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Set VH_2 Puzzle 4

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Thu Mar 12, 2009 11:53 am    Post subject: Set VH_2 Puzzle 4 Reply with quote
Code:
 +-----------------------+
 | 3 . . | . . . | . . . |
 | . . . | . 8 . | . . 4 |
 | . . 4 | . . . | . 3 2 |
 |-------+-------+-------|
 | . . . | . 2 . | . 8 . |
 | . 2 . | 8 6 1 | 3 . 9 |
 | . . . | . 4 9 | . . 5 |
 |-------+-------+-------|
 | . . . | . 3 . | 2 . 1 |
 | . . 1 | 2 . . | . . . |
 | . 6 2 | . 1 7 | 5 . . |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon Mar 16, 2009 7:41 am    Post subject: Reply with quote
good puzzle
UR 1,5
UR 7,8
xyz
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Mon Mar 16, 2009 12:49 pm    Post subject: Reply with quote
I used Norm's URs, plus a Hidden UR on 69 and finished with an XY-Wing on 897.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Mon Mar 16, 2009 2:31 pm    Post subject: Reply with quote
I also did the UR78, UR15 and the xyz-wing and then realized that the UR78 was not required to complete the puzzle.

Also, I saw (again what I think is) a 6-cell DP15, but could not do anything with it.

Ted
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Mon Mar 16, 2009 2:35 pm    Post subject: Reply with quote
Marty R. wrote:
I used Norm's URs, plus a Hidden UR on 69 and finished with an XY-Wing on 897.

Marty, I am still hazy about "Hidden URs". Would you please provide some detail about this example? Thanks much.............

Ted
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon Mar 16, 2009 5:55 pm    Post subject: Reply with quote
Code:
.---------------------.---------------------.---------------------.
| 3      15    U689   | 4      79     2     |U6789   15     78    |
| 2      79    U69    | 135    8      35    |U679    15     4     |
| 17     15789  4     | 15     79     6     | 789    3      2     |
:---------------------+---------------------+---------------------:
| 17     179    39    | 357    2      35    | 4      8      6     |
| 4      2      5     | 8      6      1     | 3      7      9     |
| 6      78     38    | 37     4      9     | 1      2      5     |
:---------------------+---------------------+---------------------:
| 5      4      7     | 6      3      8     | 2      9      1     |
| 9      3      1     | 2      5      4     | 78     6      78    |
| 8      6      2     | 9      1      7     | 5      4      3     |
'---------------------'---------------------'---------------------'


Ted,
this grid represents the state directly after the UR move on 1,5.

then notice how the 6's form a perfect x-wing.
the candidate 9 also shares those same cells.
then notice the {6,9} cell in r2c3.
we know from the rules of how to prevent the deadly pattern that those four cells can't be left with {6,9} in them because then the puzzle would have two solutions.

since the x-wing pattern exists on 6, we know that either
r2c3 or r1c6 is going to be a 6 or
r1c3 or r2c6 is going to be a 6

well guess what? if r1c3 and r2c6 are 6, then that forces 9 into r2c3,
and that would leave a 9 (and other candidates) in r1c6. ok, moving on
if 6 were in r2c3, that forces 6 in r1c6
but there are still 9's in r1c3 and r2c6
so there still exists the possibility of multiple solutions

we now know the consequences of r2c3 being either a 9 or a 6.
in either case, the only sure way to avoid the DP is to remove the 9 from r1c6 since we know that 6 is going in two of the 4 cells, we just don't know that at this point.

Code:
69..................69
69..................69

solution 1

6...................9
9...................6


solution 2

9...................6
6...................9


in a general sense.
if you see a bi-value cell like the {6,9} cell and one of the candidates form a perfect x-wing, and the other candidate, {9} in this case, shares those same 4 cells. then it can be eliminated from the opposite corner cell.

anyone have a more efficient way to explain this?
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Mon Mar 16, 2009 6:38 pm    Post subject: Reply with quote
Norm, that is a great explanation; thanks. I thought that I understood the situation, and I even noticed the possibility in this puzzle but it did not work. As to why it did not work is simple; I missed the naked triple in row2 that deleted the <6> from r2c6 so I did not have a X-wing on <6>.

Again, your post clarified Hidden URs for me ....

Ted
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