Thanks, daj!
My understanding of fish has just made a quantum leap! But I'm not sure if "quantum" means large or really tiny!
I'll find out soon enough when I next tackle that Nx(N+k) fin-elimination technique!
ronk wrote:... the only candidate of the base set in c3 is the endo-fin. Therefore c3 must be a fin sector (unit), and there is no benefit in looking at it as a cover sector.
Obi-Wahn wrote:A sector can be any row, column or box. Please note that this rule doesn't require there to be an equal number of base and cover sectors. This way you can handle Finned Fish pretty much the same way you handle Finless Fish. You just cover the fin cells with additonal cover sectors. However the requirement for an exclusion candidate is getting higher in this case.
Now, to decide which candidates can be excluded, we need to know how many excess cover sectors we have. I'll call this the number of fin sectors.
Number of fin sectors = Number of cover sectors - Number of base sectors
r67b79\r9c358 + b4 -or-
r67b79\r9c58b4 + c3
r67b79\r9c358b4
r67b79\r9c3358b4
daj95376 wrote:above, ronk (Jan.15) wrote:For this fish ...
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---------+----------+----------
9 . -9 | 9 . . | . 9 .
9 . . | 9 . . | 9 9 .
*9 . . | . *9 . | . *9 .
---------+----------+----------
. . @9 | . *9 . | . . .
. . . | 9 9 . | . *9 .
*9 . . | . . . | *9 . .
sashimi mutant jellyfish r67b79\r9c58b4 + c3 (due to endo-fin r7c3)
... the only candidate of the base set in c3 is the endo-fin.
Therefore c3 must be a fin sector,
and there is no benefit in looking at it as a cover sector.
When you follow Obi-Wahn's Arithmetic,
you may be forced to add a cover sector more than once.
Obi-Wahn doesn't seem to care as long as the Arithmetic works out.
Nitpicking aside: Your approach works and I don't have any real problem with your saying fin sector when referring to a cover sector that contains a fin cell and the elimination cell.
Pat wrote:...Obi-Wahn's creatures ( creatures which i prefer not to call fish ).
+-----------------------------------+
| / 7 / | / 7 / | / / / |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | / 7 / | . . . |
| . . . | / 7 / | . . . |
| . -7 . | 7 7 7 | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------------------+
daj95376 wrote:ronk wrote:... the only candidate of the base set in c3 is the endo-fin. Therefore c3 must be a fin sector (unit), and there is no benefit in looking at it as a cover sector.Obi-Wahn wrote:You just cover the fin cells with additonal cover sectors.
[...]
Number of fin sectors = Number of cover sectors - Number of base sectors
It seems to me that Obi-Wahn uses the phrase cover sectors all the way up until he wants to give a name to the count for excess cover sectors. He never specifies any sectors as being fin sectors. It wasn't until later that some cover sectors started being called fin sectors.
daj95376 wrote:One final thought on my part. What's to prevent you from saying ...
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r67b79\r9c358 + b4 -or-
-or-
r67b79\r9c58b4 + c3
You now have two fish that are equivalent and identical.
Sudtyro wrote:
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+-----------------------------------+
| / 7 / | / 7 / | / / / |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | / 7 / | . . . |
| . . . | / 7 / | . . . |
| . -7 . | 7 7 7 | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------------------+
Ron Moore pointed out in another forum that the traditional ER pattern shown above can also be treated as a general finned fish using Obi-Wahn's technique.
r1b5\r6c25 illustrates that r6c2 lies in two intersecting houses of the cover set, but not the base set, which implies r6c2 <> 7.
I would certainly have difficulty interpreting that grid as some sort of finned 2-Fish.
daj95376 wrote:I don't fully understand what you're doing, but I know that the results work and that's sufficient for me to accept but not be able to properly discuss as a comparison between your results and mine.
daj95376 wrote:All of the fish are finned/sashimi. Those with A/B are more complex than those with f. Most are mutant. Those with F are Franken.
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4-Fish r67b79\r9c358 A 202\130 <> 9 [r4c3]
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
---------+----------+----------
9 . -9 | 9 . . | . 9 .
9 . . | 9 . . | 9 9 .
*9 . . | . *9 . | . *9 .
---------+----------+----------
. . @9 | . *9 . | . . .
. . . | 9 9 . | . *9 .
*9 . . | . . . | *9 . .
4-Fish r67b79\r9c358 + b4
ronk wrote:Consider your fish ...daj95376 wrote:All of the fish are finned/sashimi. Those with A/B are more complex than those with f. Most are mutant. Those with F are Franken.
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4-Fish r67b79\r9c358 A 202\130 <> 9 [r4c3]
... and this illustration for it.
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. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
---------+----------+----------
9 . -9 | 9 . . | . 9 .
9 . . | 9 . . | 9 9 .
*9 . . | . *9 . | . *9 .
---------+----------+----------
. . @9 | . *9 . | . . .
. . . | 9 9 . | . *9 .
*9 . . | . . . | *9 . .
As you say, the fish is sashimi 4-fish meaning there are four base sectors and five cover sectors -- in Obi-Wahn's sense of the term. Your notation lists four of these cover sectors implying that the missing sector b4 is the "fin sector", IOW ...
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4-Fish r67b79\r9c358 + b4
When you unfin the fish -- removing the r7c3 candidate from the illustration and removing the sector to the right of the '+' in the notation -- how is base candidate r6c1 covered
r67b79\r9c358 + c3b4
daj95376 wrote:Obi-Wahn wrote:Number of fin sectors = Number of cover sectors - Number of base sectors
daj95376 wrote:As I indicated earlier, Obi-Wahn's Arithmetic would add two cover sectors to my NxN Fish -- [b4] and [c3] once more.
ronk wrote:daj95376 wrote:Obi-Wahn wrote:Number of fin sectors = Number of cover sectors - Number of base sectors
If there is an identifiable quantity of fin sectors, it follows that there must be identifiable fin sectors. Obi-Wahn just avoided the issue of identifying them.
Number of excess sectors = Number of cover sectors - Number of base sectors
ronk wrote:daj95376 wrote:As I indicated earlier, Obi-Wahn's Arithmetic would add two cover sectors to my NxN Fish -- [b4] and [c3] once more.
Then your fish looks to me like an Nx(N-1) fish with two "added cover sectors" (fin sectors) -- because c3 shouldn't even be in the initial cover set [edit: since the endo-fin is the only base candidate in c3].
ronk wrote:Obi-Wahn's "Arithmetic of Fish" is a mathematical model for identifying fish. That is not the same as the definition of fish. Moreover, Obi-Wahn didn't provide an example with an endo-fin, so we don't know how he handled them.