Simple Coloring: A Missed Scenario ?

Everything about Sudoku that doesn't fit in one of the other sections

Postby Sudtyro » Tue Jan 15, 2008 10:24 pm

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!
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Postby daj95376 » Wed Jan 16, 2008 1:05 am

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

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. In hindsight, that appears to be a mistake.

It's only when you follow Obi-Wahn's Arithmetic to the letter that you may be forced to add a cover sector more than once for a fin cell. 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.
Last edited by daj95376 on Tue Jan 15, 2008 9:46 pm, edited 2 times in total.
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Postby daj95376 » Wed Jan 16, 2008 1:37 am

ronk: One final thought on my part. What's to prevent you from saying ...

Code: Select all
r67b79\r9c358  + b4   -or-
r67b79\r9c58b4 + c3

You now have two fish that are equivalent and identical.

Suddenly, the following is starting to look very appealing for your Nx(N+1) Fish.

Code: Select all
r67b79\r9c358b4


Or Obi-Wahn's Nx(N+2) Fish.

Code: Select all
r67b79\r9c3358b4
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re: "fin sector"

Postby Pat » Wed Jan 16, 2008 10:56 am

daj95376 wrote:

above, ronk (Jan.15) wrote:For this fish ...

Code: Select all

---------+----------+----------
 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.



if you follow Obi-Wahn's method,
you've added 1-or-more sectors to the cover,
and cells which would have been fin-cells have ceased being fin-cells.


it seems to me that ronk's sashimi mutant jellyfish r67b79\r9c58b4 + c3 (due to endo-fin r7c3)
is a fish of order 4 with a fin-cell,
and not one of Obi-Wahn's creatures ( creatures which i prefer not to call fish ).
    in my understanding, the term "fin sector" -- as used by ronk -- does not refer to any sector in the cover.
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Re: re: "fin sector"

Postby Sudtyro » Wed Jan 16, 2008 1:42 pm

Pat wrote:...Obi-Wahn's creatures ( creatures which i prefer not to call fish ).


Code: Select all
+-----------------------------------+
|  /  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.
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Postby ronk » Wed Jan 16, 2008 1:49 pm

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.

At the time of Obi-Wahn's post, TUFG had already clearly defined a fish to consist of N base sectors, N cover sectors plus possible fin cells. He didn't do this forum any favor by posting a different definition of "cover sector." However, is anyone else even using his definition?

daj95376 wrote:One final thought on my part. What's to prevent you from saying ...
Code: Select all
r67b79\r9c358  + b4   -or-
   -or-
r67b79\r9c58b4 + c3

You now have two fish that are equivalent and identical.

Generally nothing prevents one from saying that, but in this specific case c3 contains an endo-fin and it must be a fin sector. It must be on the right side of the '+'.
Last edited by ronk on Wed Jan 16, 2008 9:55 am, edited 1 time in total.
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Postby Pat » Wed Jan 16, 2008 1:54 pm

Sudtyro wrote:
Code: Select all
+-----------------------------------+
|  /  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.



it is a finned Franken X-wing
    r1b5\c25 with fin = r6c46
or if you prefer,
a finned Mutant X-wing
    r1b5\r6c5 with fin = r1c2

sorry, i haven't seen Ron Moore's post.
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Postby Sudtyro » Wed Jan 16, 2008 2:11 pm

Pat wrote:it is a finned Franken X-wing ... or a finned Mutant X-wing

Thanks, Pat!
It's now confirmed..."quantum" means really tiny!:(
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Postby daj95376 » Wed Jan 16, 2008 7:40 pm

Well, after doing a Google search on this forum, my worst fears were realized. It turns out that ***I*** was the first person to refer to a fin sector as an actual entity. It occurred from my misinterpretation of Obi-Wahn's post.

My apologies to the forum:!::!::!:

ronk: 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.

Pat: Thanks for helping in the discussion.

tarek: Thanks for taking an interest and presenting your position.

Sudtyro: I hope we haven't scared you away with all of the varying opinions.
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Postby ronk » Thu Jan 17, 2008 12:07 am

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.

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.
Code: Select all
4-Fish r67b79\r9c358            A  202\130  <> 9  [r4c3]

... and this illustration for it.
Code: Select all
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
 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 ...
Code: Select all
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:?:
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Postby daj95376 » Thu Jan 17, 2008 1:47 am

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.
Code: Select all
4-Fish r67b79\r9c358            A  202\130  <> 9  [r4c3]

... and this illustration for it.
Code: Select all
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
 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 ...
Code: Select all
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:?:

My fish is a 4x4 Fish with two fin cells. Fin cell [r6c1] is in one sector of the base set and no sectors in the cover set. It's not complicated to understand. Fin cell [r7c3] is in two sectors of the base set and only one sector of the cover set. It's still a fin cell, but in a more complicates sense -- thus the A designation attached to the fish. If you unfin my fish, then you need to remove both of these cells and there's no need to cover cell [r6c1]!

As I indicated earlier, Obi-Wahn's Arithmetic would add two cover sectors to my NxN Fish -- [b4] and [c3] once more. Cover sector [b4] would cover cell [r6c1] the one time it's needed using Obi-Wahn's arithmetic. The additional cover sector [c3] is needed to make Obi-Wahn's arithmetic work properly.

dajones95376 wrote:Obi-Wahn's Nx(N+2) Fish.

Code: Select all
r67b79\r9c3358b4


The point to remember is that we started with my NxN fish and then added cover sectors to match Obi-Wahn's arithmetic and get his equivalent fish. Thus, my use of the notation ...

Code: Select all
r67b79\r9c358 + c3b4

There aren't any fin sectors in Obi-Wahn's fish. Calling the extra cover sectors fin sectors was my mistake and I think it's caused a lot of problems and confusion. Again, I apologize:!:

I always thought that this is what you were doing -- only with removing the duplicate entry for [c3]. Now, I realize that your fish are not based on Obi-Wahn's arithmetic. However, that leaves me with only an idea on what you're doing to create your fish. It also means that my comments earleir in the thread about your fish are based on an incorrect understanding.
Last edited by daj95376 on Wed Jan 16, 2008 10:32 pm, edited 1 time in total.
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Postby ronk » Thu Jan 17, 2008 2:30 am

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.

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].

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.
Last edited by ronk on Wed Jan 16, 2008 10:54 pm, edited 2 times in total.
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Postby daj95376 » Thu Jan 17, 2008 6:07 am

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.

Okay. Here's my IF. If Obi-Wahn had said ...

Code: Select all
Number of excess sectors = Number of cover sectors - Number of base sectors

... would it then be your argument that 'it follows that there must be identifiable excess sectors'? I say that Obi-Wahn's choice of words has left an ugly mess in its wake. Besides, you failed to include the previous two sentences that explain the statement you quoted.

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].

Sector [c3] is in my NxN Fish because it is used to cover the elimination cell. It is a critical sector and I don't see how you can say that it 'shouldn't even be in the initial cover set'!!!

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.

I won't argue semantics on describing Obi-Wahn's "Arithmetic of Fish".

I will accept your assertion that he never provided an example with an endo-fin. My guess is that he'd simply choose to start with one of the six 4-Fish that don't contain an endo-fin cell. Heck, he may even produce an Nx(N+k) Fish that isn't even based on a valid NxN Fish.

However, as long as you choose to build on fish with endo-fin cells, then others may have a problem interpreting your results.
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