The New Sudoku Players' Forum

by **Havard** » Thu Apr 06, 2006 5:53 pm

ronk wrote:Of course, the argument works just as well with the swordfish in r359c124.

Here I'm not following you ronk. Can you explain?

Havard

by **ronk** » Thu Apr 06, 2006 7:30 pm

Havard wrote:
ronk wrote:Of course, the argument works just as well with the swordfish in r359c124.

Here I'm not following you ronk. Can you explain?

The (row-defined) swordfish in r359c124 and the complementary (col-defined) jellyfish in r1246c3679 have exactly the same fin cells r3c3 and r3c9 ... so the deductions are the same.

You're probably looking for the deduction chains to be wholly contained within the swordfish ... as they are for the jellyfish. This is not the case, however.

by **Havard** » Wed Apr 26, 2006 10:20 am

I am not sure, but I think I might have caught the legendary Franken-Squirmbag thought to be extinct for centuries... If this find is confirmed, we need to ask ourselves these questions:

1: Is he tasty?

2: Does he taste so good that we should be fishing for him?

3: Does he have a smaller complimentary fish, and if not is the rule of jellyfish being the biggest fish in the pond under threat?

I found him in the Top95, nr. 72:

Code: Select all: Squirmbag in columns: 1 2 5 6 8 139X 3459X 1359 | 6 7 12 | 249 8 349 13789X 3479X 6 | 48 89X 12 | 5 279X 3479 789X 2 79- | 458 589X 3 | 479 6 1 ---------------------+----------------------+--------------------- 369X 1 4 | 38 368 7 | 689 5 2 679X 679X 8 | 1 2 5 | 3 4 679 2 3567 357 | 9 368 4 | 1678 17 678 ---------------------+----------------------+--------------------- 13679X 3679X 2 | 357 35 89X | 468 179X 4568 5 8 179 | 27 4 6 | 1279 3 79 4 3679X 379 | 2357 1 89X | 68 279X 568 9X 9X 9 | . . . | 9 . 9 9X 9X . | . 9X . | . 9X 9 9X . 9- | . 9X . | 9 . . ---------+----------+--------- 9X . . | . . . | 9 . . 9X 9X . | . . . | . . 9 . . . | 9 . . | . . . ---------+----------+--------- 9X 9X . | . . 9X | . 9X . . . 9 | . . . | 9 . 9 . 9X 9 | . . 9X | . 9X .

Frightful, is he not?

Havard

by **Ruud** » Wed Apr 26, 2006 10:50 am

Hi Havard,

There is an XYZ-Wing, followed by an XY-Wing that spoils the fun here:

Code: Select all: .------------------.------------------.------------------. | 139 3459 1359 | 6 7 12 | 249 8 349 | | 13789 3479 6 | 48 89 12 | 5 279 3479 | | 789 2 79 | 458 589 3 | 479 6 1 | :------------------+------------------+------------------: | 369 1 4 | 38 368 7 | 689 5 2 | | 679 679 8 | 1 2 5 | 3 4 679 | | 2 3567 357 | 9 368 4 | 1678 *17 678 | :------------------+------------------+------------------: | 13679 3679 2 | 357 35 89 | 468 -179 4568 | | 5 8 179 | 27 4 6 | 1279 3 *79 | | 4 3679 379 | 2357 1 89 | 68 *279 568 | '------------------'------------------'------------------'

However, when I disable XYZ-Wing in my solver, it only discovers the same elimination with a template check, so there is no smaller fish that my solver can catch in this pond.

I nominate this rare creature for the Greenpeace Fish-to-Avoid list, because I think we should leave it alone.

Ruud.

by **Havard** » Wed Apr 26, 2006 11:02 am

Ruud wrote:I nominate this rare creature for the Greenpeace Fish-to-Avoid list, because I think we should leave it alone.

Ruud.

But being a Norwegian, that is only a bigger incentive to haul it in!

Havard

by **ronk** » Wed Apr 26, 2006 3:28 pm

Havard wrote:3: Does he have a smaller complimentary fish, and if not is the rule of jellyfish being the biggest fish in the pond under threat?

Given that r3c3=9 creates an x-wing in r18c79 eliminating all 9s in box 6, I think a smaller [edit: fish] exists. Maybe that's a complementary "franken-swordfish" in r138c379 ... but I couldn't catch one if my life depended on it. I rarely even recognize frankenfish others catch.

[edit: But grouped coloring using the ER in box 9 yields the same exclusion.

Code: Select all: 9 9 9 | . . . | 9 . 9 9 9 . | . A . | . b 9 9 . -9 | . a . | 9 . . ----------+-----------+---------- 9 . . | . . . | 9 . . 9 9 . | . . . | . . 9 . . . | 9 . . | . . . ----------+-----------+---------- 9 9 . | . . 9 | . B . . . B | . . . | b . b . 9 9 | . . 9 | . B .

Since colors A and b share row 2, candidates that see both a and B may be excluded. Therefore, r3c3<>9.]

by **Havard** » Thu May 04, 2006 11:50 am

heh. I revisited the old "is there a simple alternative for this template discovery"-thread to find some nice ponds for my new fishing-tech, and found this puzzle:

Code: Select all: . . 3 | 6 . . | . 9 7 1 . . | . 9 . | 6 2 3 6 9 . | 2 7 3 | 1 . 5 ------+-------+------ 3 . 6 | . . . | 7 . 9 . 5 . | . 3 9 | . 6 . 4 . 9 | . . 6 | 3 . . ------+-------+------ 9 3 1 | . . 8 | . 7 6 7 4 . | 3 6 . | 9 . . . 6 . | 9 . 7 | . 3 . Mr. Nishio says we can eliminate in R5C34 and R46C8... (marked with -) 8 8 . | . 8 . | 8 . . . 8 8 | 8 . . | . . . . . 8 | . . . | . 8 . ------+-------+------ . 8 . | 8 8 . | .-8 . 8 .-8 |-8 . . | 8 . 8 . 8 . | 8 8 . | .-8 8 ------+-------+------ . . . | . . 8 | . . . . . 8 | . . . | . 8 8 8 . 8 | . . . | 8 . 8

Here is the "fish" that will do those eliminations:

Code: Select all: Cannibalistic Franken-Jellyfish in columns: 1 4 5 7 258X 28 3 | 6 1458X 14 | 48X 9 7 1 78 4578 | 58X 9 45 | 6 2 3 6 9 48 | 2 7 3 | 1 48 5 ---------------------+----------------------+--------------------- 3 128 6 | 1458X 2458X 245 | 7 1458 9 28X 5 278 | 1478X- 3 9 | 248X 6 1248 4 1278 9 | 1578X 258X 6 | 3 158 128 ---------------------+----------------------+--------------------- 9 3 1 | 45 245 8 | 245 7 6 7 4 258 | 3 6 125 | 9 18 128 258X 6 258 | 9 1245 7 | 2458X 3 1248 8X 8 . | . 8X . | 8X . . . 8 8 | 8X . . | . . . . . 8 | . . . | . 8 . ------------+-------------+------------ . 8 . | 8X 8X . | . 8 . 8X . 8 | 8X- . . | 8X . 8 . 8 . | 8X 8X . | . 8 8 ------------+-------------+------------ . . . | . . 8 | . . . . . 8 | . . . | . 8 8 8X . 8 | . . . | 8X . 8 Franken-Jellyfish in rows: 3 5 8 9 258 28 3 | 6 1458 14 | 48 9 7 1 78 4578 | 58 9 45 | 6 2 3 6 9 48X | 2 7 3 | 1 48X 5 ------------------+-------------------+------------------ 3 128 6 | 1458 2458 245 | 7 1458- 9 28X 5 278X | 147 3 9 | 248X 6 1248X 4 1278 9 | 1578 258 6 | 3 158- 128 ------------------+-------------------+------------------ 9 3 1 | 45 245 8 | 245 7 6 7 4 258X | 3 6 125 | 9 18X 128X 258X 6 258X | 9 1245 7 | 2458X 3 1248X 8 8 . | . 8 . | 8 . . . 8 8 | 8 . . | . . . . . 8X | . . . | . 8X . ---------+----------+--------- . 8 . | 8 8 . | . 8- . 8X . 8X | . . . | 8X . 8X . 8 . | 8 8 . | . 8- 8 ---------+----------+--------- . . . | . . 8 | . . . . . 8X | . . . | . 8X 8X 8X . 8X | . . . | 8X . 8X Franken-Squirmbag in columns: 1 2 4 5 7 258X 28X 3 | 6 1458X 14 | 48X 9 7 1 78X 4578 | 58X 9 45 | 6 2 3 6 9 48 | 2 7 3 | 1 48 5 ------------------+-------------------+------------------ 3 128X 6 | 1458X 2458X 245 | 7 145 9 28X 5 278- | 147 3 9 | 248X 6 1248 4 1278X 9 | 1578X 258X 6 | 3 15 128 ------------------+-------------------+------------------ 9 3 1 | 45 245 8 | 245 7 6 7 4 258 | 3 6 125 | 9 18 128 258X 6 258 | 9 1245 7 | 2458X 3 1248 8X 8X . | . 8X . | 8X . . . 8X 8 | 8X . . | . . . . . 8 | . . . | . 8 . ---------+----------+--------- . 8X . | 8X 8X . | . . . 8X . 8- | . . . | 8X . 8 . 8X . | 8X 8X . | . . 8 ---------+----------+--------- . . . | . . 8 | . . . . . 8 | . . . | . 8 8 8X . 8 | . . . | 8X . 8

if nothing else, it's good for laughs!

Havard

by **Mike Barker** » Sat May 06, 2006 1:59 pm

This may have already come up (its been a while since I've gone through the posts), but in starting to think about coding up big fish I came across this schitzophrenic fish. Can't quite seem to figure out which is its body and which is its fin. Nothing big, just a little more fun

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

by **Havard** » Sat May 06, 2006 2:04 pm

Mike Barker wrote:This may have already come up (its been a while since I've gone through the posts), but in starting to thing about coding up big fish I came across this schitzophrenic fish. Can't quite seem to figure out which is its body and which is its fin. Nothing big, just a little more fun
Code: Select all
. . . | . . . | # # . . . . | . . . | # # . . . . | . . . | # # . ------+--------+-|--|--- . . . | . X# . | | | * . . . | * | * | X# X# . . . . | . | . | | | . ------+---|----+-|--|--- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X .

This is what you would call a frankenfish type 1 AND type 2...

The type 1 is the same as an ER in this case, and is responsible for the elimination in r4c9. (the whole box 6 can be full of candidates, and it will still be valid.) The other two was pointed out by MJ as a type 2, and can have an additional 2 candidates in box5 along the fish-line, and still be valid. Here you satisfy both conditions, and hence you get the best(?) of two worlds...

Havard

by **ronk** » Sat May 06, 2006 4:31 pm

I think of your "frankenfish" in terms of Almost Constraint Subsets (ACS). The constraint subset principle applies to the following:

Code: Select all: . . . | . . . | X X * . . . | . . . | X X * . . . | . . . | X X * -------+-------+-|-|--- . . . | . . . | | | . * * * | * X * | X X * . . . | . | . | | | . -------+---|---+-|-|--- . . . | . | . | | | . . . . | . | . | | | . * * * | * X * | X X * Fig. 1 (no extra candidates)

Because all candidates in three units of set A (c5,c7,c8) are "covered" by three units of set B (b3,r5,r9), all other candidates in set B may be excluded as shown.

If extra candidates -- limited in number and existing only at certain locations -- prevent constraint subsets, then we have almost constraint subsets. Consider the following "frankefish type 1":

Code: Select all: . . . | . . . | X X . . . . | . . . | X X . . . . | . . . | X X . -------+-------+-|-|--- . . . | . . . | | | . . . . | . X . | X X . . . . | . | . | | | . -------+---|---+-|-|--- . . . | . | . | # # * . . . | . | . | # # * . . . | . X . | X X * Fig. 2 (if an extra candidate '#' is ultimately true)

There are two possiblities, either

one of the extra candidates is ultimately true, and any candidate that sees all extras may be excluded, or
none of the extra candidates is ultimately true, and the Constraint Subsets and exclusions of Fig. 1 apply.

Exclusions common to both possibilities are then valid, and for this example ...

Code: Select all: . . . | . . . | X X . . . . | . . . | X X . . . . | . . . | X X . -------+-------+-|-|--- . . . | . . . | | | . . . . | . X . | X X . . . . | . | . | | | . -------+---|---+-|-|--- . . . | . | . | # # . . . . | . | . | # # . . . . | . X . | X X * Fig. 3 (whether or not an extra candidate '#' is ultimately true)

... r9c9<>X is true in either case.

An identical argument may be made for "frankenfish type 2".

Code: Select all: . . . | . . . | X X . . . . | . . . | X X . . . . | . . . | X X . -------+-------+-|-|--- . . . | . # . | | | . . . . | * X * | X X . . . . | . # . | | | . -------+---|---+-|-|--- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X . Fig. 4

P.S. Havard, this is the type of logic argument I was looking for in our earlier discussion. Of course, I was expecting your argument to be in "fish" terms.

by **Mike Barker** » Wed May 10, 2006 3:36 am

Havard, in trying to understand some of your eliminations here it seems you are using something beyond what I understood to be Frankenfish, but which are still valid. It seems like you've got the following Frankenfish

Code: Select all: Franken Swordfish . . . | * X * | X X * . . . | * X * | X X * . . . | * X * | X X * -------+-------+-|-|--- . . . | . . . | | | * * * * | * . * | X X * . . . | . . . | . . * -------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . which is easy to show based on contraint sets {C5, C7, C8} are covered by {B2, B3, R5} or {B2, B3, B6}

Code: Select all: Franken Jellyfish . . . | * X X | X X * . . . | * X X | X X * . . . | * X X | X X * -------+---|-|-+-|-|--- . . . | . | | | | | . * * * | * X X | X X * . . . | . | | | | | . -------+---|-|-+-|-|--- . . . | . | | | | | . . . . | . | | | | | . * * * | * X X | X X * which is again easy to show based on contraint sets {C5, C6, C7, C8} are covered by {B2, B3, R5, R9}

Code: Select all: Franken Jellyfish . . . | . . . | X X * * X * | * X * | X X * . | . | . | . | X X * ---|---+---|---+-|-|--- . | . | . | . | | | . * X * | * X * | X X * . | . | . | . | | | . ---|---+---|---+-|-|--- . | . | . | . | | | . . | . | . | . | | | . * X * | * X * | X X * let me try almost constraint sets. if the digit is in r2c2, then the remaining elements of the fish {C5, C7, C8} can be covered by {B3, R5, R9}. if the digit is not in r2c2 then the remaining elements of the fish {C2, C5, C7, C8} can be covered by {B2, B3, R5, R9}. In either case the eliminations as shown are possible.

Code: Select all: Franken Jellyfish . . . | . # . | X X . . X . | * X * | X X . . | . | . # . | X X . ---|---+---|---+-|-|--- . | . | . | . | | | . . X . | . X . | X X . . | . | . | . | | | . ---|---+---|---+-|-|--- . | . | . | . | | | . . | . | . | . | | | . . X . | . X . | X X . again with almost constraint sets if a fin element contains the digit then the eliminations can be made. If not then we have the previous situation and the two eliminations can still be made.

So, Havard, did I miss the memo, have you been holding out on us, or am I missing something? I'm still trying to apply these rules to your Franken Jellyfish - it looks right, I'm just not there yet. On the other hand your cannabalistic jellyfish is, as I pointed out previously, a finned swordfish:

Code: Select all: +------------------+------------------+-------------------+ | *258 28 3 | 6 *1458 14 | *48 9 7 | | 1 78 4578 | 58 9 45 | 6 2 3 | | 6 9 48 | 2 7 3 | 1 48 5 | +------------------+------------------+-------------------+ | 3 128 6 | 1458 *2458 245 | 7 1458 9 | | *28 5 278 | -1478 3 9 | *248 6 1248 | | 4 1278 9 | 1578 *258 6 | 3 158 128 | +------------------+------------------+-------------------+ | 9 3 1 | 45 245 8 | 245 7 6 | | 7 4 258 | 3 6 125 | 9 18 128 | | *258 6 258 | 9 1245 7 | *2458 3 1248 | +------------------+------------------+-------------------+

and your Frankensquirmbag is a generalized VWXYZ-wing. Since this is not a fish, I'm not sure its a valid comparison, but I still need to work on my Frankenfish detector to understand what it is if only fish are considered.

Code: Select all: +------------------+------------------+------------------+ | 258 28 3 | 6 1458 14 | 48 9 7 | | 1 78 4578 | 58 9 45 | 6 2 3 | | 6 9 48 | 2 7 3 | 1 48 5 | +------------------+------------------+------------------+ | 3 128 6 | 1458 2458 245 | 7 *145 9 | | #28 5 -278 | 147 3 9 | *248 6 *1248 | | 4 1278 9 | 1578 258 6 | 3 *15 128 | +------------------+------------------+------------------+ | 9 3 1 | 45 245 8 | 245 7 6 | | 7 4 258 | 3 6 125 | 9 18 128 | | 258 6 258 | 9 1245 7 | 2458 3 1248 | +------------------+------------------+------------------+

Thanks for the examples. Maybe someday I'll catch up with you.

Ron, thanks for the demonstration of almost constraint sets. When I first looked at constraint sets based on your suggestion here, I felt in my heart that they should be applicable to Frankenfish, but didn't know how. Your demonstration of almost constraint sets was great.

by **ronk** » Wed May 10, 2006 10:52 am

Mike Barker wrote:
Code: Select all
Franken Jellyfish . . . | . . . | X X * * X * | * X * | X X * . | . | . | . | X X * ---|---+---|---+-|-|--- . | . | . | . | | | . * X * | * X * | X X * . | . | . | . | | | . ---|---+---|---+-|-|--- . | . | . | . | | | . . | . | . | . | | | . * X * | * X * | X X * let me try almost constraint sets. if the digit is in r2c2, then the remaining elements of the fish {C5, C7, C8} can be covered by {B3, R5, R9}. if the digit is not in r2c2 then the remaining elements of the fish {C2, C5, C7, C8} can be covered by {B2, B3, R5, R9}. In either case the eliminations as shown are possible.

While not incorrect, the "almost" is not necessary. Columns 2, 5, 7 and 8 are simply covered by box 3 and rows 2, 5 and 9. And since box 3 and row 2 intersect, r2c7<>X and r2c8<>X are valid exclusions too.

Mike Barker wrote:
Code: Select all
Franken Jellyfish . . . | . # . | X X . . X . | * X * | X X . . | . | . # . | X X . ---|---+---|---+-|-|--- . | . | . | . | | | . . X . | . X . | X X . . | . | . | . | | | . ---|---+---|---+-|-|--- . | . | . | . | | | . . | . | . | . | | | . . X . | . X . | X X . again with almost constraint sets if a fin element contains the digit then the eliminations can be made. If not then we have the previous situation and the two eliminations can still be made.

That's a true "almost" constraint set.

Mike Barker wrote:Ron, thanks for the demonstration of almost constraint sets. When I first looked at constraint sets based on your suggestion here, I felt in my heart that they should be applicable to Frankenfish, but didn't know how. Your demonstration of almost constraint sets was great.

You're welcome. I came upon the almost constraint set outlook because I just wasn't getting frankenfish (still not, I guess). I found myself always "backtesting" Havard's exclusions because they weren't obvious. It was too much like T&E. That said, like you, I haven't yet made ACS cover (pun intended) all of Havard's exclusions.

P.S. Your link is broken ... due to a missing '#' (repaired in the quote above).

by **ronk** » Wed May 10, 2006 6:26 pm

Mike Barker wrote:
Code: Select all
Franken Jellyfish . . . | . . . | X X * * X * | * X * | *X *X * . | . | . | . | X X * ---|---+---|---+--|--|--- . | . | . | . | | | . * X * | * X * | X X * . | . | . | . | | | . ---|---+---|---+--|--|--- . | . | . | . | | | . . | . | . | . | | | . * X * | * X * | X X *

If that's a franken jellyfish (r2c78<>X added), then the following should be too.

Code: Select all: Franken Jellyfish ??? . * . | . * . | X X (.) . X---|---X . |(.)(.)(.) . * . | . * . | X X (.) -------+-------+--------- . * . | . * . | * * . . X---|---X---|-X--X . . * . | . * . | * * . -------+-------+--------- . * . | . * . | * * . . * . | . * . | * * . . X---|---X---|-X--X . cells of box 3 are also be part of the fish

But I can't catch frankenfish.

Can anyone?

by **Mike Barker** » Wed May 10, 2006 6:47 pm

Based on the way you've drawn it, it looks at first that A={R2, R5, R8, B3} is covered by B={C2, C5, C7, C8}, but that is only true if r13c9 do not contain the digit (note by construction r2c789 do not). So without the added constraint I don't believe the fish is valid.

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

by **ronk** » Wed May 10, 2006 7:05 pm

Mike Barker wrote:that is only true if r13c9 do not contain the digit (note by construction r2c789 do not).

I mean those cells to be without candidates, but wasn't sure how to illustrate it. I edited the post using MJ's "(.)" for the empty cells in box 3, but like the following better.

Code: Select all: . * . | . * . | X X - - X - | - X - | - - - . * . | . * . | X X - -------+-------+--------- . * . | . * . | * * . - X - | - X - | X X - . * . | . * . | * * . -------+-------+--------- . * . | . * . | * * . . * . | . * . | * * . - X - | - X - | X X - '-' indicates cells void of candidate X '*' indicates cells for potential candidate X exclusions

Mike Barker wrote:it looks at first that A={R2, R5, R8, B3} is covered by B={C2, C5, C7, C8}

I figured you'd pick up on that right away, but I'm actually looking for someone to explain the exclusions in frankenfish terms ... not constraint set terms.

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