The New Sudoku Players' Forum

[ronk]

So, the Broken Wing is the chain

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[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.

[ravel]

You seem to talk about other things, so forgive me, when i am OT, but you still can find RW's pattern here:

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^-----------------------------------^
| *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.

[daj95376]

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  /  |
^-----------------------------------^


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# 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  /  |
^-----------------------------------^


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# 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  /  |
^-----------------------------------^


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# 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  /  |
^-----------------------------------^


[daj95376]

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.

[DanG]

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.

[RW]

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

[daj95376]

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.

[daj95376]

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?

[ronk]

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.

[DanG]

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

[ronk]

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

[DanG]

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

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