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BrainBashers Super Hard for 7/19

 
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun Jul 20, 2008 3:15 am    Post subject: BrainBashers Super Hard for 7/19 Reply with quote

Code:
 4 . 3 | 8 . 2 | 6 . 9 |
| . . . | 1 . 6 | . . . |
| 1 . . | . 9 . | . . 7 |
+-------+-------+-------+
| 6 3 . | . . . | . 7 8 |
| . . 7 | . 1 . | 3 . . |
| 2 4 . | . . . | . 9 5 |
+-------+-------+-------+
| 7 . . | . 8 . | . . 3 |
| . . . | 7 . 1 | . . . |
| 8 . 9 | 3 . 5 | 7 . 1


Not particularly hard but I found it interesting. Details: Three URs when basics completed.

It is different than the typical BrainBasher.

Ted
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Sun Jul 20, 2008 11:55 am    Post subject: Reply with quote

Indeed an interesting puzzle!

I resisted the UR temptation (although the 59 UR was interesting - I'd not use it as a type 1 but use the strong link on 9 in col 2 instead) and (again not using a rather unspectacular w-wing 24-24) hit the mother lode: skyscraper "4" rows 3 and 9. It removes 9 from r2c5, sets r3c4=4, and that solves the puzzle

edit: oops, I forgot to mention the xyz-wing (245 in row 3 and box 3). I thought it did not do much but it does in fact remove a 4 from r3 and thus enables the skyscraper!
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sun Jul 20, 2008 12:22 pm    Post subject: Reply with quote

Firstly, I appreciate these "Other Puzzle" posts - I gotta have my daily sudoku fix.
This was a good one. I didn't resist the UR temptation - used 3 of them incl a Type 4 on <49> - plus an xy wing.
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Sun Jul 20, 2008 4:03 pm    Post subject: Reply with quote

Nataraj,

I think you already know this, since you pioneered it, but there is less contrast when it's part of a quote.

No quote:

skyscraper "4" rows 3 and 9. It removes 9 from r2c5, sets r3c4=4, and that solves the puzzle

edit: oops, I forgot to mention the xyz-wing (245 in row 3 and box 3). I thought it did not do much but it does in fact remove a 4 from r3 and thus enables the skyscraper!


With quote:

Quote:
skyscraper "4" rows 3 and 9. It removes 9 from r2c5, sets r3c4=4, and that solves the puzzle

edit: oops, I forgot to mention the xyz-wing (245 in row 3 and box 3). I thought it did not do much but it does in fact remove a 4 from r3 and thus enables the skyscraper!
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Sun Jul 20, 2008 4:16 pm    Post subject: Reply with quote

I knew that there was a difference between odd-numbered and even-numbered posts (because of the darker and lighter backgrounds) and that the darker backgrounds were more of a problem.

Nifty idea to use [quote] to make sure there is a white background ...
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun Jul 20, 2008 6:13 pm    Post subject: Reply with quote

I solved the puzzle twice; with and without the three URs. The existence of the three URs at the same time immediately after completing basics was interesting to me, plus that two of them provided deletions in the same cell.

Ted
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sun Jul 20, 2008 7:55 pm    Post subject: Reply with quote

Maybe this is just another of my dumb ideas. (I really hope it is not one of my unoriginal dumb ideas!)

Is there such a thing as a finned XY-wing?

The puzzle of this thread:
Code:
4.38.26.9
...1.6...
1...9...7
63.....78
..7.1.3..
24.....95
7...8...3
...7.1...
8.93.57.1


After basics and an XYZ-wing, I get to here:
Code:
+-------------------+-------------------+-------------------+
| 4     57    3     | 8     57    2     | 6     1     9     |
| 59    25789 25    | 1     457   6     | 2458  3     24    |
| 1     2568  256   | 45a   9     3     | 258d  245   7     |
+-------------------+-------------------+-------------------+
| 6     3     1     | 2459  245c  49    | 24    7     8     |
| 59    59    7     | 24b   1     8     | 3     246   246   |
| 2     4     8     | 6     3     7     | 1     9     5     |
+-------------------+-------------------+-------------------+
| 7     1     246   | 249   8     49    | 245   2456  3     |
| 3     256   2456  | 7     246   1     | 9     8     246   |
| 8     26    9     | 3     246   5     | 7     246   1     |
+-------------------+-------------------+-------------------+

Take a look at abc. Either the XY-wing is true, or c is <4>. Either way, the cell marked d is <8>, and the puzzle is solved.

(If the XY-wing is true, a is <5>, and <8> is forced in d. If c is <4>, an <8> is forced by solving the other cells that are also <4>.)

I admit that this is a contrived example. The question is, is this type of bifurcation likely to be useful?

It is interesting (at least to me) that in this line of thinking an XYZ-wing is a finned XY-wing.

XZ-XYZ-YZ. Either the XY-wing is true, or the pivot cell is Z.

Keith
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun Jul 20, 2008 11:59 pm    Post subject: Reply with quote

Keith,

Your solution to this puzzle is elegant!

However, I am lost in your comparison of an xyz-wing to a finned xy-wing. In the chain XZ-XYZ-YZ, I think of XYZ as the pivot that "sees" both pincers, XZ and YZ. However in this puzzle it is one of the pincers that has the extra Z candidate. I seem to be missing a basic concept at this point.

Ted Confused
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Mon Jul 21, 2008 1:09 am    Post subject: Reply with quote

Ted,

My XYZ-wing example is not present in the situation I discuss in this puzzle.

What I mean by a "finned" XY-wing is that you can have an XY-wing:

XZ-XY-YZ.

The "fin" is an extra value on any one of the three cells:

VXZ-XY-YZ,

XZ-VXY-YZ, or

XZ-XY-VYZ.

Either the XY-wing is true, or "V" is true.

V = Z only makes sense in the second case, XZ-XYZ-YX, which is an XYZ-wing.

The XY-wing eliminates "Z" in all cells (maximum four) that see XZ and YZ. The XYZ-wing eliminates "Z" in only the cells (maximum two) that see XZ, XYZ, and YZ.

The reasoning of this finned XY-wing is much more like a BUG+2: Either A is true in one cell, (and/) or B is true in another cell. If they both lead to the same truth, or to the same contradiction, you can advance the puzzle.

"Elegant"? Thank you, but I think the jury is still out. (Let's hope they are not "12 Angry Men", a classic I watched with my son the other night.)

[Now, you see what I do with my idle time on Sundays when there is no NASCAR race. Even the replays of the IRL Danica Patrick cat fight only occupied me for a few minutes. Watching Greg Norman not win was, as Yogi Berra said, like deja-vu, all over again.]

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Mon Jul 21, 2008 3:53 am    Post subject: Reply with quote

Quote:
[Now, you see what I do with my idle time on Sundays when there is no NASCAR race. Even the replays of the IRL Danica Patrick cat fight only occupied me for a few minutes. Watching Greg Norman not win was, as Yogi Berra said, like deja-vu, all over again.]

At the risk of alienating racing fans (or Sudoku fans), I never visualized "NASCAR" and "Sudoku" in any sort of juxtaposition. Question Rolling Eyes Laughing
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Asellus



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

PostPosted: Tue Jul 22, 2008 12:16 am    Post subject: Reply with quote

keith wrote:
Is there such a thing as a finned XY-wing?

Why not? However, the way you've used it here doesn't strike me as what I would think of as a finned XY-wing. By analogy with finned fish, a finned xy-wing should, strictly speaking, eliminate one or more of the XY-wing victims. Of course, to do so necessarily requires "transporting" the "fin," and in a way that changes it to a different digit (the same digit as the wing pincers). This is already rather different from a finned fish, so I guess we can't be too picky about where to draw the line! In any case, this "finned XY-wing" doesn't produce a <5> victim in this way and so doesn't comply with this more limited notion.

Your determination of r3c7 as <8> requires using, at mimimum (as far as I can tell), a branched implication chain with grouped links. It seems too remote from the finned XY-wing structure itself. But, there is a more direct alternative: If the <4>-fin is false, then the XY-Wing determines both r3c4 and r4c5 as <5>. In either case, r4c5 is not <2> and this solves the puzzle. The roundabout trip to that <8> isn't required. That is at least a bit more elegant and, while it doesn't meet that "strictly speaking" notion, it is tightly contained. It might be notated as:

(4)r4c5=>[(XY Wing)r35c4|r4c5] - (5)r12c5=(5)r4c5; r4c5<>2

(The symbol "=>" means that the strong inference is unidirectional left-to-right.)

This same <2> elimination can be done with an AIC that is closely related to an M-Wing (by noting that the 24 pair in r45 is complementary):

(2=4)r4c7 - (4)r5c89=(4)r5c4 - (4)r3c4=(4)r2c5 - ALS[(4)r89c5=(2)r89c5]; r4c5<>2
______________________
Edit 28-Jul-08 to add:

I have now convinced myself that the "unidirectional" restriction is incorrect in these Finned XY Wing structures. For those so interested, I will explain.

Originally, it was not clear to me what it meant to posit that the XY Wing is false and so I was not convinced that we could use such a condition to infer the truth of the fin digit (a "right-to-left" inference). I have now convinced myself that the truth of the XY Wing is the strong inference between its pincer digits and that the Wing is thus rendered false if both pincers are false.

Here is how one can see that the inference (that the Fin digit is true) works (assuming that both pincer digits of the potential wing are false). First, consider the case where the fin is in a pincer cell: FZX-XY-YZ. If the Zs are false, this becomes: F-X-Y, and F is true. Next, consider the case where the fin is in the pivot cell: ZX-FXY-YZ. If the Zs are false, this is: X-F-Y, and F is again true.

So, the strong inference now appears to me to be bidirectional and no special precautions are required for using alternate inference methods.


Last edited by Asellus on Mon Jul 28, 2008 10:19 am; edited 1 time in total
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Tue Jul 22, 2008 7:48 am    Post subject: Reply with quote

Marty R. wrote:
Nataraj,

I think you already know this, since you pioneered it, but there is less contrast when it's part of a quote.



And now I found the solution to the contrast problem, too:
Use the color tag with a custom color code.

I've added a thread ("site help")
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Wed Jul 23, 2008 2:45 am    Post subject: Reply with quote

Asellus wrote:
keith wrote:
Is there such a thing as a finned XY-wing?

Why not? However, the way you've used it here doesn't strike me as what I would think of as a finned XY-wing. By analogy with finned fish, a finned xy-wing should, strictly speaking, eliminate one or more of the XY-wing victims ...
Your determination of r3c7 as <8> requires using, at mimimum (as far as I can tell), a branched implication chain with grouped links ...


Asellus,

I think of a "fin" as an extra candidate on any pattern. Either the pattern is true, or the fin is true. I did not think of the fin in terms of common eliminations, but rather in terms of common implications.

As I said in my original post, the determination of <8> in R3C7 is somewhat contrived. My question still is, could this idea be useful?

I think the answer is probably "yes", since the bifurcation point is something other techniques do not use. Like W- and M-wings, puzzles are not screened or graded for this. (Makes sense?)

Best wishes,

Keith
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Asellus



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

PostPosted: Wed Jul 23, 2008 7:43 am    Post subject: Reply with quote

keith wrote:
My question still is, could this idea be useful?

I thought I had answered "Yes." My only concern is that the mutual effect of the fin and the wing be reasonably "contained," and not require involved extensions that risk being something akin to forcing. (If that is the route, then one should use the unidirectional strong link and build an explicit implication chain, in my opinion.)

That is why I thought you might be impressed by the <2> elimination I described above. (You don't mention it.) It is highly contained and, I think, an excellent example of how such a "Finned XY Wing" can work.

I don't know, however, if these creatures are very common. I haven't found another since this one presented itself. But, I'm keeping my eyes peeled.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Jul 23, 2008 6:22 pm    Post subject: Reply with quote

I did like Asellus' elimination (while i needed some time to see Keith's placement of the 8's).

For me the finned xy-wing (or a finned w-wing) is something similar to a "useless" xyz-wing (one of 3 numbers must be x) or a UR with 3 extra candidates.
Here we have "either the fin must be true or one of 2 numbers must be x". Can we conclude something usefull from that ?

Its hard to say, if the chances are really better, than to start with the numbers of a trivalue cell or the 3 occurrences of a number in a unit. Probably yes, if there are cells with x, which would be eliminated by the xy- or w-wing.

The other thing is, that you might find them, when you look for the wings. So why not test them immediately ? I always check, if i can use UR's with up to 3 extra candidates (or "outside" positions of the UR digits) in harder puzzles.

I have tried another of the grids here and it took me hardly longer to look for finned xy-wings than for xy-wings alone. But i only found one, which did not lead to an elimination.
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keith



Joined: 19 Sep 2005
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Location: near Detroit, Michigan, USA

PostPosted: Wed Jul 23, 2008 9:34 pm    Post subject: Reply with quote

Asellus wrote:
That is why I thought you might be impressed by the <2> elimination I described above.


Asellus,

Now that I have taken the time to study your elimination of <2>, I must say I am very impressed!! It is very compact, whereas mine wanders off into long chains.

(I must admit I was focused on looking for the implication of the same candidate in a solved cell, not for what you saw.)

I will continue to look for these! As ravel says, if you're looking for XY-wings (or especially XYZ-wings), you can check for these at the same time.

Sort of like: If you're looking for W-wings, why not check M-wings at the same time? They have the same beginning clues.

Thank you!

Keith
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