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Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Asellus posted a spot-the-Sue de Coq grid a month or two ago - no takers, certainly not from me, for despite knowing that it was there I couldn't see it. And I've long since given up looking for them. But I think I've found one, quite accidentally. Grateful if somebody who knows these thing would tell me if this is true or false gold.

M5227263 (38)

Asellus · Posted: Fri Feb 22, 2008 10:57 pm Post subject:

Victor,

Yes, that is Sue de Coq. The 4 cells r5c578 and r6c8 contain the 4 digits {3579} and do so as two locked sets that overlap in the intersection of their two houses: a {39} locked pair in r5 and a {57} locked pair in b6 with the overlap in r5c78. So, <3> and <9> can be removed from all other cells in r5, as you note. Also, <5> and <7> could be removed from all other cells in b6 (if there were any to remove).

I see the logic this way: If r5c5 is <3>, r5c78|r8c8 become a {579} locked set. Alternately, if r5c5 is <9>, r5c78|r8c8 become a {357} locked set. Either way, there cannot be any other <5>s or <7>s in b6. A similar argument works using the {57} in r8c8 to create two alternate locked sets in r5c578 that eliminate <3>s and <9>s from the other cells of r5.

A Sue de Coq isn't limited to just 2 overlapping locked sets. There can be 3 and maybe more. And, the locked sets can be larger than locked pairs. There can also be one (or more?) conjugate linked digits embedded in the overlap cells, just to keep things interesting. In all such cases, the logic remains the same.

Some might see this as Aligned Pairs Exclusion (APE). It can probably be seen that way. Simple cases of Sue de Coq are akin to APE.

By the way... I couldn't find a Kite on <9>. However, there is an ER in b2 and c9 that eliminates <9> from r4c5. Perhaps that is what you meant. (It can also be seen as a Finned X Wing in c69.)

I can't see an ALS solution in b1 and c1 where one of the ALSs is a bivalue. However, there is an ALS present there that is useful. ALS1 is {379} in b1: r1c1|r2c3. ALS2 is {239} in r78c1. The shared exclusive is <3>. The shared common is <9>. The <9> in r3c1 can "see" all of these <9>s and so is eliminated.

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

ER / kite. We're both right. It's an ER based on c9, with the ER itself being b2. It's also a kite using the same numbers: strong links in b2 & c9 with weak link in r1, producing the same elimination. Come to that, mentally assigning 9 to each of those two cells in b2 will instantly produce the same result by common sense (again because of the conjugate 9s in c9).

My ALS. A = c1r189 = {2,3,7,9} + cell r2c3. Shared exclusive 7 instead of your 3, same common 9, same elimination of 9 in r3c1. Amusing myself, I've been pondering how to express ALS as AICs. Using my ALS, and calling the subset of 9s in A by the letter N, in a sort of bastard Eureka: (9=7)r2c3 - (7=N)A.
I.e the 9 in r2c3 & the subset of 9s in my other set A are strongly linked, by what I guess you call a grouped strong link? I mused once as to whether strong links of this sort (not conjugate,i.e either or both, called OR in many trades) exist outside of at the ends of XY-chains etc. (I think any chain that starts and finishes with the same number, and includes even one weak link has the same effect.) Anyway, the 7 in A and N (the 9s in A) are thus linked - ate least one must be true, maybe both. Always the same in ALS I suppose. How would we desribe the link between the two sets of 9 in your ALS. Double grouped strong?

Asellus · Posted: Mon Feb 25, 2008 12:49 am Post subject:

Victor,

As I understand a Kite, it must have a weak link in the box portion and pincers that lie outside the box but are each strongly linked to it. The structure resembles an ER except that the victim is always at the corner or the "rectangle" opposite the "ERI". So, if there were no <9> in r1c1 we would have a Kite and the elimination would occur at r4c9 (diagonally opposite the r1c5 "ERI").

When the box is considered as a strong link (which serves as one pincer)and the elimination occurs in either the row or column shared with the ERI, then it is an ER elimination and not a Kite. That is the case here.

Thanks for clarifying your ALS. It's funny I didn't see it since it's just a alternate way to see the ALS as I saw it.

As for expressing an ALS as an AIC... you're definitely catching on to this stuff! You've almost got it. It is a grouped strong link. However, the link involves a locked set on the other end. Any digit within an ALS is strongly linked to the other digits considered as a locked set. So, in your {2379} ALS we can consider <7> to be strongly linked with the locked set {239}: they cannot both be false. (In fact, they are a conjugate link: they can't both be true, either. So, we could also consider it to be a weak link, if we had some use for that.) In Eureka:
(7={239})r189c1

Depending on how it is being used in a chain, this same ALS can also be considered as (2={379})r189c1 or as (3={279})r189c1 or as (9={237})r189c1.

The other key thing to see is that the victim is weakly linked to the locked set: they can't both be true. The {239} locked set can be weakly linked to <2>s, <3>s, or <9>s. Here we are interested in <9>s.

So, we are ready for the Eureka notated AIC:

(9)r3c1-({239}=7)r189c1-(7=9)r2c3-(9)r3c1; r3c1<>9

We could also write it as:

(9)r3c1-(9={237})r189c1-(7=9)r2c3-(9)r3c1; r3c1<>9

Seen this way, the "shared exclusive <7>" is slightly less explicit. But, the concept is the same: the bivalue <7> is weakly linked with the {237} locked set rather than with just the <7> digit in the first ALS.

Now, for my ALS:

(9)r3c1-({29}=3)r78c1-(3={79})r1c1|r2c3-(9)r3c1; r3c1<>9
or
(9)r3c1-(9={23})r78c1-({37}=9)r1c1|r2c3-(9)r3c1; r3c1<>9

(There are two more possible ways to write it: the central weak link can have a digit <3> on one side against a locked set on the other. The first way shown above, with two digit <3>s weakly linked, probably comports best with ones "mental image" of the ALS technique. But, all of the notation options are valid.)

I hope that makes it clear. Once you see how an ALS works in an AIC, you can use them however you like in chains of any length and with various sorts of "nodes".

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

ER/kite. Somewhat counting-angels-on-a-pin stuff - I'm sure neither of us nor anyone else cares much about these names. But you have contradicted what you & Ravel said in a previous thread when I asked just this question, what one called this kind of 3-link single digit chain with one of the strong links in a box. Have a look towards the end of this thread, in which Ravel remarks that this construct is usually called a kite, and you seem to agree:
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2356&highlight=kite&sid=ea4689547306ed0f02356f01eb27c5d6
Yep, sure it's an ER, but it is also a close sibling of a 'real' kite. (Never thought it before, but I guess you can always see this construct as either ER or pseudo-kite.)

ALS. Thanks for the lesson - yep, I get that. Don't see what's wrong, though, with saying that, in each set, the shared exclusive(s) and the shared common(s) are strongly linked - can't both be false (else the set would have a candidate too few). That together with the weak link between sets in the shared exclusive gives a strong-weak-strong chain, with the usual result that the 'things' at the end are strongly linked, eliminating any other of the numbers in the 'things' that they can both see. The 'things' are the two (sub)sets of the shared common digit.
Taking your ALS, and naming the two sets A & B:
9s in A = 3s in A - 3s in B = 9s in B.
(To put it another way, I don't see the need necessarily to consider the conjugate - treated as strong here -link between the shared exclusives & and the rest of the set, rather than the strong link between the shared exclusives & the shared commons.) Also somewhat angels-on-a-pin stuff!

Asellus · Posted: Mon Feb 25, 2008 9:14 pm Post subject:

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

ERs. Guess you feel strongly about this, which I don't - thus wise to drop it. Hope this little thread has afforded gentle amusement to anyone reading it.

ALS etc. Couldn't agree more about using standard terminology - essential for pros like you. An amateur like me won't be expressing ALS in 'proper' Eureka - for my own amusement only. INteresting idea about using linked sets of numbers in a bigger chain. I suspect (not sure) that, when you've done an ALS elimination, the power of the pattern is gone. But is there any mileage in considering linked sets where there hasn't been an elimination, like a flighless XY-wing? ALS where you've got a shared exclusive & shared common but the commons don't see any other candidates that can be eliminated are 2-a-penny (2-a-cent in the US of A?).

Asellus · Posted: Tue Feb 26, 2008 4:04 pm Post subject: