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[storm_norm]

this isn't a thread about a new technique, or some breakthrough in logic. instead its an interesting way to exploit an easily found UR or almost UR. as seen before in the daily puzzles, these strong inferences derived from URs can provide bombs needed to shrink a puzzle to a more manageable form.

[storm_norm]

I just noticed another way to view the AUR. if three isn't in r8c6, then the {7,9}UR creates a naked pair on {1,6} inside box 9. the UR creates a psuedocell {1,6} between r89c8. this with the {1,6} in r7c7 would eliminate the 1 in r7c9.

[daj95376]

[storm_norm]

[daj95376]

[ravel]

Yet another way to view the AUR

[Asellus]

Norm,

While your reasoning is fine, I'm not comfortable with this part of your AIC: "-UR(79)r89c68=". Read left-to-right, it only makes sense to me if this is interpreted to mean that the DP(79) must be false. But a DP must always be false. However, the "nodes" of a bidirectional AIC must be capable of being true or false. That suggests that the right-to-left meaning must be different. And, so it is: read right-to-left, it makes sense as a Type 4 UR that must be true (when (3)r8c6 is false) which in turn means that the hp(79)r89 must be false.

In short, I suspect that a UR does not make sense as a "node" of a bidirectional AIC. Instead, I see URs or other potential DPs as serving as the basis for establishing inferences which are then used in the AIC. This is analogous to the way that, say, an ALS can establish an inference that one exploits. The structure that establishes the inference is notated outside brackets surrounding the induced inference, rather than being shown as a "node".

For instance, one way (and perhaps the clearest) to approach the AIC above is to exploit the strong inference induced by the UR(79) between (3)r8c6 and (7)r7c9, i.e. they cannot both be false since this results in the DP:

UR(79)r89c68[(3)r8c6=(7)r7c9] - (7)r1c9=(7)r1c6 - ALS[(7)r89c6=(3)r8c6]; r8c6=3

Another approach is:

UR(79)[(3)r8c6=(16)r89c8] - ALS[({16})r7c79=(7)r7c9] - (7)r1c9=(7)r1c6 - ALS[(7)r89c6=(3)r8c6]; r8c6=3

This one is trickier to understand due to this part:
(16)r89c8 - ({16})r7c79

"(16)r89c8" means the grouped <1> and <6> in r89c8. A group is true if any member is true and is false if all members are false. "({16})r7c79" means the set of <1> and <6> in r7c79. A set is true if all members are true and is false if any member is false. It should be evident that the weak inference is valid. (In fact, the link is conjugate since a strong inference is also valid.)

In any case, there is more than one way to approach the situation.

[ravel]

I suppose, that the easy it was to spot it, the hard it is to formulate my elimination as an AIC.
In my sloppy notation i would say
r1c6<>79 [i.e. none of them] => r89c6=79 [i.e. a pair] => (UR type 4)r2c8=7 => r1c6=7
==> r1c6=79 [i.e. one of them]

[storm_norm]

[storm_norm]

this is a one stepper.
notice the marked cells below, what happens if the 6 is removed from r4c6?

[Asellus]

Norm,

Go ahead and write the AIC...

You've noticed that the 49 UR induces a strong inference between (6)r4c6 and the group (4)r6c789. (These things cannot both be false or the DP occurs.) I don't believe that the "Almost" part is necessary. It is just a UR implication that does not match one of the numbered types. So:

(6)r4c9 - 49URr46c36[(6)r4c6=(4)r6c789] - (4=5)r4c8 - (5)r1c8=(5-8)r1c1=(8)r3c2 - (8)r4c2=(8-6)r4c9; r4c9<>6

It's a nice use of a UR pattern!

[ravel]

Its a nice way to find it, but after all only a part of the path (without the UR) is needed:

(4=5)r4c8-(5)r1c8=(5-8)r1c1=(8)r3c2-(8=4)r4c2;
r4c369<>4, then r4c3=9, r4c6=6