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Is this a valid DP?

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tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Sat Dec 19, 2009 4:53 am Post subject: Is this a valid DP?

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

Marty R.

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

Posted: Sat Dec 19, 2009 5:59 am Post subject:

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.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Dec 19, 2009 5:07 pm Post subject:

Ted, I believe you'll find your answer here. However, I don't understand how ronk reached his conclusion.

Marty R.

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

Posted: Sat Dec 19, 2009 6:09 pm Post subject:

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

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Dec 19, 2009 9:29 pm Post subject:

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>.

Myth Jellies

Joined: 27 Jun 2006
Posts: 64

Posted: Sun Dec 20, 2009 9:19 am Post subject:

Code:

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.

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Sun Dec 20, 2009 3:15 pm Post subject:

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

Myth Jellies

Joined: 27 Jun 2006
Posts: 64

Posted: Tue Dec 22, 2009 9:19 am Post subject:

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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