dailysudoku.com

[Victor]

Menneske 794832.

[re'born]

[ravel]

Suppose, this is the same as Victor's ALS with A {2368} in r4c3, r5c13, B {36} in r4c9, x=3, z=6, r5c79<>6.
I dont know, why Benny chose x and z to denote that and also cannot see a good alternative for this puzzle.

In other words:
r5c79=6 => r4c9=3
r5c79=6 => r5c13=28 => r4c3=3

re'born, i still dont understand the notation, maybe you can explain it with this line.

[Steve R]

In his original paper on ALSs Benny S considered pairs A and B with a restricted common candidate x and also triples A, B, C with restricted common candidates x for (A, B) and y for (A, C). In both cases z was used for the candidate to be eliminated. Custom has followed this in calling the first rule xz and the second xyz. xz is convenient, I think, in that there is no risk of a beginner inferring a connection with an xy-chain.

The traditional way of writing re’born’s chain is

r5c1 ≠ 6 => r6c1 = 6 => r6c1 ≠ 3 => r4c3 = 3 => r4c9 = 6

Steve

[ravel]

Thanks, i saw that here r6c1 was used instead of r4c3 (which was easier to spot for me than the 2 strong links).

But it is still confusing for me, that - reading it from left to right -
(6)r5c1 means r5c1<>6 and (3)r4c3 then means r4c3 = 3.
So i cannot find out, what the symbols stand for.

Is there a good link, where it is explained ?

[Steve R]

I don’t know of a link. Perhaps wrongly, I read these things like nice loops: it’s only an alternative notation after all.

Thus I would see:
(3)r4c3 as meaning r4c3 ≠ 3
- (3)r4c3 as meaning r4c3 ≠ 3
=(3)r4c3 as meaning r4c3 = 3

Steve

[nataraj]

It is an AIC (alternating inference chain).

[ravel]

Thanks nataraj, at the same time i found it by myself

Ah, then maybe i got it. It says a bit more than a nice loop (though the result is the same).

So '=' means strong links either between cells or within a cell and '-' weak links.
Then like in x-chains (and AIC's ?) the 1st, 3rd, ...., last link must be strong (if not left side then right side and vice versa). Then everything left of '=' is equivalent and an either or to everything right of '='.

[nataraj]

[nataraj]

[Victor]

Thanks re'born & others. I do get all that, tho' whether I'll be able to spot what I suppose is a sort of non-specific AIC (i.e. not a named structure) is another story!
And thanks Steve, for the x / z explanation.

[Asellus]

While this thread is a little old, no one wrote out the Eureka notation for the ALS solution described above. (Re'born's chain, while having the same result, is different since it involves r6c1.) Here is how the ALS can be expressed using Eureka:

(6)r5c79-(6={238})r5c13|r4c3-(3=6)r4c9-(6)r5c79; r5c79<>6

The "|" character means "and" and is used to concatenate cells, etc. The {2368} ALS in r5c13|r4c3 (Set "A", above) is considered as a <6> strongly linked with a {238} locked set. The {238} locked set is, in turn, weakly linked to the <3> at r4c9. (The link is conjugate, which is both strong and weak for inference purposes.) So, it can be expressed in ordinary language as:

If r5c7 or r5c9 is <6>, then the r5c13|r4c3 ALS becomes a {238} locked set (since the <6> is false), so r4c9 is not <3> so must be <6>, so r5c7 or r5c9 cannot be <6>. This contradiction means that the initial assumption is false, so r5c79<>6.

The Eureka notation make it apparent that the shared exclusive <3> is weakly linked between the two ALS's and the shared common <6> is strongly linked within the two ALS's to the complementary locked sets.

[storm_norm]

asellus wrote: