Hi Don,
DonM wrote:blue wrote:(Almost) any time someone shows a strong link in an AIC (or AIC-like network), one end or another is going to be false in the actual solution. The only thing left to question, is how hard you might need to work, to see which end is actually false. Sometimes, other links in the AIC itself, will show an answer. When you put that kind of thing into XSudo, it will show up as a "cannibal elimination"...
Cheers,
Blue.
At first, I was thinking that: Both ends of an AIC going to be false in most actual solutions? Isn't that what discontinuities are all about? Then I realized that you were likely talking about the information available following the full puzzle solution. But then, understanding that, I was wondering what kind of point you were trying to make. I'm not seeing it. Also, what is a 'cannonball elimination'?
A cannibal elimination, is an elimination for a candidate that occurs in one of the strong links in an AIC or network -- not just any elimination, but one that can be justified using (usually only some of) the strong and weak links that are already present in the AIC/network.
Edit: See
a corrected definition in
this follow on post.
[ For XSudo, its something more, since It doesn't deal with "strong (only)" links. It uses "truth sets" instead, which have both strong and weak attributes. For it, a cannibal elimination is an elimination for a candidate in one of the "truth sets" being used ... usually to justify some other elimination. ]
About the point ...
1. Steve's network included the strong link between the XYWing and 7r4c1. It isn't a typical strong link, of course, but it is a strong link.
2. Since 7r4c1 isn't part of the solution, there's would be an outside shot, at least, that it has an "easy elimination".
3. This is basic stuff of course, but one way to justify a 7r4c1 elimination, would be to follow up on the some of the consequences of it being true, and show that they lead to a conflict/contradiction. If it
really did have an "easy elimination", it wouldn't take much in the way "following up on consequences", before a conflict/contradiction point was reached.
4. Steve's network also included "(7)r4c1 - (7=1)r4c4 - (1=4)r5c5", showing that 1r4c4 and 4r5c5 would need to true (in theory), if 7r4c1 was true. Those are the kind of "implied assignments", he was talking about.
5. Danny showed that those 3 being true at once (and the line of sight eliminations that would follow), would already be leading to some kind of conflict in r6, and he mentioned a couple of possiblities.
6. My main point was that since 7r4c1 wasn't part of the solution, that shouldn't be totally unexpected, for the reasons in (3).
7. The rest of what I mentioned, about XSudo and the possibility of cannibal eliminations showing up, was either "secondary trivia", or the tip of an icberg in a conversation about large chains & nets and "1-step solutions" -vs- more steps with smaller nets, etc.
But you answer what you meant by it above. Thanks.