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No XY/XYZ-Wings: Set A Puzzle 5

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Oct 28, 2008 3:46 am    Post subject: No XY/XYZ-Wings: Set A Puzzle 5 Reply with quote

Same Rules! There are four XY-Wings -- each of which crack the puzzle. Have fun getting around them.

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



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Oct 28, 2008 7:41 am    Post subject: Reply with quote

Code:
.---------------------.---------------------.---------------------.
| 679    1      2679  | 5      3      267   | 4      8      26    |
| 3      2678   5     | 468   *27     12467 |*17     9      26    |
| 678   *2678   4     | 68     9     *1267  |*17     5      3     |
:---------------------+---------------------+---------------------:
| 4      26789  26789 | 3    *-27     267   | 69     1      5     |
| 679   *2679   1     | 469    5     *2467  | 69     3      8     |
| 5      3      69    | 69     1      8     | 2      7      4     |
:---------------------+---------------------+---------------------:
| 2      478    78    | 1      48     3     | 5      6      9     |
| 1      5      3     | 2      6      9     | 8      4      7     |
| 689    4689   689   | 7      48     5     | 3      2      1     |
'---------------------'---------------------'---------------------'


(2-7)r4c5=(7)r2c5-(7)r2c7=(7-1)r3c7=(1-2)r3c6=(2)r3c2-(2)r5c2=(2)r5c6-(2)r4c5; r4c5 <> 2

basically this is joining three chains. first it goes through the useless skyscraper on 7, then through the little two cell strong link on 1, then around the x-wing/cycle on 2.

and what it says is that if r4c5 is 2, then chain says its not 2, contradiction, r4c5 is not 2.


Last edited by storm_norm on Tue Oct 28, 2008 8:14 am; edited 1 time in total
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nataraj



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

PostPosted: Tue Oct 28, 2008 7:56 am    Post subject: Reply with quote

Oh my, four obstacles ... let's try not to step into one Smile

After basics, there are a lot of URs, which I ignored for the moment.

An x-wing (2) r35c26 brought me here (and since I had a drawing of the strong links in (2) handy, I took a closer look.

Code:

+--------------------------+--------------------------+--------------------------+
| 679     1       2679a    | 5       3       67+*     | 4       8       26       |
| 3       678     5        | 468     27+     14       | 17      9       26       |
| 678     2678    4        | 68      9       12       | 17      5       3        |
+--------------------------+--------------------------+--------------------------+
| 4       689     2689#    | 3       27#     67       | 69      1       5        |
| 679b*   2679b   1        | 469     5       24       | 69      3       8        |
| 5       3       69       | 69      1       8        | 2       7       4        |
+--------------------------+--------------------------+--------------------------+
| 2       478     78a*     | 1       48      3        | 5       6       9        |
| 1       5       3        | 2       6       9        | 8       4       7        |
| 689     4689    689      | 7       48      5        | 3       2       1        |
+--------------------------+--------------------------+--------------------------+



Cell r4c5 (with candidates {2,7}) sees several strong links in (2), I only pursued two of them:



a) (2)r4c3=r1c3, which in turn is connected to a SL in (7)r1c3=r7c3 --- marked red/"a"

b) (2)r4c3=r5c2, which in turn is connected to a SL in (7)r5c2=r5c1 --- marked green/"b"

Those two cells (r7c3, r5c1), together with the starting cell r4c5, don't do much. But, luckily, if r4c5=7, so is r1c6 (via r2c5) --- transport marked "+"

Now,
- r1c6 together with (a) r7c3 removes 7 from r1c3,
- r1c6 together with (b) r5c1 removes 7 from r1c1,

which leaves a single 7 in r1c6 and solves the puzzle.

I did notice the two overlapping 27-12-17 xy-wings in boxes 2 and 3, but since I did not actively look for xy-wings, I just hope none of the other 2 turns up in my eliminations...

__

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nataraj



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

PostPosted: Tue Oct 28, 2008 8:43 am    Post subject: Reply with quote

storm_norm wrote:
and what it says is that if r4c5 is 2, then chain says its not 2, contradiction, r4c5 is not 2.


I would read the AIC slightly different (and take away that forcing taste):

either r4c5=7 or r5c6=2 (or both), which of course implies r4c5<>2.

But never mind. How do you find those guys? Medusa? Myself, I usually stay within one candidate, and sometimes (like here) venture into one other, but I've not yet managed to get more than two into my mind without losing track completely...

And what time is it in Pennsylvania (or is that PA somewhere else?)
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Tue Oct 28, 2008 11:04 am    Post subject: Reply with quote

Quote:
And what time is it in Pennsylvania (or is that PA somewhere else?)
Pennsylvania is Eastern Time, same as New York and Detroit. Except, the USA has changed its shift to Standard time. So, we are still on Daylight time, while Europe switched to Standard time last weekend. We go to Standard time on Sunday, November 2.

Keith
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nataraj



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

PostPosted: Tue Oct 28, 2008 12:20 pm    Post subject: Reply with quote

keith wrote:
Pennsylvania is Eastern Time, same as New York and Detroit.


Thx, Keith! I did not know that you guys are still on DST.

So that would make the time of Norm's post around 3 in the morning? Shocked

Amazing stamina !!!
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Oct 28, 2008 2:17 pm    Post subject: Reply with quote

storm_norm wrote:
(2-7)r4c5=(7)r2c5-(7)r2c7=(7-1)r3c7=(1-2)r3c6=(2)r3c2-(2)r5c2=(2)r5c6-(2)r4c5; r4c5 <> 2

Too bad you didn't perform the X-Wing on (2) first. Then I could have eliminated the part in red and asked why the remaining chain wasn't sufficient for a contradiction. After all, it would have logically eliminated (2) in [b2].
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Oct 29, 2008 10:55 am    Post subject: Reply with quote

After the x-wing you can write:
Code:
+--------------------------+--------------------------+--------------------------+
| 679     1       2679     | 5       3       67       | 4       8       26       |
| 3       678     5        | 468    *27      14       |*17      9       26       |
| 678     2678    4        | 68      9      *12       |*17      5       3        |
+--------------------------+--------------------------+--------------------------+
| 4       689     2689     | 3       27      67       | 69      1       5        |
| 679     2679    1        | 469     5       24       | 69      3       8        |
| 5       3       69       | 69      1       8        | 2       7       4        |
+--------------------------+--------------------------+--------------------------+
| 2       478     78       | 1       48      3        | 5       6       9        |
| 1       5       3        | 2       6       9        | 8       4       7        |
| 689     4689    689      | 7       48      5        | 3       2       1        |
+--------------------------+--------------------------+--------------------------+

r2c5=7 => r3c6=2 => r3c7=1 => r2c7=7 (contradiction, r2c5<>7) or
(2)r2c5=(2-1)r3c6=(1)r3c7-(1=7)r2c7-(7=2)r2c5 (in any case r2c5=2)
This way you dont need to use the contradiction, that box 2 has no 2's.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Oct 29, 2008 3:10 pm    Post subject: Reply with quote

This should really be a separate topic, but I don't mind hijacking my thread for a tangent topic.

There are (forcing) chains and there are forcing networks. Basically, chains use a logical approach and don't perform assignments and eliminations during the process. Forcing networks perform assignments and eliminations during the process.

I'm talking abut a third approach that acts like a chain, but logically tracks eliminations in the cells of the chain and using this information as part of the process -- like a scaled down forcing network.

If you use this third approach, then Norm's chain can be terminated sooner -- sans the part I highlighted in red -- because the tracking process would have detected a contradiction in [b2] for (2).
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Oct 29, 2008 9:11 pm    Post subject: Reply with quote

Quote:
and take away that forcing taste

I don't normally look for this, I only just started venturing into the AIC that start out with a weak inference. I thank the practice I am getting with these puzzles.

Quote:
But never mind. How do you find those guys? Medusa? Myself, I usually stay within one candidate, and sometimes (like here) venture into one other, but I've not yet managed to get more than two into my mind without losing track completely...

what I do is use susser to highlight the individual candidates and I think in my head about if this was, then that is, then that isn't, and so forth and try and form a AIC. and I have to give credit to all the hints and direction about using useless skyscrapers, kites, etc for finding those nice patterns especially when they come together to make a poweful elimination. the one I want to find next is that UR strong link. but i am afraid it will only enhance my desire to find those one steppers. Laughing and keep me up late at night. Shocked
the US gov has found a new DST for the USA. only a matter of 40 years or so til it gets switched again. and again. and again.
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