## ultimate fish and nishio

Advanced methods and approaches for solving Sudoku puzzles
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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.
ravel

Posts: 998
Joined: 21 February 2006

Updating my pattern to include fin cells that restrict eliminations to one cell in [b7] or [b9].

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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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

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.
DanG

Posts: 20
Joined: 28 March 2007

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
RW
2010 Supporter

Posts: 1010
Joined: 16 March 2006

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

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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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

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
DanG

Posts: 20
Joined: 28 March 2007

DanG, have you ever illustrated the location of the "guardians" for your SoPT
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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..
DanG

Posts: 20
Joined: 28 March 2007

Previous