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Nightmare

 
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Wed Dec 05, 2007 5:26 pm    Post subject: Nightmare Reply with quote

I'm stuck on the daily nightmare, Help !

Earl

Code:

+----------------+-----------------+---------------+
| 7    689  5    | 389 23489 1     | 26   246  49  |
| 2    189  148  | 789 6     4789  | 5    147  3   |
| 1469 169  3    | 5   2479  2479  | 1267 8    479 |
+----------------+-----------------+---------------+
| 8    137  9    | 6   237   5     | 1237 1247 47  |
| 5    4    2    | 378 1     378   | 37   9    6   |
| 16   1367 167  | 4   2379  2379  | 8    127  5   |
+----------------+-----------------+---------------+
| 146  2    1467 | 37  347   3467  | 9    5    8   |
| 3    6789 4678 | 2   5     46789 | 67   67   1   |
| 69   5    678  | 1   789   6789  | 4    3    2   |
+----------------+-----------------+---------------+

Play this puzzle online at the Daily Sudoku site
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Wed Dec 05, 2007 5:37 pm    Post subject: Reply with quote

After basics, you get to
Code:
.------------------.------------------.------------------.
| 7     689   5    | 389   348   1    | 26    246   49   |
| 2     189   48   | 789   6     478  | 5     147   3    |
| 49    16    3    | 5     247   247  | 16    8     479  |
:------------------+------------------+------------------:
| 8     37    9    | 6     237   5    | 1237  1247  47   |
| 5     4     2    | 378   1     378  | 37    9     6    |
| 16    37    16   | 4     2379  2379 | 8     27    5    |
:------------------+------------------+------------------:
| 146   2     167  | 37    347   3467 | 9     5     8    |
| 3     89    48   | 2     5     49   | 67    67    1    |
| 69    5     67   | 1     789   6789 | 4     3     2    |
'------------------'------------------'------------------'

where there is a potential DP in r67c13 which will eliminate 6 from r7c13. Clean up and there will be a couple of things to do on the candidate 4. Finally look for an xy-wing that eliminates another 4 and the puzzle will be solved.
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Wed Dec 05, 2007 6:20 pm    Post subject: nightrmare Reply with quote

Re'born,

I would appreciate the specifics on the type 2 UR (DP) and how it eliminates 6 from R7C13. Thanks

Earl
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Wed Dec 05, 2007 7:02 pm    Post subject: Reply with quote

Earl,

I don't think it is a type 2 (at least my reference in that matter: http://www.sudoku.com/boards/viewtopic.php?t=2000 says:

Code:
So the Type-1 Unique Rectangle is:

Code:
12|12A..
12|12

ie:
12|123
12|12


and permits the 12A... to be reduced to A... (A... stands for 1-n other possibilities)

The Type-2 Unique Rectangle is:

Code:
12|123
12|123


and permits 3 to be removed from the common groups (houses) of the 123 squares. If I'm not mistaken, this variant:

Code:
12 |12
123|123


is the Type-2B form (I haven't implemented it yet) and permits removal of 3 from the common group of the 123 squares (in this case, a row)


I thought this would be a type 3 but I was mistaken...

I think the elimination works like this:
To avoid the DP (16 16) in c13r7, either r7c1=4 or r7c3=7

in both cases r7c6=6.

if r7c1=4, there is a naked pair 3,7 in box 8
if r7c1=7, then r7c4=3 and r7c5=4

_____

edit: it is a type 3 after all (described later in that thread):

Quote:

A Type-3 unique rectangle.
12|12A... A... are the 1 or more extra possibilities in one roof square;
12|12B... B... the extras in the other. The quantum-square is the union of A... and B...


A very comprehensive source of UR-types and explanations: http://www.sudoku.com/boards/viewtopic.php?p=29105#29105
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Wed Dec 05, 2007 8:55 pm    Post subject: Reply with quote

Here is how I thought of it: r7c1 = 1 or r7c3 = 1 (since there are only two 1's in row 7) and hence neither of r7c1 or r7c3 can be a 6, else we would have a deadly pattern.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Dec 05, 2007 9:02 pm    Post subject: Reply with quote

With more words:

The point of this UR type 2 is, that in one line (row or column) you only have the 2 numbers and in the other line a strong link for one number. Then you can eliminate the other number from the second line.

E.g.
Code:
12    .   12
 .    .    .
 .    .    .
-----------------
12345 .   1235789
No other 2 in this line -> eliminate 1 here 


Reasoning:
A pattern
Code:
 1.2
 ...
 ...
-----
 2.1

always is deadly, if none of the 4 numbers is a given, because no 1 or 2 can be in the same row, column or box. That means, if this pattern is possible, you always can exchange the numbers to get a second solution.

Now because of the strong link for 2 a 1 in the second line just would lead to this pattern.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Dec 05, 2007 9:07 pm    Post subject: Reply with quote

Code:
------------------------------------------------------------------------------|
| 7       689     5       | 389     348#    1       | 26      246     49      |
| 2       189     48      | 789     6       478     | 5       147     3       |
| 49#     16      3       | 5       247#    27-4    | 16      8       479     |
------------------------------------------------------------------------------|
| 8       37      9       | 6       237     5       | 1237    1247    47      |
| 5       4       2       | 378     1       378     | 37      9       6       |
| 16      37      16      | 4       2379    2379    | 8       27      5       |
------------------------------------------------------------------------------|
| 146#    2       167     | 37      347#    3467    | 9       5       8       |
| 3       89      48      | 2       5       49      | 76      76      1       |
| 69      5       76      | 1       789     6789    | 4       3       2       |
------------------------------------------------------------------------------|



# is finned x-wing on 4,  takes out 4 in r3c6
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Dec 05, 2007 9:12 pm    Post subject: Reply with quote

so the UR takes out the 6's in r7c13 ???

then if that is the case, there is an x-wing on 4 that takes out a 4 in r2c8
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Wed Dec 05, 2007 9:36 pm    Post subject: Reply with quote

ravel wrote:
The point of this UR type 2 is, that in one line (row or column) you only have the 2 numbers and in the other line a strong link for one number. Then you can eliminate the other number from the second line.


That is a VERY useful rule. I'll remember it.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Dec 05, 2007 9:49 pm    Post subject: Reply with quote

Thanks, but i am not sure now, if this isn't type 4. Anyway you can use the same reasoning for all types, that make eliminations of the UR candidates themselves (e.g. type 6).
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Wed Dec 05, 2007 10:29 pm    Post subject: Reply with quote

storm_norm wrote:
so the UR takes out the 6's in r7c13 ???

then if that is the case, there is an x-wing on 4 that takes out a 4 in r2c8


Code:
.------------------.------------------.------------------.
| 7     689   5    | 389   348   1    | 26    246   49   |
| 2     189   48   | 789   6     478  | 5     147   3    |
| 49    16    3    | 5     247   247  | 16    8     479  |
:------------------+------------------+------------------:
| 8     37    9    | 6     237   5    | 1237  1247  47   |
| 5     4     2    | 378   1     378  | 37    9     6    |
| 16    37    16   | 4     2379  2379 | 8     27    5    |
:------------------+------------------+------------------:
| 146   2     167  | 37    347   3467 | 9     5     8    |
| 3     89    48   | 2     5     49   | 67    67    1    |
| 69    5     67   | 1     789   6789 | 4     3     2    |
'------------------'------------------'------------------'


I believe this is a Type 3. The technique I learned for this situation was called a "reduced set." One of the two roof cells must be = 4 or 7. These two cells combine with r7c45 to be a de facto 347 triple, thus solving r7c6 = 6. I don't see many of these but they're fun when they do appear.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Dec 05, 2007 11:02 pm    Post subject: Reply with quote

You are right, its also a type 3.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Dec 06, 2007 12:35 am    Post subject: Reply with quote

Re: my comments two posts above: I did not notice at the time that this was a Type 4 with a strong link on 1.
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