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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Fri Feb 15, 2008 11:54 am    Post subject: Dozens Reply with quote

Hope you like this one, M3723414 (108)
After basics:

Code:

+--------------+---------------+-----------------+
| 26  1   29   | 89  7     5   | 2689  3    4    |
| 5   3   279  | 6   4     128 | 12789 1278 1279 |
| 267 4   8    | 19  12    3   | 12679 1267 5    |
+--------------+---------------+-----------------+
| 78  9   5    | 2   18    6   | 1478  1478 3    |
| 3   278 6    | 4   5     178 | 1278  9    127  |
| 1   278 4    | 3   9     78  | 5     2678 267  |
+--------------+---------------+-----------------+
| 9   5   127  | 17  126   4   | 3     1267 8    |
| 4   78  1237 | 178 12368 9   | 1267  5    1267 |
| 278 6   1237 | 5   1238  128 | 12479 1247 1279 |
+--------------+---------------+-----------------+

Play this puzzle online at the Daily Sudoku site
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nataraj



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

PostPosted: Fri Feb 15, 2008 2:50 pm    Post subject: Reply with quote

First an ER (box 7) kills 2 in r2c3 (via strong link in col 6). Alas, nothing after that. How about this not-quite-xy-wing then:

Pincers 89 in r1c4 and 78 in r8c2.
If r1c4<>8 then r1c3=2 then r1c1=6 then r3c1=7 then r4c1=8 then r56c2<>8 then r8c2=8.

Therefore r8c4<>8 which gives a naked pair 17 in col 4 and a few steps later I found a kite to remove 8 from r4c5.

Nice going, but here , again, a difficult position:
Code:

+--------------------------+--------------------------+--------------------------+
| 2       1       9        | 8       7       5        | 6       3       4        |
| 5       3       7        | 6       4       1        | 289     28      29       |
| 6       4       8        | 9       2       3        | 17      17      5        |
+--------------------------+--------------------------+--------------------------+
| 78      9       5        | 2       1       6        | 478     478     3        |
| 3       278     6        | 4       5       78       | 1278    9       127      |
| 1       278     4        | 3       9       78       | 5       6       27       |
+--------------------------+--------------------------+--------------------------+
| 9       5       12       | 17      6       4        | 3       127     8        |
| 4       78      123      | 17      38      9        | 127     5       6        |
| 78      6       13       | 5       38      2        | 1479    147     179      |
+--------------------------+--------------------------+--------------------------+


In order to avoid the DP 28-78-27 in r56c269, either r56c2=7 or r5c9=1.
If r56c2=7 then r4c1=8 then naked pair 47 in r4c78. Either way, r5c9<>7.

This leads to a skyscraper (col 1 and 9) in 7 and that finally solves the puzzle.

I am curious to find out what you guys did, especially how to avoid that first grouped AIC.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Feb 15, 2008 3:09 pm    Post subject: Reply with quote

The X-wing on 8 in columns 1 and 5 eliminates 8 from r9c6. This leaves its candidates as (12), matching r3c5 and forming a W-wing using the conjugates with respect to 1 in column 4.

The W-wing places 2 r3c5 but the X-wing/skyscraper on 7 is still needed to complete the puzzle.

Thanks, Victor.

Steve
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nataraj



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

PostPosted: Fri Feb 15, 2008 3:41 pm    Post subject: Reply with quote

Steve R wrote:
The X-wing on 8 in columns 1 and 5 eliminates 8 from r9c6.


There are 3 8s in col 5. Can't be an x-wing, at least not immediately from Victor's grid?
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Feb 15, 2008 4:24 pm    Post subject: Reply with quote

I think perhaps you know it as a skyscraper rather than a (finned) X-wing.

Steve
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nataraj



Joined: 03 Aug 2007
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Location: near Vienna, Austria

PostPosted: Fri Feb 15, 2008 5:15 pm    Post subject: Reply with quote

finned! of course!

neat.

Thx, Steve

____


N.B. The "un-finned" or original X-wing looks like this (click to get full article) Very Happy Exclamation



Quote:
The X-wing takes its name from its pair of double-layered wings, deployed into the familiar X formation for combat.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Feb 15, 2008 8:09 pm    Post subject: Reply with quote

That’s interesting.

This is Wayne Gould in Extreme Su Doku (Harper Collins, 2007):

Quote:
“When I was working on my program, I devised a new solving technique which I nicknamed X-Wings. At least, it seemed new to me. The idea was sparked after studying puzzles on a few Japanese websites. In a given collection of perhaps 100 puzzles, all were solveable with known techniques, bar one. At first I assumed that the puzzle was faulty. Perhaps it had been entered into the website with a typo.

After closer examination, I discovered that the puzzle could be solved with what I know call X-Wings. Did the owners of the website intend the puzzle to be solveable with X-Wings? If so, why was the puzzle not #100 in the collection, instead of being buried in the middle somewhere? Or was the puzzle simply a mistake which just happened to be solveable with an advanced technique that had not been anticipated?

Certainly, Nikoli and Gakken (the publishers) did not use X-Wings in their puzzles. However, just before I went public with my program, the Japanese puzzle-master Tetsuya Nishio came out with a book which included three X-Wing puzzles. I'm still not clear whether I devised X-Wings as an original technique or whether I unwittingly picked up on something Testuya Nishio had already devised.

In any event, I called the technique 'X-Wings' because the diagonal struts of the pattern reminded me of the shape of the X-Wing fighters of Star Wars fame. You might see what I mean when you study the X-Wing.”


I’m not sure that the last paragraph carries the same meaning as your quotation. What do you think?

At any rate I should be interested to know the origin of the quotation.

Steve
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Fri Feb 15, 2008 8:28 pm    Post subject: Reply with quote

Working from Nataraj's grid:
There is a UR elimination of the 7 in r5c2 (to avoid a DP of 78s in R56C2^, but I don't think it helps much. I too needed a finned thing in 7s, based on R49C19 to finish (killing the 7s in r4c78). Isn't it called a sashimi finned x-w, because the 7 in r4c9 is actually missing?

And to start with, I just used 2 ERs, one to kill the 2 in r2c3, the other the 8 in r9c6, which as you've pointed out gives a pair of 12s which are linked .... equivalently? - wish we'd a word for a TT/FF link like this. (I actually noted that now R9C6 = 1 => R3C5 = 1 AND R4C5 = 1, which => R9C6 <> 1.)
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Asellus



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

PostPosted: Fri Feb 15, 2008 8:55 pm    Post subject: Reply with quote

Victor wrote:
Isn't it called a sashimi finned x-w, because the 7 in r4c9 is actually missing?

Yes, it is a Sashimi X-Wing.

A Skyscraper can be seen as a Sashimi X-Wing with a single-cell fin.

Victor wrote:
wish we'd a word for a TT/FF link like this.

You can call it a grouped strong link.

For instance, a 2-cell finned Sashimi X-Wing (as here) can be seen as a sort of Skyscraper with a grouped strong link.
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Fri Feb 15, 2008 10:10 pm    Post subject: dozens Reply with quote

Is there such a thing as a "finned skyscraper?"

In Nataraj's grid, consider the 7's in C19.
If R5C9 is not a 7, the resultant skyscraper eliminates 7's in R4C78;
If R5C9 is a 7, the same 7's are also eliminated.

Am I correct? Is there a name for it?

"Earl's Skyscraper?"


Earl


Last edited by Earl on Fri Feb 15, 2008 11:11 pm; edited 1 time in total
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nataraj



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

PostPosted: Fri Feb 15, 2008 10:18 pm    Post subject: Reply with quote

Steve R wrote:


I’m not sure that the last paragraph carries the same meaning as your quotation. What do you think?


Yes, definitely.

I'm not a Star Wars addict myself but when I googled for x-wing most references turned out to be the Star Wars fighter plane. And I thought it made sense too, with the rectangular pattern of the sudoku x-wing.
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Asellus



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

PostPosted: Fri Feb 15, 2008 11:19 pm    Post subject: Reply with quote

Earl wrote:
Is there such a thing as a "finned skyscraper?"

That's what I meant by "a sort of Skyscraper with a grouped strong link." It certainly works to think of it as a "finned skyscraper." But, it's already well-known (perhaps less confusingly) as a Sashimi X-Wing so doesn't really need the new name.
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Sat Feb 16, 2008 10:36 am    Post subject: Reply with quote

I'd agree with anyone who said that seeing this sort of thing as a "grouped skyscraper" is easier than as a finned x-w. But Sashimi sort of rolls of the tongue!
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Victor



Joined: 29 Sep 2005
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Location: NI

PostPosted: Wed Feb 20, 2008 3:56 pm    Post subject: Reply with quote

Asellus, about the only thing you've written of which I think "Mmmm - not sure" is this:
Quote:
You can call it a grouped strong link.
of a name for a TT/FF link (even no. of steps in an all-conjugate chain such as plain colouring).

I'm sure that every discipline that uses set theory in general, Boolean algebra in particular, has names / symbols for the things they're particularly interested in. E.g. Logic gates in computing use NAND (Not 1 AND 1) for what we call a weak link, etc. I'd forgotten what the inverse of EOR / XOR (= conjugate) was called but looked it up - XNOR apparently, which I suppose is a bit better that NXOR or NEOR or ENOR, but doesn't have a nice ring.

We all think differently, & I happen to like thinking in terms of links - Weak, Conjugate, Strong, and XNOR of the bi-directional ones. XNOR is no good, but 'Grouped Strong' doesn't roll off the tongue either!
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Asellus



Joined: 05 Jun 2007
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PostPosted: Wed Feb 20, 2008 6:59 pm    Post subject: Reply with quote

Victor,

I think we may be talking apples and oranges here.

I was referring to the sort of link that exists, for example, in an ER:
Code:
~ ~ a
~ ~ b      or     ~ a b | ~ ~ ~ | c d e
e d c

In the ER (on the left) the grouped abc cells are strongly linked with the grouped cde cells. (It is an inferential strong link, not a conjugate link.) In the row (on the right) the grouped ab cells are strongly linked with the grouped cde cells. (In this case, it is conjugate, so is also weak.)

I now suspect you are talking about something else:
Code:
 .  .  . | . .  .
 .  .  . | . .  .
 . a34 . | . .  .
--------+---------
 .  .  . | . .  .
 . b34 . | . . c34
 .  .  . | . .  .

Given the three matching bivalue cells shown, the <3>s in ac are either both true or both false. (The same is true of the <4>s.) I don't know of a name for such a link. It seems to me that it isn't of much use in a solution.
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Fri Feb 22, 2008 3:08 pm    Post subject: Reply with quote

As you say, Asellus, apples & oranges. Silly of me really - I do know what a grouped link is. I don't quite agree with you about the lack of usefulness of the sort of link that I meant. If nothing else, it's the basis for Keith's splendid M-wings. In your abc 34 example, b could be 74 say. Because the 4s are * linked, then so are the 3s: now you can continue colouring on 3s. In general, I have met chains of all-conjugate links: if there's an even number of links, then you can (for instance) continue the chain with a strong link in either direction to get a valid AIC, because you can think of an even number of conjugate links as Either weak then strong Or strong then weak. So although I totally agree that these links aren't of much use, I think they are of some use. In his M-wing thread Keith calls this link complementary, but I'm not enthusiastic about that term (love the idea, don't like this name).

And to finish, THE most confusing thing I found when I was reading up about new techniques was the terminology for links / inferences - e.g. "There's a strong link from Cell A to Cell B in number x, but actually it's a weak link." I once made the mistake of treating a strong link (ends of an XY-chain as far as I remember) as a conjugate link & tried to continue colouring an odd number of steps from each end. And I'm not the only one - I've seen other people make this sort of mistake. There are just 4 kinds of bi-directional link that we meet (I think). Why not have a distinct and appropriate name for each? It would protect us from the kinds of mistake I've mentioned.
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Asellus



Joined: 05 Jun 2007
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PostPosted: Fri Feb 22, 2008 11:46 pm    Post subject: Reply with quote

Victor,

I am afraid the M-Wing is not a good example of the usefulness of this "complementary" sort of link. An M-Wing is a simple AIC involving only the usual strong and weak inferences. The presence of the "complementary" link in the structure is an artifact of the bivalue cell pattern that the M-Wing involves.

In my abc {34} schematic, I did not assume that the <3>s or the <4>s are strongly linked with each other in any way. The cells marked with "." can be anything. However, if you replace "b" with {47} then, indeed, the <4>s in c2 and in r5 must be strongly linked in order to have the "complementary" link between the "ac" <3>s.

The pincers at the ends of, say, an XY Chain have a strong inference between them (and are not a conjugate pair), as you note. This means that they are each attached to the ends of an AIC (that of the XY Chain for instance) with a strong link.

In the case of a "complementary" link pair, they are attached to the ends of an AIC with dissimilar links: one weak and one strong. I know you are not fond of Eureka, but...

In the case of the three "abc" {34} bivalues, we can write:
(3=4)r3c2-(4=3)r5c2-(3)r5c6
or we can write:
(3)r3c2-(3=4)r5c2-(4=3)r5c6
Reading from left to right, in the first chain, the <3>s on the ends are both false. In the second chain, they are both true. Note that the <4>s in the row and column do not need to be conjugates.

Now, with {47} at "b", we must have conjugate <4>s in the row and column and the AICs are different:
(3=4)r3c2-(4)r5c2=(4-3)r5c6
or
(3-4)r3c2=(4)r5c2-(4=3)r5c6
Again, in the first chain both <3>s are false and in the second both are true. In the first chain, the <4>s in r5 must be conjugate and in the second the <4>s in c2 must be conjugate. Since the "complementary" link depends upon both of these chains, then both the r5 and c2 <4>s must be conjugate.

It is true that you could use this "complementary" link in <3> coloring to "jump" in your color chain (using them to have two adjoining "red" or two adjoining "green" <3>s). This amounts to a "multi-coloring shortcut." As such, then I suppose it is useful.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Sat Feb 23, 2008 2:57 pm    Post subject: Reply with quote

Steve R wrote:
The X-wing on 8 in columns 1 and 5 eliminates 8 from r9c6. This leaves its candidates as (12), matching r3c5 and forming a W-wing using the conjugates with respect to 1 in column 4.


Steve,

Starting with the code after basics as originally posted by Victor, I had found the finned X-wing and noticed the possible W-wing on <12> in r3c5 & r9c6, but I did not find a strong link in either <12>. After reading your input, I reviewed the code again and still do not see the strong link one <1> in column 4; Box 7 has a <1> in both r78 and not in r9. I assume it is an implicit link of some sort that I still do not fully understand/appreciate. Could you please clarify this for me?

Ted
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CORUJA



Joined: 16 Jun 2007
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Location: BRUMADINHO - MG; BRAZIL

PostPosted: Sat Feb 23, 2008 3:04 pm    Post subject: DOZENS Reply with quote

Thanks for the fine discussion! Learned a lot!
Seems I finally understood what a skyscraper is.
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Asellus



Joined: 05 Jun 2007
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PostPosted: Sun Feb 24, 2008 12:03 am    Post subject: Reply with quote

Ted wrote:
I reviewed the code again and still do not see the strong link one <1>

The strong link is in box 5. The easiest way to see this sort of W-Wing is to note that <1> is not present in r456c4. Since <1> must be in either r456c5 or r456c6, one or both of the {12} bivalues must be <2>.
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