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Is this a valid DP?

 
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tlanglet



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

PostPosted: Sat Dec 19, 2009 4:53 am    Post subject: Is this a valid DP? Reply with quote

The following code is after basics for daj,s puzzle NR 09/12/18 (A).
Code:
 *--------------------------------------------------------------------*
 | 6      149    8      | 3      7      1459   | 15     459    2      |
 | 12479  12479  149    | 6      8      12459  | 3      459    1457   |
 | 12479  3      5      | 129    14     1249   | 6      8      147    |
 |----------------------+----------------------+----------------------|
 | 5      149    149    | 7      3      8      | 19     2      6      |
 | 8      6      3      | 125    9      12     | 4      7      15     |
 | 27     27     19     | 4      15     6      | 159    3      8      |
 |----------------------+----------------------+----------------------|
 | 149    1459   7      | 159    2      149    | 8      6      3      |
 | 49     8      2      | 59     6      3      | 7      1      45     |
 | 3      145    6      | 8      145    7      | 2      45     9      |
 *--------------------------------------------------------------------*


A type 3 UR 27 exists in r26c12 forming a pseudocell <149> which, in conjunction with the <149>s in r1c2 & r2c3, eliminates <149> in r3c1. Cleanup then leaves this code:
Code:
*-----------------------------------------------------------*
 | 6     149   8     | 3     7     145   | 15    459   2     |
 |a149   27   b149   | 6     8     1245  | 3     459   1457  |
 | 27    3     5     | 129   14    1249  | 6     8     147   |
 |-------------------+-------------------+-------------------|
 | 5    c149  d149   | 7     3     8     | 19    2     6     |
 | 8     6     3     | 125   9     12    | 4     7     15    |
 | 27    27    19    | 4     15    6     | 159   3     8     |
 |-------------------+-------------------+-------------------|
 |e149  f1459  7     | 159   2     149   | 8     6     3     |
 | 49    8     2     | 59    6     3     | 7     1     45    |
 | 3     145   6     | 8     145   7     | 2     45    9     |
 *-----------------------------------------------------------*

Now, look at cells abcdef in r247c123. Five of the six cells contain the digits <149>; the remaining cell, f, contains <1459>.

Is this a valid DP? If so, what digits are involved? My "mostly mechanical" understanding of a Deadly Pattern does not cover this condition. If I treat this situation as a type 1 condition and force r7c2=5, it is valid (according to Simple Sudoku).

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sat Dec 19, 2009 5:59 am    Post subject: Reply with quote

Code:

+-------------+-------+-------+
| .   .   .   | . . . | . . . |
| 149 .   149 | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+
| .   149 149 | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+
| 149 149 .   | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+

Play this puzzle online at the Daily Sudoku site
My uninformed opinion says it's not a DP because in each box, column or row you have two cells involved but three numbers in each of those cells. But let's wait for someone more knowledgeable to chime in.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Dec 19, 2009 5:07 pm    Post subject: Reply with quote

Ted,

I believe you'll find your answer here.

However, I don't understand how ronk reached his conclusion.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sat Dec 19, 2009 6:09 pm    Post subject: Reply with quote

For those of us who are dense and have difficulty with diagrams, what is Ronk's answer?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Dec 19, 2009 9:29 pm    Post subject: Reply with quote

Marty R. wrote:
For those of us who are dense and have difficulty with diagrams, what is Ronk's answer?

I'm pretty sure he's saying that Ted is correct -- r7c2=5 is needed to break up a layered BUG-Lite in <149>.
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Myth Jellies



Joined: 27 Jun 2006
Posts: 64

PostPosted: Sun Dec 20, 2009 9:19 am    Post subject: Reply with quote

Code:

+-------------+-------+-------+
| .   .   .   | . . . | . . . |
| 149 .   149 | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+
| .   149 149 | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+
| 149 149 .   | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+

This is not a deadly pattern. A couple of placements external to these cells could still let you form a unique solution using only these digits.

For example, this...
Code:

+-------------+-------+-------+
| .   (1) .   | . . . | . . . |
| 149 .   149 | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+
| .   149 149 | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   (9) | . . . | . . . |
+-------------+-------+-------+
| 149 149 .   | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+

...would reduce uniquely to this...
Code:

+-------------+-------+-------+
| .   (1) .   | . . . | . . . |
| 9   .   4   | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+
| .   4   1   | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   (9) | . . . | . . . |
+-------------+-------+-------+
| 1   9   .   | . . . | . . . |
| .   .   .   | . . . | . . . |
| .   .   .   | . . . | . . . |
+-------------+-------+-------+
...and notice that no additional digit, such as a five, is required in those cells.
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tlanglet



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

PostPosted: Sun Dec 20, 2009 3:15 pm    Post subject: Reply with quote

Myth,

Does this pattern still allow me to use strong inferences as needed to prevent a DP? For instance, either r1c2=1 or r8c1=9.
Code:
*-----------------------------------------------------------*
 | 6     (1)49 8     | 3     7     145   | 15    459   2     |
 | 149   27    149   | 6     8     1245  | 3     459   1457  |
 | 27    3     5     | 129   14    1249  | 6     8     147   |
 |-------------------+-------------------+-------------------|
 | 5     149   149   | 7     3     8     | 19    2     6     |
 | 8     6     3     | 12-5  9     12    | 4     7     15    |
 | 27    27    19    | 4     15    6     | 159   3     8     |
 |-------------------+-------------------+-------------------|
 | 149   1459  7     | 159   2     149   | 8     6     3     |
 | 4(9)  8     2     | 59    6     3     | 7     1     45    |
 | 3     145   6     | 8     14-5  7     | 2     45    9     |
 *-----------------------------------------------------------*


(5=1)r6c5 - r9c5 = r7c46 - r7c12 = r9c2 - DP149[(1)r1c2 = (9)r8c1]r247c123 - (9=5)r8c4; r5c4, r9c5<>5 to complete the puzzle.

Ted
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Myth Jellies



Joined: 27 Jun 2006
Posts: 64

PostPosted: Tue Dec 22, 2009 9:19 am    Post subject: Reply with quote

tlanglet wrote:
Myth,

Does this pattern still allow me to use strong inferences as needed to prevent a DP?


Assuming I am interpreting your question correctly, the answer is no. Any strong inference is dependent upon some impossible pattern/situation to be avoided. For example, the two digits in a bivalue cell are strongly linked because a cell with no digits is an impossible situation that has to be avoided. There is no obvious deadly pattern to be avoided that supports your contentions.
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