dailysudoku.com

[tlanglet]

I found today's Vanhegan Fiendish to be much more difficult than the normal puzzles. I was not able to find any VH moves after basics. I did find four xy-wings with extensions of one pincer but was not able to complete the puzzle!

[storm_norm]

[arkietech]

[Asellus]

Norm,

I don't believe that this inference sequence
(8-6)r4c9 = (hp(16)-4)r78c9 = (4)r8c2
is valid. This is obscured by the lack of clear notation for such situations. Understanding the inferences depends upon how you conceive of the 16 pair.

First, it can be considered as a group. I assume this is how you see it since parentheses are generally used for groups. A group is false if all its members are false and true in all other cases. So, the weak inference
(hp(16)-4)r78c9
is not valid with (16) considered as a group since 14 and 46 both result in both sides of the inference being true. Alternately, you can realize that if the group were false, i.e. both <1> and <6> are false, the ALS is starved and there is no valid solution to the puzzle!

Second, it can be considered as a set, which is true if all its members are true and false in all other cases. I rarely see sets used in AICs so I'm not aware of a clear notation convention. I use braces to denote a set:
(hp{16}-4)r78c9
Considered as a set, the weak inference within the ALS is valid. However, the strong inference
(6)r4c9 = (hp{16})r78c9
is not valid. The set {16} is false if the ALS collapses to 46. Thus, both sides of the inference can be false.

As you might tell from this discussion, working with sets as AIC "nodes" can be confusing and requires care, which is probably why it's not much seen. And when getting creative with groups, care must be taken to assure you aren't unintentionally treating a group as a set. Working explicitly with sets in AICs requires carefully working out the possible valid inferences. For instance, an ALS weak inference could be exploited with the following valid structure (given a suitable grid ... the one in this thread does not offer this structure):
... - Group(16)=ALS[Set{16}-4]= ...
This would occur if the group and set shared a house and there were no other instances of <1> or <6> in the house.

For now, just remember: a grouped weak inference within an ALS is not valid.

[arkietech]

[storm_norm]

hmm, ok, so maybe writing out all the inferences?

[Steve R]

In traditional style the implication snippet would be:

r4c9 ≠ 6 => r78c9 = (16) => r8c2 = 4

This looks OK to me.

Steve

[Asellus]

My bad!

I didn't notice that the <1>s in c9 are conjugate. Thus, Norm really is working with a Hidden Pair and, only coincidentally, with an ALS. I was focused on the ALS. IF those <1>s were not conjugate (i.e. if there were other <1>s in c9) then what I wrote would be correct.

And, yes, I definitely think it is notationally clearer (at least for me ) to write out the strong inference between the <1>s explicitly.

[storm_norm]

[Asellus]

Norm,

Your UR elimination could be even more concise:

UR48[(8)r1c6 = (8)r12c8]; r6c8 <> 8