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a rather unusual xy-chain

 
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Fri Nov 02, 2007 7:43 pm    Post subject: a rather unusual xy-chain Reply with quote

Trying to solve today's nightmare, I came across this position:
Code:

+--------------------------+--------------------------+--------------------------+
| 27      1       5        | 24      3       47       | 8       9       6        |
| 6       8       4        | 5       9       1        | 2       7       3        |
| 237     37      9        | 8       27      6        | 14*     45#     15       |
+--------------------------+--------------------------+--------------------------+
| 1       5       2        | 7       4       38       | 36      368     9        |
| 78      4       3        | 16      68      9        | 5       2       17       |
| 9       6       78       | 13*     5       2        | 17*     38      4        |
+--------------------------+--------------------------+--------------------------+
| 378     237     1        | 9       68      5        | 3467    346     27       |
| 5       9       6        | 24      27      347      | 37      1       8        |
| 4       237     78       | 36#     1       378      | 9       3-56    25       |
+--------------------------+--------------------------+--------------------------+


Having exhausted my usual arsenal, I tried some Medusa coloring and quickly hit a contradiction which solved the puzzle. That final stroke is delivered by an xy-chain that is unusual in that it does not end in two "pincers" with the same candidate, but with two different candidates at the ends, and it removes BOTH candidates from the cell they both see.

The chain is marked above with # and *: 54-...-36

When read from top to bottom it says: if r3c8<>5 then r9c4=3 and r9c8=6
When read from bottom to top it says: if r9c4<>6 then r3c8=4 and r9c8=5

the first statement removes 5, the second removes 6 from r9c8.

Could someone please enlighten me how this thing is called - it looks rather useful and not too hard to find ... (or is it just that: a Medusa wrap?)

Thanks in advance,
nataraj

edit:
P.S. maybe this is the right moment to ask another question:

Since the puzzle is from the excellent sudocue.net site, it would be only natural to post there. But the forum there seems abandoned ... no posts in months. So I sure hope I don't offend anyone by posting here. There are just so many nice and helpful people here ...
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sat Nov 03, 2007 6:26 am    Post subject: Reply with quote

In my opinion, it's best to see it as a Medusa Wrap. I haven't found any simpler way to "see" it.

I can't follow your chain as you've marked it. I see two different XY Chains, each involving 6 cells, that link R3C8 with R9C4 and give the implications you mention. In any case, your assignment conclusions require use of ALS's and/or strong links in C8 and in R9 that are independent of those chains. The nice thing about Medusa is that it takes all those things into "consideration."
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sat Nov 03, 2007 6:46 am    Post subject: Reply with quote

If you want to avoid coloring, your grid is solvable as follows:

(1) Sashimi X-Wing in R19 removes <7> from R7C1
(2) XY Wing removes <3> from R9C2
(3) A long XY chain with pincers at R6C3 and R9C2 removes <7> from R9C3

No doubt there are other ways.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Nov 03, 2007 8:09 am    Post subject: Reply with quote

Asellus, I am not trying to avoid coloring at all. Especially Medusa and even "extreme" coloring are great methods to make one aware of certain possibilities that exist in the grid. But in the end, when the coloring leads to results like the elimination of a candidate or even (as with color wrap) of a whole lot of candidates, I don't feel comfortable with just saying "well, guys, I did some magic. The magic is great. It even has a fancy name. I solved the puzzle". I like to be able to point to a part of the grid and to say: "look here, this is why r9c8 must be 3".

I am aware that equivalence marks ("r" and "g") are just as valid once you've "bought into" the concept, but for communication purposes I prefer to steer clear of these. The reason might be that once I got into a nasty (and completely unnecessary) argument with someone who just didn't trust the colorful arguments ("why red" "why green" "you're making these up" ...).

Actually I was hoping to have found some well established and well understood pattern (like "xy-wing"), that can be used as a kind of shorthand, so one doesn't have to go through the individual proof every time.

Quote:
In my opinion, it's best to see it as a Medusa Wrap. I haven't found any simpler way to "see" it.


In that case, I am happy to go along with Medusa Wrap. It's fast, it's clean, it's efficient (and wipes out candidates by the truckload Smile )

--------

P.S. The best I could come up with in terms of "color"-free logic is the good old trusted AIC:

Quote:
I can't follow your chain as you've marked it.

Small wonder, it is not "clean".

The main body of the chain:
(6)r9c8=(6=3)r9c4=(3=1)r6c4=(1)r6c7=(1=4)r3c7=(4=5)r3c8=(5)r9c8

Notice there are ten links in the chain, all of them strong links.

If we close the loop by the (weak!) link in r9c8, we get eleven links, and a discontinuous nice loop that can be read both ways:

a) -(6)r9c8-(6=3)r9c4-(3=1)r6c4-(1)r6c7=(1-4)r3c7=(4-5)r3c8=(5)r9c8- => r9c8<>6

and

b) -(6)r9c8=(6-3)r9c4=(3-1)r6c4=(1)r6c7-(1=4)r3c7-(4=5)r3c8-(5)r9c8- => r9c8<>5


Last edited by nataraj on Sat Nov 03, 2007 8:24 am; edited 1 time in total
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Nov 03, 2007 8:20 am    Post subject: Reply with quote

I like the "sashimi"...

Just to make sure I understand this fishy business: the sashimi is like an "almost-skyscraper" (poor critter needs some serious growing, I'd say) :

If r9c3 is NOT "7", then we'd have a skyscraper in 7 (r1c1=r1c8-r9c8=r9c2), either way, the 7 in r7c1 is toast.

Thx. Smile
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sat Nov 03, 2007 8:52 am    Post subject: Reply with quote

Since it's nearly 2am here, I can't digest all of your posts right now. But, as regards "Sashimi" fish: they are finned fish with a piece of the fish missing. (Presumably, some high priced diner is munching away on the missing piece.)

So, while a Sashimi X-Wing can be seen as an "almost Skyscraper" (or, in some cases, an actual Skyscraper), it is more true to the concept to say that it is an "almost finned fish" ... in this case, an "almost Finned X-Wing."

PS: I only offered the non-coloring route for those who eschew coloring. Me, I'm very colorful.
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