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AIC with Groups

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Grouped nodes were discussed on the Grouped X-Cycles page and it is very relevant to Alternating Inference Chains. Luckily, there’s nothing too scary about them although they may be harder to spot.

Grouped AIC
Grouped AIC : Load Example or : From the Start

The example on the right shows a classic and relatively simple deduction based on a loop that is predominantly candidates 3 and 4. But the two bi-value cells E8 and E9 containing 4/5 and 2/4 allow us to form strong links that continue the number 4 we’re tracing from E2 to F8. We end up with two weak links pointing to B7, where the 1 can be removed, thanks to Nice Loop Rule 3. Our grouped node on [E8|E9] acts just as a normal cell. The solver gives us:

AIC on 1 (Grouped Discontinuous Alternating Nice Loop, length 10):
+1[B7]-3[B7]+3[B2]-3[E2]+4[E2] -4[E8|E9]+4[F8]-1[F8]+1[F7]-1[B7]
- Contradiction: When B7 is set to 1 the chain implies it cannot be 1 - it can be removed

Grouped Cell AIC
Grouped Cell AIC : Load Example or : From the Start
Just a few steps later in this puzzle we get another AIC which shows Rule 2 - two strong links - which allows us to place with certainty 8 on E4.

AIC on 8 (Grouped Discontinuous Alternating Nice Loop, length 10):
-8[E4]+8[A4]-8[A8]+4[A8]-4[E8|F8]
+4[E9]-2[E9]+2[E5]-8[E5]+8[E4]
- Contradiction: When 8 is removed from E4 the chain implies it must be 8 - other candidates 3/5 can be removed

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