ultimate fish and nishio

Advanced methods and approaches for solving Sudoku puzzles

Postby ronk » Wed Apr 18, 2007 9:57 am

daj95376 wrote:So, the Broken Wing is the chain

Code: Select all
[r2c2]=[r2c7]-[r3c9]=[r4c9]-[r4c2] => [c2]=invalid

being blocked by at least one Guardian cell.

You got it:)

All that remains is to show that (any of) [r9c34568]=9 results in all of the Guardian cells being eliminated.

Or conversely, find the common eliminations of each guardian being individually true.
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Postby ravel » Wed Apr 18, 2007 10:48 am

You seem to talk about other things, so forgive me, when i am OT, but you still can find RW's pattern here:
Code: Select all
^-----------------------------------^
| *9  /  9  | *9 *9 *9  |  /  9  /  |
|  / *9  9  |  /  /  /  | *9  9  /  |
|  /  /  9  | *9 *9 *9  |  /  9 *9  |
|-----------+-----------+-----------|
|  / *9  9  |  9  9  9  |  /  9 *9  |
| *9  /  9  |  9  9  9  | *9  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|-----------+-----------+-----------|
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|  9  9 -9  | -9 -9 -9  |  9 -9  9  |
^-----------------------------------^
and it is easy to see, that all '-' marked 9's reveal it.
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Postby daj95376 » Wed Apr 18, 2007 4:19 pm

Updating my pattern to include fin cells that restrict eliminations to one cell in [b7] or [b9].
[Addendum: adding details to explain why pattern works.]

Code: Select all
General grid containing NoFish4 as a subset pattern.

^-----------------------------------^
|  9  /  9  |  9  9  9  |  /  9  /  |
|  /  9  9  |  /  /  /  |  9  9  /  |
|  /  /  9  |  9  9  9  |  /  9  9  |
|-----------+-----------+-----------|
|  /  9  9  |  9  9  9  |  /  9  9  |
|  9  /  9  |  9  9  9  |  9  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|-----------+-----------+-----------|
|  #  #  9  |  9  9  9  |  #  9  #  |
|  #  #  9  |  9  9  9  |  #  9  #  |
|  9  9 -9  | -9 -9 -9  |  9 -9  9  |
^-----------------------------------^

Code: Select all
# ignoring fin cells
# after common eliminations in [r9] from (one of) [r9c34568]=9
^-----------------------------------^
|  9  /  9  |  9  9  9  |  /  9  /  |
|  /  9  9  |  /  /  /  |  9  9  /  |
|  /  /  9  |  9  9  9  |  /  9  9  |
|-----------+-----------+-----------|
|  /  9  9  |  9  9  9  |  /  9  9  |
|  9  /  9  |  9  9  9  |  9  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|-----------+-----------+-----------|
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  / -9  | -9 -9 -9  |  / -9  /  |
^-----------------------------------^

Code: Select all
# after Locked Candidate (1) in (each of) [b79]
^-----------------------------------^
|  9  /  /  |  9  9  9  |  /  /  /  |
|  /  9  /  |  /  /  /  |  9  /  /  |
|  /  /  /  |  9  9  9  |  /  /  9  |
|-----------+-----------+-----------|
|  /  9  /  |  9  9  9  |  /  /  9  |
|  9  /  /  |  9  9  9  |  9  /  /  |
|  /  /  /  |  9  9  9  |  /  /  /  |
|-----------+-----------+-----------|
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  / -9  | -9 -9 -9  |  / -9  /  |
^-----------------------------------^

Code: Select all
# after Locked Candidate (2) in [r6]
^-----------------------------------^
|  9  /  /  |  9  9  9  |  /  /  /  |
|  /  9  /  |  /  /  /  |  9  /  /  |
|  /  /  /  |  9  9  9  |  /  /  9  |
|-----------+-----------+-----------|
|  /  9  /  |  /  /  /  |  /  /  9  |
|  9  /  /  |  /  /  /  |  9  /  /  |
|  /  /  /  |  9  9  9  |  /  /  /  |
|-----------+-----------+-----------|
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  / -9  | -9 -9 -9  |  / -9  /  |
^-----------------------------------^

Code: Select all
# after Colors => [r15c1]=Green + [r24c2]=Blue => invalid sub-grid => [r9c34568]<>9
^-----------------------------------^
|  G  /  /  |  9  9  9  |  /  /  /  |
|  /  B  /  |  /  /  /  |  G  /  /  |
|  /  /  /  |  9  9  9  |  /  /  B  |
|-----------+-----------+-----------|
|  /  B  /  |  /  /  /  |  /  /  G  |
|  G  /  /  |  /  /  /  |  B  /  /  |
|  /  /  /  |  9  9  9  |  /  /  /  |
|-----------+-----------+-----------|
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  /  9  |  9  9  9  |  /  9  /  |
|  /  / -9  | -9 -9 -9  |  / -9  /  |
^-----------------------------------^
Last edited by daj95376 on Wed Apr 18, 2007 7:57 pm, edited 2 times in total.
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Postby daj95376 » Wed Apr 18, 2007 4:29 pm

RW wrote:After some thinking I'm sure the SoT will never provide any more eliminations than the broken wing. And as your example in NoFish 4 shows, SoT leads to fewer eliminations than the broken wing pattern that only needs a small part of the SoT cells (your SoT needs 14 pattern cells and 8 guardian cells and leads to one elimination, broken wing needs 5 pattern cells and 4 guardian cells to give two eliminations...).

And I guess both SoT and Broken Wing miss [r9c5]<>9 in NoFish4.
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Postby DanG » Wed Apr 18, 2007 7:19 pm

daj95376 wrote:And I guess both SoT and Broken Wing miss [r9c5]<>9 in NoFish4.

Please explain [r9c5]<>9.

To RW:
The Bicorporate Turbot (sharing same sloper) reveals all the Guardians except the CEC. That's why CEC can be cleared. And that's why the two methods are equivalent. But School of Perfect Turbots (SoPT) doesn't care about guardians, it just clears them all!

I will be using SoPT from now on because it makes a difference.
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Postby RW » Wed Apr 18, 2007 9:51 pm

daj95367 wrote:And I guess both SoT and Broken Wing miss [r9c5]<>9 in NoFish4.

No, the broken wing takes care of that elimination also. I didn't pay attention to that cell as it wasn't mentioned earlier in the thread.

But School of Perfect Turbots (SoPT) doesn't care about guardians, it just clears them all!

What you are saying essentially means that all cells but the cells in the School of Perfect Turbots are guardians.

RW
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Postby daj95376 » Wed Apr 18, 2007 11:17 pm

DanG wrote:
daj95376 wrote:And I guess both SoT and Broken Wing miss [r9c5]<>9 in NoFish4.

Please explain [r9c5]<>9.

RW made a comment about SoT and Broken Wing for eliminations [r9c3]<>9 and [r9c8]<>9; but, other than my pattern, I don't recall there being any mention of the elimination [r9c5]<>9 in NoFish4. So, I added onto RW's comment that the elimination [r9c5]<>9 seems to have been ovelooked by both techniques.
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Postby daj95376 » Thu Apr 19, 2007 12:19 am

RW wrote:After a second look, none of the examples in this thread are any different from Rod Hagglunds broken wing with loops of five strong links and guardian cells.

Okay, all of these examples can be explained by Broken Wings. To me, the question naturally pops up ...

Q: Are there any Broken Wing examples that can't be explained by DanG's method?
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Postby ronk » Thu Apr 19, 2007 3:31 am

daj95376 wrote:Are there any Broken Wing examples that can't be explained by DanG's method?

It only takes one invalid turbot fish -- one chain of an odd number of conjugate links -- to yield the exclusion. So I don't see a purpose in proving whether or not such fish occur in multiples.
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Postby DanG » Thu Apr 19, 2007 3:59 am

daj95376 wrote:Q: Are there any Broken Wing examples that can't be explained by DanG's method?

I thought I already answer that here and again here.
No difference, same elimination. I just thought it is easier to use it. Alter all it is a matter of preference.
There is nothing else for me to be said on this thread.

Thank you all.
Dan
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Postby ronk » Sun Jul 06, 2008 11:03 am

DanG, have you ever illustrated the location of the "guardians" for your SoPT:?:
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Postby DanG » Sun Jul 06, 2008 8:25 pm

ronk wrote:DanG, have you ever illustrated the location of the "guardians" for your SoPT:?:

Hi Ronk,
I think I did here, however incomplete might be..:D
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