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Set E Puzzle 25

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Dec 05, 2008 5:10 am    Post subject: Set E Puzzle 25 Reply with quote

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

Play this puzzle online at the Daily Sudoku site
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Fri Dec 05, 2008 9:39 am    Post subject: Reply with quote

Quote:
xyz-wing {2,3,7,} box 4, leaves...


Code:
.---------------------.---------------------.---------------------.
| 9      57     1     | 4      27     6     | 3      8      25    |
| 357    8      37    | 279    279    1     | 6      4      25    |
| 2      6      4     | 3      8      5     | 9      7      1     |
:---------------------+---------------------+---------------------:
| 37     23479  237   | 6      379    478   | 5      1      78    |
| 1      347    6     | 578    357    478   | 2      9      78    |
| 8      79     5     | 79     1      2     | 4      3      6     |
:---------------------+---------------------+---------------------:
| 4      15     8     | 15     6      9     | 7      2      3     |
| 6      127    27    | 127    4      3     | 8      5      9     |
| 357    2357   9     | 2578   257    78    | 1      6      4     |
'---------------------'---------------------'---------------------'

Quote:
(3)r5c5 = (3)r5c2 - (3)r9c2 = (3-5)r9c1 = (5)r2c1 - (5=7)r1c2 - (7=9)r6c2 - (9)r6c4 = (9)r4c5; r4c5 <>3... done.
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tlanglet



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

PostPosted: Sat Dec 06, 2008 3:20 pm    Post subject: Reply with quote

This puzzle really made me work. I initially found an ER and then a w-wing and but got stuck at that point. Finally on my second pass through everything, I found the xyz-wing noted by Norm that I had previously missed. It still found another ER and a xy-wing to complete it.

Specifics:
Quote:
1. ER <5> pivot box5 sl row7
2. W-wing <78> r5c9 & r9c6 sl <8> row4 (A type 4 UR <78> makes same deletion)
3. xyz-wing <237> pivot r4c3
4. ER <7> pivot box1 sl row6
5. xy-wing <379> pivot <37> r4c1


Is scotch permissible at 6:00AM?

Ted
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cgordon



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

PostPosted: Sat Dec 06, 2008 5:05 pm    Post subject: Reply with quote

I'm not into w-wings. I used ERs on <5> and <7> and the xyz wing. But then I got stuck and used a technique that has often worked in the past - I looked for the answer in the Forum. The xy wing finished it off.
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sun Dec 07, 2008 1:21 am    Post subject: Reply with quote

I'm sure I didn't solve this puzzle as efficiently as possible. But it's another one of the type that I really enjoy, one that bends but doesn't break. I used 10 assorted moves, ending it with an XY-Wing.

Quote:
(3)r5c5 = (3)r5c2 - (3)r9c2 = (3-5)r9c1 = (5)r2c1 - (5=7)r1c2 - (7=9)r6c2 - (9)r6c4 = (9)r4c5; r4c5 <>3... done.

Norm,

What actual move or technique does this notation represent?
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sun Dec 07, 2008 2:42 am    Post subject: Reply with quote

Marty R. wrote:
I'm sure I didn't solve this puzzle as efficiently as possible. But it's another one of the type that I really enjoy, one that bends but doesn't break. I used 10 assorted moves, ending it with an XY-Wing.

Quote:
(3)r5c5 = (3)r5c2 - (3)r9c2 = (3-5)r9c1 = (5)r2c1 - (5=7)r1c2 - (7=9)r6c2 - (9)r6c4 = (9)r4c5; r4c5 <>3... done.

Norm,

What actual move or technique does this notation represent?


Marty,
this represents a show off move on my part Smile
but... you have opened the can of worms now

the answer to this next question is YES.
the question is... can you extend a M-wing with a M-wing??
this puzzle shows how it can be done. please also note that there are no direct eliminations via the m-wings. AND this solution also incorporates a useless kite/skyscraper.

Asellus brought up something interesting in a previous posting about how a W-wing can have mixed ends. in other words the two true ends don't necessarily have to be identical and you can still make valid/easy eliminations via a few extensions.

this is sort of the same concept. we know that a generalized m-wing can have multiple candidates in the third cell. that is what I am going to exploit. Exclamation

step by step...

Code:
.---------------------.---------------------.---------------------.
| 9     *57     1     | 4      27     6     | 3      8      25    |
| *357   8      37    | 279    279    1     | 6      4      25    |
| 2      6      4     | 3      8      5     | 9      7      1     |
:---------------------+---------------------+---------------------:
| 37     23479  237   | 6      379    478   | 5      1      78    |
| 1      347    6     | 578    357    478   | 2      9      78    |
| 8      79     5     | 79     1      2     | 4      3      6     |
:---------------------+---------------------+---------------------:
| 4      15     8     | 15     6      9     | 7      2      3     |
| 6      127    27    | 127    4      3     | 8      5      9     |
|*357    2357   9     | 2578   257    78    | 1      6      4     |
'---------------------'---------------------'---------------------'

above is a useless M-wing {5,7} strong links on 5, using only the first three cells
(7=5)r1c2 - (5)r2c1 = (5)r9c1... please note that either the 7 or the 5 is true on each end

next...

Code:
.---------------------.---------------------.---------------------.
| 9      57     1     | 4      27     6     | 3      8      25    |
| 357    8      37    | 279    279    1     | 6      4      25    |
| 2      6      4     | 3      8      5     | 9      7      1     |
:---------------------+---------------------+---------------------:
| 37     23479  237   | 6     *379    478   | 5      1      78    |
| 1      347    6     | 578    357    478   | 2      9      78    |
| 8     *79     5     |*79     1      2     | 4      3      6     |
:---------------------+---------------------+---------------------:
| 4      15     8     | 15     6      9     | 7      2      3     |
| 6      127    27    | 127    4      3     | 8      5      9     |
| 357    2357   9     | 2578   257    78    | 1      6      4     |
'---------------------'---------------------'---------------------'

notice the useless m-wing {7,9} strong links on 9, using only the first three cells
(7=9)r6c2 - (9)r6c4 = (9)r4c5... and again, note that either the 7 or the 9 is true on each end.

the beauty of AIC formation is that they work in both directions Exclamation
Marty, its funny that you asked this because you asked this question in a post about if you can extend a M-wing from the beginning to make inferences.

these two chains are actually end to end. both starting points are in the same column, means they are joined weakly. see it?
since we are stringing them together starting with the {7,9} m-wing...
(9)r4c5 = (9)r6c4 - (9=7)r4c2 - (7=5)r1c2 - (5)r2c1 = (5)r9c1
this shows that either the 9 in r4c5 is true or the 5 in r9c1 is true. ok?

now to extend our first m-wing {5,7} by??

Code:
.---------------------.---------------------.---------------------.
| 9      57     1     | 4      27     6     | 3      8      25    |
| 357    8      37    | 279    279    1     | 6      4      25    |
| 2      6      4     | 3      8      5     | 9      7      1     |
:---------------------+---------------------+---------------------:
| 37     23479  237   | 6      379    478   | 5      1      78    |
| 1     *347    6     | 578   *357    478   | 2      9      78    |
| 8      79     5     | 79     1      2     | 4      3      6     |
:---------------------+---------------------+---------------------:
| 4      15     8     | 15     6      9     | 7      2      3     |
| 6      127    27    | 127    4      3     | 8      5      9     |
|*357   *2357   9     | 2578   257    78    | 1      6      4     |
'---------------------'---------------------'---------------------'

above is a useless skyscraper on 3.
(3)r9c1 = (3)r9c2 - (3)r5c2 = (3)r5c5... this means that either of the 3's on the ends are true. and it can also be written backwards.
guess what? the end of the skyscraper shares the same cell as the end of the useless {5,7} m-wing. AGAIN, this means "weakly" connected. "-"

string it all together

(9)r4c5 = (9)r6c4 - (9=7)r4c2 - (7=5)r1c2 - (5)r2c1 = (5)r9c1- (3)r9c1 = (3)r9c2 - (3)r5c2 = (3)r5c5

now what does this mean?

this means that either the 9 in r4c5 is true or the 3 in r5c5 is true. hmmm, if you know your AIC rules, in either case, the 3 can't exist in r4c5
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sun Dec 07, 2008 5:32 am    Post subject: Reply with quote

Thanks Norm. It's evident that you went to some time and trouble to post this, but it'll take me awhile to digest it.

Thanks again.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sun Dec 07, 2008 10:01 am    Post subject: Reply with quote

I believe typing it out in such a way that is understandable is the hardest part.
the concept here is the same old AIC formation rules. alternate the inferences. nothing new about that.

the important thing is that once the inferences are made and the AIC is valid then you can keep building on.
this is why we extend a w-wing or a xy-wing. we can see the inferences in our mind already.

just a reminder that medusa bridging accomplishes the same thing.
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