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Stumped again!

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Jan 05, 2008 7:58 pm    Post subject: Stumped again! Reply with quote
I've stared at this one for hours, it seems. Any suggestions?

Thank you in advance,

Keith

Code:
Puzzle: M5459715sh(21)
+-------+-------+-------+
| . 7 1 | 6 . . | 8 2 . |
| . . . | . . 2 | . . . |
| 2 9 . | . . . | . 4 3 |
+-------+-------+-------+
| . 1 9 | . . 8 | . . . |
| 4 . . | . 5 . | . . 7 |
| . . . | 9 . . | 1 8 . |
+-------+-------+-------+
| 1 4 . | . . . | . 7 9 |
| . . . | . . 5 | . . . |
| . 3 7 | 2 . . | 4 6 . |
+-------+-------+-------+

Here is where I am stuck, after an XYZ-wing:
Code:
+-------------------+-------------------+-------------------+
| 3     7     1     | 6     49    49    | 8     2     5     |
| 8     56    4     | 357   37    2     | 679   19    16    |
| 2     9     56    | 1578  178   17    | 67    4     3     |
+-------------------+-------------------+-------------------+
| 67    1     9     | 347   23467 8     | 236   5     246   |
| 4     28    38    | 13    5     136   | 2369  39    7     |
| 67    25    35    | 9     23467 467   | 1     8     246   |
+-------------------+-------------------+-------------------+
| 1     4     2     | 38    368   36    | 5     7     9     |
| 9     68    68    | 47    47    5     | 23    13    12    |
| 5     3     7     | 2     19    19    | 4     6     8     |
+-------------------+-------------------+-------------------+

I see a flightless W-wing, XYZ-wing, and two XY-wings. Question Question
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Jan 05, 2008 8:51 pm    Post subject: Reply with quote
Well, I found that the two XY-wings are linked, and you can make a couple of eliminations that solve R5C4 as <1>. Revealing a W-wing that takes out <7> in R46C5.

Then Question

Working ...

Keith
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
PostPosted: Sat Jan 05, 2008 10:58 pm    Post subject: Reply with quote
There is a 4-cell xy-chain with pincer ends in R8C9 and R6C2, that takes out <2> in R6C9, that results in a naked [467] triple in R6.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sat Jan 05, 2008 11:23 pm    Post subject: Reply with quote
Code:
+-------------------+-------------------+-------------------+
| 3     7     1     | 6     49    49    | 8     2     5     |
| 8     56    4     | 357   37    2     | 679   19    16    |
| 2     9     56    | 578   178   17    | 67    4     3     |
+-------------------+-------------------+-------------------+
| 67    1     9     | 347   2346  8     | (2)36  5    g246  |
| 4     G28   38    | 13    5     36    | R2369 39    7     |
| 67    R25   35    | 9     23    47    | 1     8     46    |
+-------------------+-------------------+-------------------+
| 1     4     2     | 38    368   36    | 5     7     9     |
| 9     68    68    | 47    47    5     | g23   13    1r2   |
| 5     3     7     | 2     19    19    | 4     6     8     |
+-------------------+-------------------+-------------------+
 


after Johan's elimination you can kill the 2 in r4c7 by multicoloring.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Jan 05, 2008 11:59 pm    Post subject: Reply with quote
storm_norm wrote:
after Johan's elimination you can kill the 2 in r4c7 by multicoloring.

norm,

That is not correct. In fact, R4C7 is <2> in the solution.

Each leg of the multicoloring needs to have an even number of cells, which is also an odd number of links.

Johan,

How do you find XY-chains? I see your elimination, but I would never have found it myself. Clearly, I have something to learn.

I think we are here:

Code:
+----------------+----------------+----------------+
| 3    7    1    | 6    49   49   | 8    2    5    |
| 8    56   4    | 357  37   2    | 679  19   16   |
| 2    9    56   | 578  178  17   | 67   4    3    |
+----------------+----------------+----------------+
| 67   1    9    | 347  2346 8    | 236  5    246  |
| 4    28   38   | 1    5    36   | 2369 39   7    |
| 67   25   35   | 9    23   47   | 1    8    46   |
+----------------+----------------+----------------+
| 1    4    2    | 38   368  36   | 5    7    9    |
| 9    68   68   | 47   47   5    | 23   13   12   |
| 5    3    7    | 2    19   19   | 4    6    8    |
+----------------+----------------+----------------+


Keith
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sun Jan 06, 2008 12:33 am    Post subject: Reply with quote
sorry keith I thought i saw something that actually isn't there. everyone ignore my post.

xy-chains - very hard to look for because they don't actually involve just one candidate, they can involve many candidates. its actually a powerful technique when you have many bi-value cells. xy-chains exploit bi-value cells.

an xy-wing is the simplest xy-chain.

the ends of the xy-chain act the same as the pincers in an xy-wing.

I know there are very good examples of xy-chains out there, but most are very hard to illustrate if you create it from scratch. the xy-chain that johan used is a nice example.

r6c9 is not a 2 if:

r8c9=1 then r2c9=6 then r2c2=5 then r6c2=2
and !! that 2 has to be there on the other end going the other way

r6c2=5 then r2c2=6 then r2c9=1 then r8c9=2

since there is a two on both ends, any {2} those ends see can be eliminated.

most people show this as johan did by describing the end cells, but might also list the combinations: 12-16-56-25... the 2 on both ends can see the r6c9 cell.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sun Jan 06, 2008 12:59 am    Post subject: Reply with quote
also here is a good link for xy- chains explanation.

http://www.scanraid.com/AdvanStrategies.htm#XYC
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
PostPosted: Sun Jan 06, 2008 2:09 am    Post subject: Reply with quote
Quote:
How do you find XY-chains? I see your elimination, but I would never have found it myself. Clearly, I have something to learn.


Keith,

This is one of the advanced steps that i first learned, I've more trouble finding an x-wing than an xy-chain, but for finding those chains I use a simple
method, when I use the first digit(x) of a bivalue cell, I mark the other bivalue cells( I'm a P&P solver) which contain digit y,then I look if the both
cells(x and y) can see an y digit( pincer effect)

Now there is another one in R8C7, using digit <3>(x) you must find bivalue cells that contains an y digit(2), two of them <28>,<25> are in Box 4 and another
one <23> is in Box 5, but only one has a pincer effect,then i'll try to find me a way through the bivalue cells to end up in R5C2, eliminating <2> in R5C7.

[23-31-19-93-38-82]
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI
PostPosted: Mon Jan 07, 2008 12:12 am    Post subject: Reply with quote
For a change, I did a puzzle quite quickly - luck of the draw I guess. I've been inspired by the way in which Steve & others can build chains from a couple of conjugate links. Here it is:

R5C7 ≠ 2 ==> R5C2 = 2 ==> R6C2 = 5 ==> now just an XY-chain that ends ==> R8C9 = 2.

Since as with any AIC you can reverse this (i.e. R8C9 ≠ 2 ==> R5C7 = 2), we can eliminate the 2 in R8C7. And, perhaps surprisingly, that's it - not another non-basic move needed.
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