Sudoku make it more complicated (and fruitful) with the extra linking possibilities.

by **tarek** » Wed Jan 08, 2020 1:44 pm

I may look at adding the Cannibalistic elimination feature to Sukaku explainer. I'm skeptical on adding the opposite which is the endofin as we would have a situation where you think you have an X-Loop when actually you don't

by **SpAce** » Thu Jan 09, 2020 4:27 am

Hi tarek,

tarek wrote:I may look at adding the Cannibalistic elimination feature to Sukaku explainer. I'm skeptical on adding the opposite which is the endofin as we would have a situation where you think you have an X-Loop when actually you don't

What kind of situation is that? I can't imagine how I could ever think I'd have an X-Loop when I don't

More specifically, I don't see how the presence of an endofin could go unnoticed by someone looking at the chain/loop perspective, because it's clearly a net instead of a simple chain.

That said, endofins are pretty complex features, and rarely if ever necessary because most of the time simpler equivalent fishes exist. The same is mostly true about cannibalistic eliminations, though they're much simpler. Of course both can exist at the same time too. I'm not really sure why you'd want to have one but not the other, as both have educational value (even if they should be normally avoided). If one understands endofins, then one can also understand base triplets in XSudo parlance. I think that's valuable.

Btw, here's a couple more cannibalistic variants (cannibal eliminations marked with ^):

Code: Select all: 9C2 [9B28] 9C8 .-------------------------.-----------------------.-------------------. | 34568-9 *489 3456-9 | *89 ^178-9 *1789 | 1246 *369 1234 | 9r1 | 67-9 *79 1 | 2 3 4 | 5 *69 8 | 9r2 | 3489 2 349 | 6 *189 5 | 14 7 134 | :-------------------------+-----------------------+-------------------: | 249 5 8 | 49 267-9 679 | 3 1 4679 | | 2349 6 349 | 3489 1278-9 1789 | 47 5 479 | | 349 1 7 | 3459 56-9 69 | 8 2 469 | :-------------------------+-----------------------+-------------------: | 15689 3 569 | 7 *5689 2 | 16 4 15 | | 5678 78 2 | 1 4 3 | 9 68 57 | | 145678-9 *4789 456-9 | *589 ^568-9 *689 | 1267 368 12357 | 9r9 '-------------------------'-----------------------'-------------------' 9c5

(Cannibal) Mutant Jellyfish: 9'C28B28\r129c5 => -9 r1c13,r2c1,r9c13,r456c5,^r19c5

4x4 SPM: Show

Code: Select all: 9c1 9c3 9c5 .---------------------------.-----------------------.------------------. | 34568-9 489 3456-9 | 89 178-9 1789 | 1246 369 1234 | | 67-9 79 1 | 2 3 4 | 5 69 8 | | *3489 2 *349 | 6 *189 5 | 14 7 134 | 9R3 :---------------------------+-----------------------+------------------: | *249 5 8 | 49 267-9 679 | 3 1 4679 | | *2349 6 *349 | 3489 1278-9 1789 | 47 5 479 | [9B4] | *349 1 7 | 3459 56-9 69 | 8 2 469 | :---------------------------+-----------------------+------------------: | *15689 3 *569 | 7 *5689 2 | 16 4 15 | | 5678 78 2 | 1 4 3 | 9 68 57 | [9B78] | ^145678-9 *4789 ^456-9 | *589 ^568-9 *689 | 1267 368 12357 | 9r9 '---------------------------'-----------------------'------------------'

(Cannibal) Mutant Jellyfish: 9'R3B478\r9c135 => -9 r12c1,r1c3,r1456c5,^r9c135

4x4 SPM: Show

And your original looping cannibal:

Code: Select all: 9C2 9c5 .---------------------------.-----------------------.------------------. | 34568-9 *489 3456-9 | 89 178-9 1789 | 1246 369 1234 | | 67-9 *79 1 | 2 3 4 | 5 69 8 | [9b1] | *3489 2 *349 | 6 *189 5 | 14 7 134 | 9R3 :---------------------------+-----------------------+------------------: | 249 5 8 | 49 267-9 679 | 3 1 4679 | | 2349 6 349 | 3489 1278-9 1789 | 47 5 479 | | 349 1 7 | 3459 56-9 69 | 8 2 469 | :---------------------------+-----------------------+------------------: | 15689 3 569 | 7 *5689 2 | 16 4 15 | | 5678 78 2 | 1 4 3 | 9 68 57 | [9B8] | 145678-9 *4789 456-9 | *589 ^568-9 *689 | 1267 368 12357 | 9r9 '---------------------------'-----------------------'------------------'

(Cannibal) Grouped L1-Ring: 9r3c5 = r3c13 - r12c2 = r9c2 - r9c456 = 9r7c5 - loop => -9r1456c5,9b1p134,9r9c13,^9r9c5

(Cannibal) Mutant Swordfish: 9'R3C2B8\r9c5b1 => -9r1456c5,9b1p134,9r9c13,^9r9c5

3x3 SPM/TM: Show

As we know, we also have plenty of non-cannibalistic fishes that are equivalent, so there's no real reason to use any of the above. First, your original, and imho the simplest possible fish here:

Code: Select all: 9C2 9c5 .---------------------------.---------------------.------------------. | 34568-9 *489 3456-9 | 89 178-9 1789 | 1246 369 1234 | | 67-9 *79 1 | 2 3 4 | 5 69 8 | [9b1] | *3489 2 *349 | 6 *189 5 | 14 7 134 | 9R3 :---------------------------+---------------------+------------------: | 249 5 8 | 49 267-9 679 | 3 1 4679 | | 2349 6 349 | 3489 1278-9 1789 | 47 5 479 | | 349 1 7 | 3459 56-9 69 | 8 2 469 | :---------------------------+---------------------+------------------: | *15689 3 *569 | 7 *5689 2 | 16 4 15 | 9R7 | 5678 78 2 | 1 4 3 | 9 68 57 | [9b7] | 145678-9 *4789 456-9 | 589 568-9 689 | 1267 368 12357 | '---------------------------'---------------------'------------------'

Grouped L1-Ring: 9r3c5 = r3c13 - r12c2 = r9c2 - r7c13 = 9r7c5 - loop => -9 r14569c5,b1p134,b7p79

Mutant Swordfish: 9'R37C2\c5b17 => -9 r14569c5,b1p134,b7p79

3x3 SPM/TM: Show

Technically this is simpler because it's the same size but Franken:

Code: Select all: c1 c3 c5 .--------------------------.---------------------.------------------. | 34568-9 489 3456-9 | 89 178-9 1789 | 1246 369 1234 | | 67-9 79 1 | 2 3 4 | 5 69 8 | | *3489 2 *349 | 6 *189 5 | 14 7 134 | R3 :--------------------------+---------------------+------------------: | *249 5 8 | 49 267-9 679 | 3 1 4679 | | *2349 6 *349 | 3489 1278-9 1789 | 47 5 479 | [B4] | *349 1 7 | 3459 56-9 69 | 8 2 469 | :--------------------------+---------------------+------------------: | *15689 3 *569 | 7 *5689 2 | 16 4 15 | R7 | 5678 78 2 | 1 4 3 | 9 68 57 | | 145678-9 4789 456-9 | 589 568-9 689 | 1267 368 12357 | '--------------------------'---------------------'------------------'

Franken Swordfish: 9'R37B4\c135 => -9 r129c1,r19c3,r14569c5

3x3 SPM: Show

However, despite being "just" Franken, and pretty simple as such, I think it's harder to spot than your looping Mutant. The difference is easy to see in the matrix form, one being a basic triangle (indicating a non-branching chain/loop) and the other not. Perhaps it could be spotted more easily if specifically looking for fishes, but since I rarely do that, I'd be much more likely to find the one that forms a simple loop.

by **tarek** » Fri Jan 10, 2020 8:56 am

When the Weak link (Cover sector) is a box that links 2 grouped strong links in a line intersecting at the "heart cell" as I call it. That heart cell is the endofin if it has a candidate in that situation. It is the cannibalistic elimination if it was an empty rectangle (base sector). I'm avoiding both of these situations in Sukaku explainer at the moment by disallowing any base sector intersection & ignoring any cover sector intersection.

I've given you an example of the cannibalistic elimination. I need to find an example with an endofin now!

tarek

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