The New Sudoku Players' Forum

[tlanglet]

Long ago, Luke present a solution based on an oddagon and I tried to add it to my bag of tricks but over time it fell out through a hole in my bag. However, this post renews my interest.

Thanks Don

Ted

[DonM]

Other names for "Broken Wings" are "Oddagons" and "Impossible Loops".

They derive a strong inference that one of the guardians must be true and so can be notated in much the same way as other deadly patterns.

I would therefore write:

(2)r5c8 =[(2)BW:r69c8,r9c1,r68c3]= (2)r3c8,r9c9 - (2)r1c9 etc.

Note the guardians are considered to be external to the pattern and the strong link between them is justified by identifying the pattern.

Thanks for addressing the notation.

edit: removed initial response.

Now I understand your notation more clearly and it expresses what I intended better than mine (translating the notation broadly): the BW would be true if (2)r5c8 isn't true and (2)r3c8,(2)r9c9 aren't true so if (2)r5c8 isn't true then (2)r1c9 can't be true because it would eliminate (2)r3c8,(2)r9c9 etc.[/i].

Revised notation using David's changes:

(2)r5c8 = [(2)BW:r69c8,r9c1,r68c3] = (2)3c8,r9c9 - (2)r1c9=r9c9-r9c1=(2-6)r8c3=r6c3-r6c5=(6)r5c4 => -2r5c4 stte

[DonM]

Long ago, Luke present a solution based on an oddagon and I tried to add it to my bag of tricks but over time it fell out through a hole in my bag. However, this post renews my interest.

Thanks Don

Ted

Glad to replace the trick in your repaired bag- If I recall, that was an oddagon/BW that Luke presented to the tune of 'Blackbirds singing in the dead of night...'

[David P Bird]

(2)r5c8 =[(2)BW:r69c8,r9c1,r68c3]= (2)3c8,r9c9 - (2)r1c9 etc.

What is highlighted in blue represents a justified strong link. ie =[Some Pattern]= is a single strong link derived from that pattern.
To make my chains reader friendly, I add spaces on either side of links between cells, but here there are no spaces between the square braces and the link symbol which makes them stand out. For those who don't like extra spaces, using a colour or bold type could serve just as well.
In AICs the links must alternate, and when they don't appear to at first glance, the second glance should soon tell the story.

In words: guardian 1 and guardians 2 & 3 can't all be false, because of the deadly pattern threat.

This isn't the only notation option, but whatever way is used will attract critics. The most important thing is picking one that is versatile enough to hand every type of derived inference – which this one does.

[eleven]

Note the guardians are considered to be external to the pattern and the strong link between them is justified by identifying the pattern.

So if you use a turbot fish (skyscraper, kite), be aware, that you destroy an impossible pattern, which might help you per guardians.
(on the other hand of course there are impossible patterns with usefull guardians, where there is no turbot fish elimination)

[daj95376]

[Withdrawn: I made a mistake in supporting a Broken Wing pattern that wasn't based on a single-digit.]

[DonM]

DonM's Broken Wing pattern is interesting ... and not the only one present. Congratulations to DonM for the find!

Thanks Danny. In my experience with more basic usable Broken Wing/oddagon patterns like this, you can often re-arrange cells using the same digits (as in the 2s here) to come up with other BWs, but almost always I find that you end up with the same number of Guardians and much the same final solution.