The New Sudoku Players' Forum

by **tarek** » Mon Mar 13, 2006 2:37 pm

vidarino wrote:Fixed, and the hunt continues... ;-)

good, could you retest your first squirmbag ?
It looks like a pure one....unless there is a lesser fish with 2 vertices in the box next to the fin which I've miseed.

Tarek

by **vidarino** » Mon Mar 13, 2006 2:40 pm

tarek wrote:It looks like a pure one....unless there is a lesser fish with 2 vertices in the box next to the fin which I've miseed.

The first one was a false positive, unfortunately;

Code: Select all: 2 159 1579 | 8 1367 4 | #167 379 13679 4 3 17 | 167 9 2 | 5 8 167 *78 189 6 | 157 137 *357 | *4 2 -1379 -------------------------+--------------------------+-------------------------- *568 45689 2589 | 124679 12367 *367 | *167 34579 13569 56 7 259 | 12469 1236 36 | 16 3459 8 1 469 3 | 4679 5 8 | 2 479 679 -------------------------+--------------------------+-------------------------- *5678 568 578 | 3 4 *567 | *9 1 2 9 2 4 | 57 8 1 | 3 6 57 3 156 157 | 2567 267 9 | 8 57 4 Finned Swordfish with 7 in R347C167 + fin R1C7 -> R3C9 <> 7

But again, how about this one?

Code: Select all: 1358 7 138 | 2 6 4 | 35 389 389 2 9 *4 | 3 *5 *78 | *6 *78 1 3568 68 *368 | 1 *78 *9 | *357 *4 2 ----------------------+-----------------------+----------------------- -379 5 *2 | 6 *789 *78 | *1 *37 4 3678 68 #3678 | 4 1 2 | 9 5 367 4 1 #679 | 79 3 5 | 8 2 67 ----------------------+-----------------------+----------------------- 6789 2 *678 | 5 *79 *36 | *4 *1 389 16789 4 *16789 | 89 *2 *36 | *37 *3789 5 89 3 5 | 789 4 1 | 2 6 789 Finned Squirmbag with 7 in R23478C35678 + fin R56C3 -> R4C1 <> 7

I *think* (again, heh) it's legit.

Vidar

by **ravel** » Mon Mar 13, 2006 2:51 pm

Must be easier, i dont need the upper 3 boxes for the elimination.

by **Havard** » Mon Mar 13, 2006 2:56 pm

vidarino wrote:
Code: Select all
7 456 346 | 45 2 8 | 36 9 1 8 9 23 | 67 67 1 | 23 5 4 *56 1 *2456 | 9 *45 *3 | 268 7 *28 ----------------------+-----------------------+----------------------- 2 3456 8 | 356 1 9 | 45 46 7 *56 34567 *9 | 367 *8 *47 | 1245 146 *25 *1 467 *4567 | 2 *567 *457 | 9 8 *3 ----------------------+-----------------------+----------------------- *3 578 *57 | -1457 *457 *6 | 14578 2 *9 4 2 1 | 8 9 #57 | 57 3 6 *9 5678 *567 | -1457 *3 *2 | 14578 14 *58 Finned Squirmbag with 5 in R35679C13569 + fin R8C6 -> R7C4 <> 5 -> R9C4 <> 5

(And yes, I know multi-coloring / an X-cycle can zap the one in R9C4. Possibly the other one, too, but I haven't studied it. (Actually, the whole thing can be solved just by cracking the 5s. ) )

Here is one possible way to "crack the 5s"

Code: Select all: . . . | . . . | . . . . . . | . . . | . . . 5 . . | . * . | . . . |-----+-------+------ | . . | . . . | . . . 5 . . | . . . | . . 5 . . 5-----5-5 | . . | ------+-------+-----| . . . | . . . | . . | . . . | . . 5---5 . | . . . | . . . | . . 5

by **vidarino** » Mon Mar 13, 2006 3:00 pm

OK, one more snack;

Code: Select all: 234 8 124 | 7 236 14 | 9 2346 5 *5 6 *247 | 9 238 *48 | *2347 *2347 1 *2347 9 *1247 | 345 236 *145 | *2347 *23467 8 ----------------------+-----------------------+----------------------- 1 347 5 | 2 47 6 | #347 8 9 9 47 6 | 8 1 3 | #247 5 247 *28 347 *28 | 45 9 *457 | *6 *1 -347 ----------------------+-----------------------+----------------------- *478 2 *478 | 34 5 *9 | *1 *347 6 *47 1 *9 | 6 38 *478 | *5 *2347 2347 6 5 3 | 1 47 2 | 8 9 47 Finned Sashimi Squirmbag with 7 in R23678C13678 + fin R45C7 -> R6C9 <> 7

And in the very same grid!

Code: Select all: *234 8 *124 | *7 236 *14 | *9 *2346 5 *5 6 *247 | *9 238 *48 | *2347 *2347 1 *2347 9 *1247 | *345 236 *145 | *2347 *23467 8 ----------------------+-----------------------+----------------------- 1 347 5 | 2 47 6 | #347 8 9 9 47 6 | 8 1 3 | #247 5 247 *28 347 *28 | *45 9 *457 | *6 *1 -347 ----------------------+-----------------------+----------------------- *478 2 *478 | *34 5 *9 | *1 *347 6 *47 1 *9 | *6 38 *478 | *5 *2347 2347 6 5 3 | 1 47 2 | 8 9 47 Finned Whale with 4 in R123678C134678 + fin R45C7 -> R6C9 <> 4

Now, obviously I'm not trusting my solver 100% yet, but they look okay to me.

Vidar

by **ravel** » Mon Mar 13, 2006 3:19 pm

vidarino wrote:But again, how about this one?

Code: Select all
1358 7 138 | 2 6 4 | 35 389 389 2 9 *4 | 3 *5 *78 | *6 *78 1 3568 68 *368 | 1 *78 *9 | *357 *4 2 ----------------------+-----------------------+----------------------- -379 5 *2 | 6 *789 *78 | *1 *37 4 3678 68 #3678 | 4 1 2 | 9 5 367 4 1 #679 | 79 3 5 | 8 2 67 ----------------------+-----------------------+----------------------- 6789 2 *678 | 5 *79 *36 | *4 *1 389 16789 4 *16789 | 89 *2 *36 | *37 *3789 5 89 3 5 | 789 4 1 | 2 6 789 Finned Squirmbag with 7 in R23478C35678 + fin R56C3 -> R4C1 <> 7

Isnt there a finned swordfish in rows 569?

by **vidarino** » Mon Mar 13, 2006 3:29 pm

ravel wrote:Isnt there a finned swordfish in rows 569?

Hmm, I don't think so... Well, there appears to be, but will that be able to make the elimination in R4C1? I was under the impression that you could only eliminate candidates in the fish's columns.

If so this particular finned swordfish could only eliminate from R4C3, which doesn't have a 7...

Hmm, you might be on to something, though. I'll experiment a bit.

Thanks,
Vidar

by **ronk** » Mon Mar 13, 2006 3:31 pm

Havard wrote:Here is the simpler counterpart:
Code: Select all
. . . | . . . | 7 . . . . . | . . . | | . . 7 . . | . . 7 | | . * |-----+-----|-+-|---- | . . | . . 7 | 7 . . | . . | . . | | . . . | . . | . . | | . . . |-----+-----|-+------ 7 . . | . . 7 | . . . . . . | . . . | . . . . . . | . . . | . . .

Given that column six has three candidates in three different boxes, how do you group candidates to end up with a strong link? Or if your vertical line in col 6 doesn't represent a strong link, what does it represent?

Ron

by **ravel** » Mon Mar 13, 2006 3:40 pm

vidarino wrote:... Well, there appears to be, but will that be able to make the elimination in R4C1?

Im sure that i can make the elimination, but not sure about the definition of the finned swordfish.

by **ravel** » Mon Mar 13, 2006 3:45 pm

ronk wrote:Given that column six has three candidates in three different boxes, how do you group candidates to end up with a strong link?
Ron

It gives an x-wing.

by **aeb** » Mon Mar 13, 2006 5:07 pm

vidarino wrote:I just merely looking for high-order N-fish that didn't have a smaller counterpart. My stance on the subject is wavering badly right now, though. ;-)

Anyway, my solver has now been fixed, and the search for big fish continues.

But you have already seen the proof that big fish are equivalent to small fish, and big finned fish equivalent to small finned fish. Now what is the search for?

vidarino wrote:Here's one more for you all to scrutinize;

Code: Select all
7 456 346 | 45 2 8 | 36 9 1 8 9 23 | 67 67 1 | 23 5 4 *56 1 *2456 | 9 *45 *3 | 268 7 *28 ----------------------+-----------------------+----------------------- 2 3456 8 | 356 1 9 | 45 46 7 *56 34567 *9 | 367 *8 *47 | 1245 146 *25 *1 467 *4567 | 2 *567 *457 | 9 8 *3 ----------------------+-----------------------+----------------------- *3 578 *57 | -1457 *457 *6 | 14578 2 *9 4 2 1 | 8 9 #57 | 57 3 6 *9 5678 *567 | -1457 *3 *2 | 14578 14 *58 Finned Squirmbag with 5 in R35679C13569 + fin R8C6 -> R7C4 <> 5 -> R9C4 <> 5

The argument for the big finned fish is: all occurrences of digit 5 in columns 13569 are in rows 35679, with the possible exception of a 5 at (8,6). If (7,4)5 or (9,4)5 then we lose the possible exception and a row, contradiction.
But the statement that all occurrences of digit 5 in columns 13569 are in rows 35679 is precisely equivalent to the statement that all occurrences of digit 5 in rows 1248 are in columns 2478, of course with precisely the same possible exception of 5 at (8,6). If (7,4)5 or (9,4)5 then we lose the possible exception and a column, contradiction.
This argument is general - go from sets of rows and columns to the complementary sets.

by **tarek** » Mon Mar 13, 2006 5:42 pm

aeb,

what you're saying is true only when there are more than one candidate per line......

if there exists a big fish of certain candidates in a set of lines.......
iif the the rest of the lines have a line whre the candidate has been uncovered.........

The reduction will not be possible...

tarek

by **aeb** » Mon Mar 13, 2006 5:48 pm

tarek wrote:aeb,

what you're saying is true only when there are more than one candidate per line......

if there exists a big fish of certain candidates in a set of lines.......
iif the the rest of the lines have a line whre the candidate has been uncovered.........

The reduction will not be possible...

tarek

Hmm. I am not sure I can interpret what you are saying.
Gaining information does never harm.
Also, in the example above there is a line with only one candidate. There is nothing special about that. Since the argument holds, it holds whatever the situation.

by **ravel** » Mon Mar 13, 2006 5:49 pm

If you have a line with a fixed candidate, it gives an N-1 fish.

by **aeb** » Mon Mar 13, 2006 6:01 pm

ravel wrote:If you have a line with a fixed candidate, it gives an N-1 fish.

Yes. Every N-fish is equivalent to an (9-N)-fish. This holds both in the finned and non-finned case. Every N-fish with a fixed candidate is also an (N-1)-fish. Also this holds both in the finned and non-finned case. It follows that there is never the need to search for N-fish with N > 4.

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