The New Sudoku Players' Forum

[daj95376]

Swordfish r348/c567 w/remote cell [r8c9]

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(2) [r8c9]-[r7c7]
          -[r6c9]=[r45c7]-[r3c7]=[r3c56]-([r1c6],[r2c5])

 2  .  . |  .  . -2 |  .  2  2
 2  .  . |  2 -2  . |  .  .  2
 .  .  . |  . *2 *2 | *2  .  .
---------+----------+----------
 .  .  . |  .  . *2 | *2  .  .
 .  .  2 |  2  .  . |  2  .  .
 .  .  2 |  2  .  . |  .  .  2
---------+----------+----------
 .  .  . |  2  .  . | -2  2  .
 .  .  . |  . *2 *2 | *2  . #2
 .  .  . |  .  .  . |  .  .  .


Note: Remote cell chains should only be read from left-to-right!

[ronk]

If I may. There's a squirmbag eliminating r2c5.

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*2  .  . | .  .  2 | . *2  2
#2  .  . | 2 -2  . | .  .  2
 .  .  . | . *2 *2 |*2  .  .
---------+---------+---------
 .  .  . | .  . *2 |*2  .  .
 .  .  2 | 2  .  . | 2  .  .
 .  .  2 | 2  .  . | .  .  2
---------+---------+---------
 .  .  . | 2  .  . | 2 *2  .
 .  .  . | . *2 *2 |*2  . *2
 .  .  . | .  .  . | .  .  .

Sashimi Mutant Squirmbag r348c18/r1c567b9 with fin r2c1


I prefer your (N+1)-fish with a local fin over my N-fish with a remote fin, but I just didn't see it. A minor improvement would be to use b1 instead of c1 in the base sector. Then the squirmbag (with b1) requires no more empty cells than already used by the jellyfish (without b1).

I just realized that this is a very cool example. When you look at the way my solver sees it, the output is r348c18/r12c567b9 yielding all three possible exclusions. Now you can take any one of the six cover sectors as the fin sector getting two different finned squirmbags for each of the three exclusions.

The concept of a fin is starting to look less and less useful to me. As you explained on the Programmers' Forum, if all the candidates of a set of N base sectors are covered by N+1 cover sectors, then any candidate of the cover set that is not a candidate of the base set may be excluded, if that candidate is in the intersection of two or more cover sectors.

For the r12c567b9 cover of this example, the cells in the intersection of cover sectors are the six cells r12c567 and the three cells r789c7. Only r8c7 is a member of the base set, so exclusions at the other eight cells are valid.

[Pat]

about equivalent fishes

take our diagram 4C for example:
Mutant Jellyfish r58c58\r2c2b68

an equivalent Franken Whale:
r1358b59\c24679b1

interesting -- let's look at this example in the opposite direction -- we have a Franken 6th-order -- is there a smaller equivalent Franken ??

all we seem to have is a smaller equivalent (Jellyfish) which is not Franken but Mutant --

("smaller" -- actually meaning: lower-order)

[Obi-Wahn]

we have a Franken 6th-order -- is there a smaller equivalent Franken ??

If I'm not mistaken then there is only one way to get an equivalent Franken Fish with no columns in the base set and no rows in the cover set.
The only other equivalent Franken Fish would then be c1358b59\r24679b1 which is of the same order.

I prefer your (N+1)-fish with a local fin over my N-fish with a remote fin, but I just didn't see it.

Actually you could have calculated it. I'll show in a seperate Topic how.

[tarek]

The concept of a fin is starting to look less and less useful to me. As you explained on the Programmers' Forum, if all the candidates of a set of N base sectors are covered by N+1 cover sectors, then any candidate of the cover set that is not a candidate of the base set may be excluded, if that candidate is in the intersection of two or more cover sectors.

Are you signalling the end of finned fish

It was all going fine until that Exo fin showed up

tarek

[ronk]

Are you signalling the end of finned fish

Oh no! I merely think finned fish may be a stepping stone -- likely a required stepping stone -- to something else, maybe something better.

It was all going fine until that Exo fin showed up

It's still all going fine IMO. We just needed some way to distinguish between two types of fin cells.

[edit3: The "old" fin cell is a member of the base set but not a member of the cover set. It is outside the cover set, and hence was labeled "exo-fin" or "exo-fin-cell."] daj95376 had been using [edit: exo-fin to mean remote fin but has relinquished his usage].

The "new" fin cell is a candidate in the intersection of two base sectors, "inside" the intersection if you will, and hence was labeled "endo-fin."

Each type of fin may be seen directly by an exclusion cell, in which case it is a "local" fin. If seen by way of a chain, then it is a "remote" fin.

Carrying things to an extreme, we have

• local exo-fin
• local endo-fin
• remote exo-fin
• remote endo-fin

But I'm not suggesting all these long-winded terms need be used. Just like we omit "basic" in "basic swordfish", we can omit the prefixes "local" and "exo-."

[Pat]

We just needed some way to distinguish between two types of fin cells


The "old" fin cell is a member of the cover set but not a member of the base set. It is outside the base set, and hence was labeled "exo-fin" or "exo-fin-cell."

The "new" fin cell is a candidate in the intersection of two base sectors, "inside" the intersection if you will, and hence was labeled "endo-fin."

the old, familiar type of fin-cell is in base\cover
i.e. in "base" and not in "cover" -- reverse of your phrasing

the new type of fin-cell is in the overlap between units of "base"

both conditions may be true for the same fin-cell,
what would you call this type ?

[ronk]

the old, familiar type of fin-cell is in base\cover
i.e. in "base" and not in "cover" -- reverse of your phrasing

Thanks, it's corrected. Thought it sounded weird while writing it, but didn't go back and check.

the new type of fin-cell is in the overlap between units of "base"

both conditions may be true for the same fin-cell,
what would you call this type ?

If an endo-fin can't be covered, it would still be an endo-fin to me. I see no benefit in even saying it's both.

[ronk]

Even more interesting, here's one with two fins:

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#02: Mutant Squirmbag (r15,c24,b9): r1c1568|r5c58|r2379c2|r278c4|r7c789|r89c8 => r9c5<>5
Cover=r7,c58,b12, fins=r9c2,r8c4
+---------------------+-------------------+-------------------+
|   159*     7    14  |   6   1259*  459* |    3  1258*   28  |
|     8  13459*  134  | 157* 12379  2459  | 1457  1257     6  |
|     6   1345*    2  |   8    137   345  | 1457     9   145  |
+---------------------+-------------------+-------------------+
|   129     19     5  |   3      6     7  |  148   128  1248  |
|   237     23     8  |   4     25*    1  |   67  2567*    9  |
|     4      6    17  |   9      8    25  |  157     3   125  |
+---------------------+-------------------+-------------------+
| 12357    125*    9  | 157*     4    36  | 1568* 1568*  158* |
|   135      8  1346  |  15#    39   369  |    2  1456*    7  |
|   157    145#  167  |   2   17-5     8  |    9  1456*    3  |
+---------------------+-------------------+-------------------+

As a result of a question by daj95376, I now see that using an endo-fin-cell results in a smaller fish with a single fin instead of two.

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   159*     7    14  |   6   1259*  459* |    3  1258*   28
     8  13459   134  | 157* 12379  2459  | 1457  1257     6
     6   1345     2  |   8    137   345  | 1457     9   145
---------------------+-------------------+------------------
   129     19     5  |   3      6     7  |  148   128  1248
   237     23     8  |   4     25*    1  |   67  2567*    9
     4      6    17  |   9      8    25  |  157     3   125
---------------------+-------------------+------------------
 12357    125     9  | 157#     4    36  | 1568  1568   158
   135*     8  1346  |  15@    39   369  |    2  1456*    7
   157    145   167  |   2   17-5     8  |    9  1456     3

 sashimi mutant jellyfish r158c4\c158b2 plus fin r78c4, implies r9c5<>5

Note that r7c4 is an exo-fin-cell ('#') and r8c4 is an endo-fin-cell ('@') ... but the two fin cells together form a single fin.

As recently defined here:

endo-fin-cell <==> A cell with a candidate inside the intersection of two base sectors (units)
exo-fin-cell <==> A cell with a candidate in the base sector but outside the cover sectors

[daj95376]

I'd like to use the finned X-Wing below as a specific example of a recent observation.

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..9....5.4.75....652...91.79...4.5......1......1.5...41.83...657....59.8.9....3.. #F001

    b5  -  3     Locked Candidate (1)
r4c23   <> 3     Sashimi X-Wing c19/r1(456)

# finned X-Wing r27/c67 w/fin [r2c5]
 *---------------------------------*
 |  .  .  .  | -2  2 -2 |  .  .  2 |
 |  .  .  .  |  . #2 *2 | *2  .  . |
 |  .  2  .  |  .  .  . |  .  .  . |
 |-----------+----------+----------|
 |  .  .  2  |  2  .  2 |  .  2  2 |
 |  2  .  .  |  2  .  2 |  2  2  . |
 |  2  .  .  |  .  .  2 |  2  2  . |
 |-----------+----------+----------|
 |  .  .  .  |  .  . *2 | *2  .  . |
 |  .  .  2  |  .  2  . |  .  .  . |
 |  2  .  .  |  2  2  . |  .  2  2 |
 *---------------------------------*


It's very easy to see the elimination [r1c6]<>2 because it follows directly from the finned X-Wing. What bothered me was the elimination [r1c4]<>2 that exists as well. This is not the first time that I've encountered this general scenario ... just the first time that I can explain the second elimination without resorting to another fish. Specifically,

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1 ) X-Wing   => [r2c6]=2 or [r7c6]=2
1a) [r2c6]=2 =>                            [r1c46]<>2
1b) [r7c6]=2 => [r89c5]<>2 => [r12c5]=2 => [r1c46]<>2

2 ) [r2c5]=2 =>                            [r1c46]<>2


Note: In general, the X-Wing r27/c67 will explain both eliminations as long as [r123c5]=2 and [r456c5]<>2 are true.

Is this of interest to anyone? Search for a fish to explain [r1c4]<>2 before answering this question.

[ronk]

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# finned X-Wing r27/c67 w/fin [r2c5]
 *---------------------------------*
 |  .  .  .  | -2  2 -2 |  .  .  2 |
 |  .  .  .  |  . #2 *2 | *2  .  . |
 |  .  2  .  |  .  .  . |  .  .  . |
 |-----------+----------+----------|
 |  .  .  2  |  2  .  2 |  .  2  2 |
 |  2  .  .  |  2  .  2 |  2  2  . |
 |  2  .  .  |  .  .  2 |  2  2  . |
 |-----------+----------+----------|
 |  .  .  .  |  .  . *2 | *2  .  . |
 |  .  .  2  |  .  2  . |  .  .  . |
 |  2  .  .  |  2  2  . |  .  2  2 |
 *---------------------------------*


(...)

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1 ) X-Wing   => [r2c6]=2 or [r7c6]=2
1a) [r2c6]=2 =>                            [r1c46]<>2
1b) [r7c6]=2 => [r89c5]<>2 => [r12c5]=2 => [r1c46]<>2

2 ) [r2c5]=2 =>                            [r1c46]<>2


Is this of interest to anyone? Search for a fish to explain [r1c4]<>2 before answering this question.

That's an excellent example of an endo-finned mutant swordfish.

Here's a permuted version of exemplar Fig 3B2, permuted to fit your puzzle.

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 .  .  . |  *  X  * |  *  .  .
 /  /  / |  X  /  X |  X  /  /
 .  .  . |  *  X  * |  *  .  .
---------+----------+----------
 .  .  . |  .  /  . |  *  .  .
 .  .  . |  .  /  . |  *  .  .
 .  .  . |  .  /  . |  *  .  .
---------+----------+----------
 /  /  / |  X  /  X |  X  /  /
 .  .  . |  *  X  * |  *  .  .
 .  .  . |  *  X  * |  *  .  .

 mutant swordfish r27c5\c7b28

The '*' exclusions shown are valid when there are no fins, that is, when all the '/' empty cells are indeed empty. In your digit 2 grid however, the cell in the intersection of r2 and c5 -- an endo-fin-cell -- is not empty. Now ask yourself, which of the exclusion cells see the endo-fin?

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 .  .  . | **  X ** |  *  .  .
 /  /  / |  X  @  X |  X  /  /
 .  .  . | **  X ** |  *  .  .
---------+----------+----------
 .  .  . |  .  /  . |  *  .  .
 .  .  . |  .  /  . |  *  .  .
 .  .  . |  .  /  . |  *  .  .
---------+----------+----------
 /  /  / |  X  /  X |  X  /  /
 .  .  . |  *  X  * |  *  .  .
 .  .  . |  *  X  * |  *  .  .

 mutant swordfish r27c5\c7b28 plus endo-fin r2c5

[Pat]

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 .  .  . |  *  X  * |  .  .  .
 /  /  / |  X  #  X |  X  /  /
 .  .  . |  *  X  * |  .  .  .
---------+----------+----------
 .  .  . |  .  /  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .
---------+----------+----------
 /  /  / |  X  /  X |  X  /  /
 .  .  . |  .  X  . |  .  .  .
 .  .  . |  .  X  . |  .  .  .



finned Franken Swordfish rrb\ccc: r27b5\c467
fin = r2c5

-- instead of a fin, Obi-Wahn would add b2 to the "cover" -- r27b5\c467b2

[ronk]

Code: Select all

 .  .  . |  *  X  * |  .  .  .
 /  /  / |  X  #  X |  X  /  /
 .  .  . |  *  X  * |  .  .  .
---------+----------+----------
 .  .  . |  .  /  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .
---------+----------+----------
 /  /  / |  X  /  X |  X  /  /
 .  .  . |  .  X  . |  .  .  .
 .  .  . |  .  X  . |  .  .  .



finned Franken Swordfish rrb\ccc: r27b5\c467
fin = r2c5

Yes, exemplar Fig 3B1 is shown to be equivalent to Fig 3B2, but then the endo-fin "lesson" would have been lost.

BTW your b5 should contain the candidates, not c5. Also I don't think you should present altered quotes as quotes, even nameless ones.

[Pat]

your b5 should contain the candidates, not c5

yes, ronk, sorry, i had the "X" cells incorrectly marked

actually i prefer the diagrams without marking "X" cells at all -- the caption should make things clear!

this is what i should've posted:

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 .  .  . |  *  .  * |  .  .  .
 /  /  / |  .  .  . |  .  /  /
 .  .  . |  *  .  * |  .  .  .
---------+----------+----------
 .  .  . |  .  /  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .
---------+----------+----------
 /  /  / |  .  /  . |  .  /  /
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .



• finned Franken Swordfish rrb\ccc: r27b5\c467, fin = r2c5
• instead of a fin, Obi-Wahn would add b2 to the "cover" -- r27b5\c467b2

mis-quotifying is a regular sin of mine

~ Pat

[StrmCkr]

i found this intresting pattern,
i was wondering if it is some kind of fish pattern or something eles

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 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  x |  x  .  .
 .  .  . |  *  .  # |  .  x  .
---------+----------+----------
 .  .  * |  .  .  . |  #  x  .
 .  .  . |  .  .  . |  .  .  .
 .  x  # |  .  .  . |  *  .  .
---------+----------+----------
 .  x  . |  #  .  * |  .  .  .
 .  .  x |  x  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .


the x's are dirctly linked chains's of the same number (2 per row/box/line)

when the chain resolves in all views the *'s are not true.
while activating either chain in both views, looking at both chains at once:

if the #'s are true the *'s are removed.
if the #'s are false the *'s form a deadly pattern out of the #'s + stars.

and it reduces down to this pattern

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 .  .  . |  .  .  . | .  .  .
 .  .  . |  .  .  x | x  .  .
 .  .  . |  .  .  # | .  x  .
---------+----------+----------
 .  .  . |  .  .  . | #  x  .
 .  .  . |  .  .  . | .  .  .
 .  x  # |  .  .  . | .  .  .
---------+----------+----------
 .  x  . |  #  .  . | .  .  .
 .  .  x |  x  .  . | .  .  .
 .  .  . |  .  .  . | .  .  .