dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Deadly Pattern includes solved cells

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Solving techniques, and terminology
View previous topic :: View next topic  
Author Message
keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Sat Mar 20, 2010 8:36 pm    Post subject: Deadly Pattern includes solved cells Reply with quote

I thought of this some time ago, but did not find a useful example until now.
Code:
Puzzle: daj100320A
+-------+-------+-------+
| . . . | 3 . . | . . . |
| . 2 . | . 7 . | . 9 . |
| . . 6 | . . 9 | 2 . . |
+-------+-------+-------+
| 2 . . | 9 . 7 | 8 . . |
| . 9 . | . 5 . | . 7 . |
| . . 3 | 4 . . | . . . |
+-------+-------+-------+
| . . 9 | 2 . . | 7 1 . |
| . 6 . | . 1 . | 9 5 3 |
| . . . | . . . | . 2 4 |
+-------+-------+-------+
After basics:
Code:
+----------------+----------------+----------------+
| 9    1578 1578 | 3    248  1258 | 15   48   6    |
| 1458 2    1458 | 6    7    158  | 3    9    15   |
| 135  135  6    | 15   48   9    | 2    48   7    |
+----------------+----------------+----------------+
| 2    145  145  | 9    6    7    | 8    3    15   |
| 6    9    18   | 18   5    3    | 4    7    2    |
| 1578 1578 3    | 4    28   128  | 15   6    9    |
+----------------+----------------+----------------+
| 45   45   9    | 2    3    6    | 7    1    8    |
| 78   6    2    | 78   1    4    | 9    5    3    |
| 1378 1378 178  | 578  9    58   | 6    2    4    |
+----------------+----------------+----------------+
(There is a Type 6 UR 28 in R16C56 that takes out 8 in R1C6, but let's pretend we missed that.)

After the Type 1 UR 48 in R13C58 we get to:
Code:
+----------------+----------------+----------------+
| 9    578  57   | 3    2    18   | 15   4    6    |
| 458  2    45   | 6    7    18   | 3    9    15   |
| 13   13   6    | 5    4    9    | 2    8    7    |
+----------------+----------------+----------------+
| 2    145  145  | 9    6    7    | 8    3    15   |
| 6    9    8    | 1    5    3    | 4    7    2    |
| 157  157  3    | 4    8    2    | 15   6    9    |
+----------------+----------------+----------------+
| 45   45   9    | 2    3    6    | 7    1    8    |
| 78   6    2    | 78   1    4    | 9    5    3    |
| 1378 1378 17   | 78   9    5    | 6    2    4    |
+----------------+----------------+----------------+
Note the potential 28 Deadly Pattern (DP) in R16C56. R1C6 cannot be 8, and the puzzle is solved.

Note that the potential DP cannot include any cells whose values are given as initial clues. Also, the DP rectangle must be within two boxes (not four).

How common is this? I have no idea, since I have never looked for it. But, consider the following:
Code:
+-----------+-----------+-----------+
|  .  .  .  |  X  .  *  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  Y  .  X  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
X and Y are solved cells whose values are not given as initial clues. Cell * cannot contain Y.

It seems to me this must be extremely common. In practice, after you do the basics, it may not be that common or useful, I don't know.

(Or, everyone knows this, and I am just having an afternoon with stupid. But, the example puzzle is a long slog (two more UR's and an X-wing and a BUG+1) without this DP elimination.)

Keith
Back to top
View user's profile Send private message
wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Sat Mar 20, 2010 11:18 pm    Post subject: Reply with quote

I have seen it mentioned before but never found a puzzle that I used it in.

http://www.sudoku.com/boards/viewtopic.php?p=22180#22180

hobiwan uses "avoidable rectangles" in his solver. ( Hudoku )

http://www.sudopedia.org/wiki/Avoidable_Rectangle
Back to top
View user's profile Send private message
wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Sat Mar 20, 2010 11:30 pm    Post subject: Reply with quote

Using hobiwan's solver / generator I made this one.

Code:
. . 7|2 5 .|. 8 .
. 3 .|9 . .|. . .
. 2 .|. . .|. 4 5
-----+-----+-----
3 5 6|8 . .|. . .
. . .|. 3 .|. . .
. . .|. . 2|3 5 6
-----+-----+-----
1 9 .|. . .|. 2 .
. . .|. . 3|. 6 .
. 4 .|. 8 9|1 . .


Your shown technique is the "easiest" last hard step. Very Happy
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Sun Mar 21, 2010 2:14 am    Post subject: Reply with quote

Wapati,

Thank you. I will study this further.

Keith
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Sun Mar 21, 2010 2:51 am    Post subject: Reply with quote

wapati wrote:
Using hobiwan's solver / generator I made this one.

Code:
. . 7|2 5 .|. 8 .
. 3 .|9 . .|. . .
. 2 .|. . .|. 4 5
-----+-----+-----
3 5 6|8 . .|. . .
. . .|. 3 .|. . .
. . .|. . 2|3 5 6
-----+-----+-----
1 9 .|. . .|. 2 .
. . .|. . 3|. 6 .
. 4 .|. 8 9|1 . .


Your shown technique is the "easiest" last hard step. Very Happy
After a 58 UR, this puzzle becomes:
Code:
+-------------+-------------+-------------+
| 4   6   7   | 2   5   1   | 9   8   3   |
| 5   3   8   | 9   467 467 | 267 17  12  |
| 9   2   1   | 3   67  8   | 67  4   5   |
+-------------+-------------+-------------+
| 3   5   6   | 8   19  47  | 27  179 124 |
| 2   17  49  | 6   3   5   | 8   179 14  |
| 8   17  49  | 47  19  2   | 3   5   6   |
+-------------+-------------+-------------+
| 1   9   3   | 47  467 467 | 5   2   8   |
| 7   8   5   | 1   2   3   | 4   6   9   |
| 6   4   2   | 5   8   9   | 1   3   7   |
+-------------+-------------+-------------+

There is a 78 DP in R68C12. R6C2 must be 1. Laughing Laughing

Keith
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Sun Mar 21, 2010 3:11 am    Post subject: Reply with quote

If I may paint with a broad brush:

"Basic" techniques use solved cells to infer values in unsolved cells.

"Advanced" techniques use unsolved cells to infer values in other unsolved cells. (i.e., use "pencil marks".)

If you accept that characterization, the current discussion is about a basic technique, perhaps lost in the clutter of the discussion of advanced techniques.

Just looking at the simple pattern:
Code:
+-----------+-----------+-----------+
|  .  .  .  |  X  .  *  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  Y  .  X  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
I have to believe it is quite common.

(As Wapati's links show, the observation of this pattern is not new.)

Keith
Back to top
View user's profile Send private message
Marty R.



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

PostPosted: Sun Mar 21, 2010 5:05 am    Post subject: Reply with quote

Quote:
There is a 78 DP in R68C12. R6C2 must be 1.

Keith, this is a pretty interesting concept. I didn't play this particular puzzle, but can these DPs come up and be used to solve a cell that wasn't previously solvable by a more conventional DP pattern?
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Sun Mar 21, 2010 3:16 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:
There is a 78 DP in R68C12. R6C2 must be 1.

Keith, this is a pretty interesting concept. I didn't play this particular puzzle, but can these DPs come up and be used to solve a cell that wasn't previously solvable by a more conventional DP pattern?
I believe the answer is yes. But, be careful you are not including an initial cell in the DP!

Keith
Back to top
View user's profile Send private message
wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Mon Mar 22, 2010 3:39 pm    Post subject: Reply with quote

They are pretty rare in useful form. I leave out ones where BUG+1 is also a one-step. That is the most common time to find them because there are the most solved cells.

Of the ones I have found (all type 1, equivalent to UR1, easy) they all follow, and use at least one corner cell as, a UR1.

..67......7..513.....2...876941....5...4.7...7....649394...2.....391..4......45.. (3/4)

.3.24.....1.98.2....7...58.......17....738....78.......26...8....4.53.2.....92.5.
(1/7)

68...........9.......548.67.57..61.4.1.....7.4.23..85.37.469.......1...........96
( 2 / 8 )

...312.5.2..5...3.1.........8.934..64.......86..128.4.........9.6...5..4.9.681...
(4/6)

7.46......6.41...9.1....6.....85.....89...47.....42.....2....9.3...26.1......38.4
(1/5)

5.6.2........7.68......6.2......7.648.31649.776.9......9.2......18.4........8.3.1
(3/4)

9....76......6.14....2.87..3.....86...87.64...16.....5..31.5....62.9......76....4
(4/5)

.3.......28.345.......9254.5......27..6...4..72......1.5461.......589.34.......5.
(8/9)

2.15....4..697......4.1.6...1......75..749..16......3...5.6.9......913..3....57.6
(2/5)

.3......5....5..861..84.2...1...5.7...72346...5.7...9...1.86..757..9....4......6.
( 4 / 8 )

9....81277.....4...4.....6.....23....8.546.3....97.....3.....1...2.....34513....2
(3/5)
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Thu Mar 25, 2010 3:21 pm    Post subject: Reply with quote

Purely anecdotally, I started looking for URs with one solved square about 2 years ago after I stumbled across one in a puzzle I was doing.

I have only seen another one since so concluded, that they were rare..........
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Solving techniques, and terminology All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group