The New Sudoku Players' Forum

by **Myth Jellies** » Sat Mar 18, 2006 8:15 am

That's a nice demonstration, Ruud.

Some of those who believe in the existence of the semi-mythical creatures known as Franken-swordfish and Franken-jellyfish postulate the existance of a creature from the benthic depths, so hideous, it can only be called, "Frankensquirmbag." This is probably not a term that should be employed in mixed company; however, in the interest of science, I shall press on.

In most cases, Frankensquirmbag degenerates quickly into a little line-box interaction that quickly dissolves into insignificance. But when the moon and the sun produce just the right tidal forces....Behold...

Code: Select all: -X- *X *X | X *X X | *X *X . -X- *X *X | X *X X | *X *X . X #X #X | X . X | . . . -----------+-----------+------------ X . . | X . X | . . . X *X *X | X *X X | *X *X . X *X *X | X *X X | *X *X . -----------+-----------+------------ X **X **X | X **. X |**. **. X X ##X ##X | X . X | . . X X ##X ##X | X . X | . . X * ? ? | . X . | X X . * ? ? | . X . | X X . ? ? ? | . | . | | | . --|-|-+---|---+-|-|-- ? | | | . | . | | | . ? X X | . X . | X X . ? X X | . X . | X X . --|-|-+-------+------ ? ? ? | . . . | . . . ? ? ? | . . . | . . . ? ? ? | . . . | . . .

Note that you could solve for one of the X's in box nine (top diagram), and the "fish" still retains most all of its gruesomeness.

Actually, I've just noticed that frankenfish are sort of a filet of a filet kind of a deal. If you go with the idea that this...

Code: Select all: . . . | . . . | # # * . . . | . . . | # # * . . . | . . . | # # * ------+-------+-|-|-- . . . | . . . | | | . * * * | * X * | X X * . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . * * * | * X * | X X *

...is a superposition of three headless sashimi swordfish, then all frankenfish is, is a filet-of-headless seafood with the new fin in the cell where you make the reduction. It doesn't have to be a box in line with the original fin. It could be a filet taken from any box containing an X and a *.

Code: Select all: . . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . . . | | | . . . . | . X . | X X . . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | # # . . . . | . | . | # # . . . . | . X . | X X *

Code: Select all: . . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . # . | | | . . . . | * X * | X X . . . . | . # . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X .

by **Jeff** » Sat Mar 18, 2006 9:52 am

Myth Jellies wrote:
Code: Select all
. . . | . . . | # # * . . . | . . . | # # * . . . | . . . | # # * ------+-------+-|-|-- . . . | . . . | | | . * * * | * X * | X X * . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . * * * | * X * | X X *

MJ, It is the red wine that caused me to respond to your post. Do forgive me for being hasty. I am not a fillot-O-seafood player, so I cannot explain in terms of seafood . However, with nice loop I can prove this deduction by adding one more X, ie.

Code: Select all: . . . | . X . | # # * . . . | . . . | # # . . . | . . . | # # ------+-------+-|-|-- . . . | . . . | | | . * * * | * X * | X X * . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . * * * | * X * | X X *

[r1c9]-x-[r123c78]=x=[almost swordfish:r159c578]-x-[r1c9] => r1c9<>x
IOW, one of r123c9 has to be an x in your candidate grid quoted.

Could you explain how that X could be dropped?

by **ronk** » Sat Mar 18, 2006 11:46 am

Ruud wrote:... until it requires a finned Jellyfish for digit 1 at this point:
Code: Select all
.------------.------------.------------. | 7 *19 2 | 4 3 5 | 69 8 *169| |*18 3 6 |*18 9 2 | 5 7 4 | | 189 4 5 | 7 18 6 | 29 12 3 | :------------+------------+------------: |*16 16 7 | 5 4 8 | 3 9 2 | | 4 89 89 | 3 2 1 | 7 6 5 | | 5 2 3 | 9 6 7 | 1 4 8 | :------------+------------+------------: | 3 689 189| 168 158 4 | 269 125 7 | | 2 5 4 |*16 7 39 | 8 #13 *169| | 69 7 189| 2 158 39 | 4 135-169| '------------'------------'------------'

Ruud, until now I thought your solver was reporting the smaller of two complementary finned fish. The smaller finned swordfish is:

Code: Select all: .------------.------------.------------. | 7 19 2 | 4 3 5 | 69 8 169| | 18 3 6 | 18 9 2 | 5 7 4 | | 189 4 5 | 7 *18 6 | 29 *12 3 | :------------+------------+------------: | 16 16 7 | 5 4 8 | 3 9 2 | | 4 89 89 | 3 2 1 | 7 6 5 | | 5 2 3 | 9 6 7 | 1 4 8 | :------------+------------+------------: | 3 689*189| 168*158 4 | 269*125 7 | | 2 5 4 | 16 7 39 | 8 #13 169| | 69 7 *189| 2 *158 39 | 4 *135-169| '------------'------------'------------'

Ron

by **Havard** » Sat Mar 18, 2006 11:47 am

Jeff wrote:
Code: Select all
. . . | . X . | # # * . . . | . . . | # # . . . | . . . | # # ------+-------+-|-|-- . . . | . . . | | | . * * * | * X * | X X * . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . * * * | * X * | X X *

Could you explain how that X could be dropped?

The trick is to concider this little nifty pattern first:

Code: Select all: . . . | . . . | b d x . . . | . . . | b d x . . . | . . . | b d x ------+-------+-|-|-- . . . | . . . | | | y z z z | z z z | A C y . . . | . . . | . . y ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . If A is true => C and bbb and yyy and zzz are false, and then xxx falls to line-box with ddd. If A is false => bbb are true => ddd and xxx is false => C is true => yyy and zzz is false

or with fish-symbols:

Code: Select all: . . . | . . . | # # * . . . | . . . | # # * . . . | . . . | # # * ------+-------+-|-|-- . . . | . . . | | | * * * * | * * * | X X * . . . | . . . | . . * ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .

You would recognize this as a grouped x-cycle Jeff.

Now you could just think of the strong link in column 4 as connecting up the links in column 7 and 8, and making the elimination valid.

Now if the x was NOT dropped, you could only eliminate the * in R1C9.

Code: Select all: . . . | . X . | # # * . . . | . | . | # # . . . . | . | . | # # . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . X . | X X . . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X .

havard

by **Jeff** » Sat Mar 18, 2006 12:39 pm

Thanks Havard,

Code: Select all: . . . | . . . | # # * . . . | . . . | # # * . . . | . . . | # # * ------+-------+-|-|-- . . . | . . . | | | . * * * | * X * | X X * . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . * * * | * X * | X X *

So, in terms of nice loop, this is really an almost x-wing disguised as an almost skinny swordfish.

[r123c9]-x-[r123c7]=x=[almost x-wing:r59c57]-x-[r59c8]=x=[r123c8]-x-[r123c9] => r123c9<>x

This certainly makes an excellent example for grouped x-cycle with all grouped nodes. Enough wine for the day!

by **ronk** » Sat Mar 18, 2006 1:39 pm

Jeff wrote:So, in terms of nice loop, this is really an almost x-wing disguised as an almost skinny swordfish.

[r123c9]-x-[r123c7]=x=[almost x-wing:r59c57]-x-[r59c8]=x=[r123c8]-x-[r123c9] => r123c9<>x

Treating it as two almost x-wings ...

[r123c9]-x-[r123c7]=x=(almost x-wing:[r59c7]-x-[r59c5])=x=(almost x-wing:[r59c5]-x-[r59c8])=x=[r123c8]-x-[r123c9]

... results in a certain elegance from the symmetry of the nice loop.

Ron

by **Mike Barker** » Sat Mar 18, 2006 1:44 pm

Ron, I updated the summary based on your reply. I added a reference to big fins, but did keep reference to multiple fins since I believe this is in keeping with the discussion and makes for a clear explaination by identifying when a big fin is allowed and avoiding reference to phantom cells. If this is not okay let me know and I'll modify the description. By the way I specifically used the term multiple fins since I don't know of any reason why there couldn't be three fins. In the 2nd case I showed there could still be eliminations in the non-finned row. Now that would be an interesting catch.

Also, if Myth is right I need to update the post further, but I don't believe these are valid finned fish:

Code: Select all: . . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . . . | | | . . . . | . X . | X X . . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | # # . . . . | . | . | # # . . . . | . X . | X X *

Code: Select all: . . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . # . | | | . . . . | * X * | X X . . . . | . # . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X .

by **Havard** » Sat Mar 18, 2006 2:16 pm

Mike Barker wrote:... but I don't believe these are valid finned fish:
Code: Select all
. . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . . . | | | . . . . | . X . | X X . . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | # # . . . . | . | . | # # . . . . | . X . | X X *

WHAT?!?! You not think Frankenfish is valid fish?! Frankenfish will EAT you so that YOU not valid! ARRR!!!
Frankenfish

Myth Jellies demonstrated himself that franken-swordfish (your example)is just an Empty Rectangle. However Franken-Jellyfish (and possibly Franken-Squirmbag, unless this one can be proven to be smaller fish...) is very valid!

...and the only thing that annoys me with this one:

Code: Select all: . . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . # . | | | . . . . | * # * | X X . . . . | . # . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X .

...is that I did not catch it first... Good one MJ!

very easy to make it look like proper fish:

Code: Select all: . . . | . . . | # # . . . . | .(X). | X X . . . . | . | . | # # . ------+---|---+-|-|-- . . . | . # . | | | . . . . | * X * | X X . . . . | . # . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X .

the more fins, the more maneuverable fish!

havard

by **Mike Barker** » Sat Mar 18, 2006 2:31 pm

Thanks, I'll update the post

by **Ruud** » Sat Mar 18, 2006 2:32 pm

ronk wrote:
Ruud wrote:... until it requires a finned Jellyfish for digit 1 at this point:
Code: Select all
.------------.------------.------------. | 7 *19 2 | 4 3 5 | 69 8 *169| |*18 3 6 |*18 9 2 | 5 7 4 | | 189 4 5 | 7 18 6 | 29 12 3 | :------------+------------+------------: |*16 16 7 | 5 4 8 | 3 9 2 | | 4 89 89 | 3 2 1 | 7 6 5 | | 5 2 3 | 9 6 7 | 1 4 8 | :------------+------------+------------: | 3 689 189| 168 158 4 | 269 125 7 | | 2 5 4 |*16 7 39 | 8 #13 *169| | 69 7 189| 2 158 39 | 4 135-169| '------------'------------'------------'

Ruud, until now I thought your solver was reporting the smaller of two complementary finned fish. The smaller finned swordfish is:
Code: Select all
.------------.------------.------------. | 7 19 2 | 4 3 5 | 69 8 169| | 18 3 6 | 18 9 2 | 5 7 4 | | 189 4 5 | 7 *18 6 | 29 *12 3 | :------------+------------+------------: | 16 16 7 | 5 4 8 | 3 9 2 | | 4 89 89 | 3 2 1 | 7 6 5 | | 5 2 3 | 9 6 7 | 1 4 8 | :------------+------------+------------: | 3 689*189| 168*158 4 | 269*125 7 | | 2 5 4 | 16 7 39 | 8 #13 169| | 69 7 *189| 2 *158 39 | 4 *135-169| '------------'------------'------------'

Ron

Actually, it does. The Jellyfish contains 7 vertices, the swordfish has 8. I did not realize that the smaller creature could have more vertices than the bigger one.

Thanks. I will update the code.

Ruud.

by **ronk** » Sat Mar 18, 2006 3:24 pm

Havard wrote:
ronk wrote:
Havard wrote:what do you think? does Frankenfish have the right of life, or should we send him back to the deep?

Isn't there a rule that an "exclusion cell" must see ALL the fin cells?

Frankenfish does not care about rules...

Frankenfish EATS rules! ...mmmm....jummy rules... ..mmm...

Code: Select all: . . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . . . | | | . . . . | . X . | X X . . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | # # . . . . | . | . | # # . . . . | . X . | X X *

Code: Select all: . . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+-------+-|-|-- . . . | . # . | | | . . . . | * # * | X X . . . . | . # . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X .

In light of these better examples of two-finned fish, do you have a less flippant answer to my question ...

"Isn't there a rule that an "exclusion cell" must see ALL the fin cells?"

One of the beauties of the finned fish technique has been a simple rule which was pattern independent. Now it appears we have dependency upon specific patterns.

Ron

by **Jeff** » Sat Mar 18, 2006 4:32 pm

Mike Barker wrote:............. but I don't believe these are valid finned fish:

Hi Mike, Viewing this pattern as a finned swordfish of 332 formation with grouped nodes [r123c8] & [r123c9] in any combinations of ? being X, it is a valid finned fish. Any ? cells may contain X. If none of the ? cells contain X, then the finned swordfish reduces to a finned skinny swordfish of 330 formation. Likewise, any # cells may contain X. If none of the # cells contain X, then the finned swordfish reduced to a simple swordfish.

Code: Select all: . . . | . . . | ? ? . . . . | . . . | ? ? . . . . | . . . | ? ? . ------+-------+-|-|-- . . . | . . . | | | . . . . | . X . | X X . . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | # # . . . . | . | . | # # . . . . | . X . | X X * [r9c9]-x-[Fin:r78c78]=x=[almost grouped swordfish:r12359c578]-x-[r9c9] => r9c9<>x

Code: Select all: . . . | . . . | ? ? . . . . | . . . | ? ? . . . . | . . . | ? ? . ------+-------+-|-|-- . . . | . # . | | | . . . . | * X * | X X . . . . | . # . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X . [r5c46]-x-[Fin:r46c5]=x=[almost grouped swordfish:r12359c578]-x-[r5c46] => r5c46<>x

However, from the same perspective, the following pattern is not a valid finned fish because it has no fin.

Code: Select all: . . . | . . . | ? ? * . . . | . . . | ? ? * . . . | . . . | ? ? * ------+-------+-|-|-- . . . | . . . | | | . * * * | * X * | X X * . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . * * * | * X * | X X * [Grouped swordfish:r12359c578] => r123c9<>x and r59c123469<>x

by **Ruud** » Sat Mar 18, 2006 5:52 pm

I happended to notice a remarkable feature of sashimi fish, when I ran a few more tests.

The following puzzle does not look too difficult, but it actually contains 7 finned fish :!:

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

This is the candidate grid where it all starts:

Code: Select all: .------------------.------------------.------------------. | 5 26 3 | 1 7 9 | 26 8 4 | | 4 28 7 | 5 6 238 | 1 23 9 | | 268 1 9 | 4 38 238 | 236 5 7 | :------------------+------------------+------------------: | 1368 368 2 | 368 9 4 | 5 7 136 | | 367 9 4 | 27 1 5 | 8 236 236 | | 13678 5 168 | 27 38 368 | 9 4 1236 | :------------------+------------------+------------------: | 2368 2368 5 | 9 4 7 | 23 1 2368 | | 9 4 68 | 368 2 1 | 7 36 5 | | 12368 7 168 | 368 5 368 | 4 9 2368 | '------------------'------------------'------------------'

To clarify my observation, I have isolated the candidates for 3. This is the first finned swordfish detected:

Code: Select all: . . . | . . . | . . . . . . | . . 3 | . 3 . . *. . | . *3 3 |*3 . . ---------+---------+--------- 3 #3 . | 3 . . | . . 3 3 . . | . . . | . 3 3 -3 *. . | . *3 . |*. . 3 ---------+---------+--------- 3 *3 . | . *. . |*3 . 3 . . . | 3 . . | . 3 . 3 . . | 3 . 3 | . . 3

Now this is the remarkable thing: Another finned swordfish can be constructed using exactly the same candidates:

Code: Select all: . . . | . . . | . . . . . . | . . 3 | . 3 . . *. . | . *3 3 |*3 . . ---------+---------+--------- 3 *3 . |-3 *. . |*. . 3 3 . . | . . . | . 3 3 3 . . | . #3 . | . . 3 ---------+---------+--------- 3 *3 . | . *. . |*3 . 3 . . . | 3 . . | . 3 . 3 . . | 3 . 3 | . . 3

This may be a better example of my * Heisenberg * principle. It is possible to interpret these patterns in totally different ways.

I wonder what more is lurking in these seas?

Ruud.

by **Myth Jellies** » Sat Mar 18, 2006 7:07 pm

The Life Aquatic with Steve Zissou and we are all on the boat

by **ronk** » Sat Mar 18, 2006 7:18 pm

Ruud wrote:To clarify my observation, I have isolated the candidates for 3. This is the first finned swordfish detected:
.............
Now this is the remarkable thing: Another finned swordfish can be constructed using exactly the same candidates:
.............
This may be a better example of my * Heisenberg * principle. It is possible to interpret these patterns in totally different ways.

Suspect the only uncertainty is whether there are two candidates to eliminate. Otherwise, the existence of Havard's "extended skyscraper", aka x-cycle of length 7, aka turbot chain of length 7, should always provides the opportunity to define two finned swordfish ...

Code: Select all: . . . | . . . | . . . . . . | . . . | . . . . . . | . B . | C . . -------+---|---+-|----- . A . | * | * | | . . . | . | . | . | | . . * | * | . b . | | . . ---|---+-------+-|----- . a . | . . . | c . . . . . | . . . | . . . . . . | . . . | . . .

... once each with each of the elimination rows shown above.

Ron

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