Ambiguous Pairs: A New Basic Strategy?

Advanced methods and approaches for solving Sudoku puzzles

Ambiguous Pairs: A New Basic Strategy?

Postby John Meyer » Wed Jun 11, 2008 11:51 pm

Let me know if you've seen this before but I can't find anything similar and it seems simple enough to be considered a basic strategy. Look at Friday's (6/6/08) Mepham Group sudoku after the basic strategies fail. I have a 5 and 6 in squares A5 and A6 and a 3, 5 and 6 in squares H5 and H6. If the 3 in row H were in H4, H5 and H6 would only have a 5 and 6. Only 5s and 6s in A5, A6, H5 and H6 would lead to an ambiguous situation that would not produce a unique solution. Since the sudoku does have a unique solution H5 or H6 must be a 3. This means that H4 cannot be a 3. Now the sudoku can be solved to completion. I have several more examples with graphics on a Word file I would be glad to send anyone interested. My email address is jmeyer2@knology.net. If you have an archive you might also want to check out The Mepham Group's 1/11/08, 2/29/08, 3/28/08 and 4/25/08 before looking at my examples. 1/11/08 doesn't seem to lead to a solution but is still interesting.
John Meyer
John Meyer
 
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Joined: 11 June 2008

Postby Glyn » Thu Jun 12, 2008 9:45 am

The Mepham group produce a number of different daily puzzles. After a little detective work it seems that you were refering to the Los Angeles Times puzzle 0f 6/6/08 ,which is:
Code: Select all
. 9 .|8 . .|2 1 .
4 6 .|. . .|. . 5
. . 5|. . 1|9 . .
-----+-----+-----
. . 2|. 8 .|. . .
. . .|9 . 7|. . .
. . .|. 2 .|3 . .
-----+-----+-----
. . 3|1 . .|8 . .
9 . .|. . .|. 4 2
. 5 4|. . 8|. 3 .

The point you are refering to is probably something like:
Code: Select all
---------------.----------------.---------------.
| 3    9    7   | 8    *56  *56  | 2    1    4   |
| 4    6    1   | 23    39   29  | 7    8    5   |
| 28   28   5   | 4     7    1   | 9    6    3   |
:---------------+----------------+---------------:
| 17   147  2   | 36    8    346 | 5    9    16  |
| 5    3    6   | 9     1    7   | 4    2    8   |
| 18   148  9   | 56    2    456 | 3    7    16  |
:---------------+----------------+---------------:
| 6    27   3   | 1     4    29  | 8    5    79  |
| 9    17   8   |-3567 *356 *356 | 16   4    2   |
| 127  5    4   | 267   69   8   | 16   3    79  |
'---------------'----------------'---------------'

The elimination of the 3 at r8c4 is fairly commonly called Unique Rectangle Type 2-a or Unique Side.
For more on these have a look here, Standardizing the Uniqueness descriptions...
Glyn
 
Posts: 357
Joined: 26 April 2007

Thanks Glyn

Postby John Meyer » Wed Jun 18, 2008 2:24 am

Thanks Glyn

The unique rectangles are indeed what I'm talking about. I've posted some examples of loops, triples and quads on (I think) the link you supplied above.
John Meyer
 
Posts: 3
Joined: 11 June 2008


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