The New Sudoku Players' Forum

[jco]

Hello kurbads,

Based on your reply to my post, this is my last message to you
(I really don't like debates).
I am really trying to help, so please read the following with this in mind.

First, it is necessary to really know what a deadly pattern is.
For instance, this is a deadly pattern

Code: Select all

12 21 .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
--------- ----------- ---------
21 .  .  |  12 .  .  |  .  .  .
.  12 .  |  21 .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .

because if this pattern appears in the final configuration of a
puzzle, by exchanging 1 by 2, we get

Code: Select all

21 12 .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
--------- ----------- ---------
12 .  .  |  21 .  .  |  .  .  .
.  21 .  |  12 .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .

and no matter the distribution of the other digits in this final
configuration, the second configuration satisfy the rules of Sudoku
and so we get another solution.
** The patterns that you considered do not have this property (you can check it yourself) **

In what follows I am considering only puzzles with a unique solution.
Why bother to identify a deadly pattern?
It will certainly not appear in the final configuration,
but once you learn to identify them, the reason that they cannot
exist in a puzzle with a unique solution gives a "free" inference
that can be used to eliminate false candidates that otherwise would
take longer to eliminate.

For instance, if you find a state in a puzzle with the following "almost"
deadly pattern (cells marked with *)

Code: Select all

*123 *21 .  |  4-3 .  .  |  .  .  .
 .    .  .  |  .   .  .  |  .  .  .
 .    .  .  |  .   .  .  |  .  .  .
 ---------- ------------ ---------
 *21  .  .  | *12  .  .  |  .  .  .
 .   *12 .  | *213 .  .  |  .  .  .
 .    .  .  |  .   .  .  |  .  .  .

you can eliminate the digit 3 from r1c4 (marked with minus) because although
certainly the deadly pattern will be absent from the final configuration
of the puzzle, we have one key inference:

we must have r1c1=3 or r5c4=3 (or both).
Since the 3 at r1c4 sees both (3)r1c1 and (3)r5c4, is must be false.

From a real puzzle (from the Puzzle section)
----except ---------
Re: One Trick 4
Postby Cenoman » Tue Apr 24, 2018 10:23 pm

Code: Select all

+------------------+------------------+-----------------+
|  3     19   19   |  6    4     2    |  8    7    5    |
|  4     2    6    |  7    58*   58*  |  1    9    3    |
|  7     5    8    |  9    3     1    |  4    2    6    |
+------------------+------------------+-----------------+
|  1     4    7    |  5    2     6    |  3    8    9    |
|  6     8    2    |  3    1     9    |  5    4    7    |
|  9     3    5    |  8    7     4    |  6    1    2    |
+------------------+------------------+-----------------+
| a28    7    19   |  4    6     3    |  29   5    1-8  |
|  258*  19   3    |  12   589   58*  |  7    6    4    |
| b258*  6    4    |  12  b589*  7    |  29   3   c18   |
+------------------+------------------+-----------------+

DP(58)r2c56,b8p68,r89c1 (*) using mixed internal-external 8r7c1==9r9c5
(8)r7c1==(95-8)r9c15 = (8)r9c9 => -8 r7c9; stte
Cenoman
----- end of except --------------
Here we have the a deadly pattern (58)r2c56, r8c16,r9c15. Cenoman used
an external guardian (8)r8c1 and the internal guardian (9)r9c5. At least one of them
must be true: (8)r7c1 or (9)r9c5. If r9c5=9, the only remaining place for 5 in row 9
is at r9c1, but then the only place for 8 at that row is at r9c9, so when r9c5=9 we
must have r9c9=8. Thus, at least of them must be true: (8)r7c1 or (8)r9c9. Since
(8)r7c9 see both, it must be false. So, in Cenoman's solution the DP(58) with external guardian
(9)r7c1 and internal guardian (9)r9c5 were used to infer that 8 is false at r7c9, solving the puzzle.

That's it. This is the use of knowing deadly patterns.
Instead of re-inventing the wheel and trying to come up with all patterns with that key property (exchanging digits lead to another solution), the known patterns are available at the
Sudopedia site (of course threads in the Forum too). Some of the pattern are too complicated
for anyone to remember, but there are many (like the one above) that are
very useful. There are also many types of Deadly Patterns. One of my favourites is the Oddagon,
based on the fact that is impossible for have a loop (in a digit) forming a polygon with an odd
number of sides. See this neat solution using three digits 6 external to the pattern
(the so-called external guardians) that see a common cell causing a key elimination.

Deadly patterns are useful to make key eliminations that many times
enables one to solve quickly a puzzle that would otherwise require
a lot more work. Of course, if one mistakenly thinks that a pattern
is deadly, when it is not (I commented above how one can check this),
this may lead to incorrect eliminations (unless one is lucky) producing
no solution.

Edit: added real example of resolution of a puzzle using a DP.

[RSW]

The definition of a deadly UR pattern is: the same digit pairs in four cells that form the corners of a rectangle, plus they must occupy a total of exactly two boxes. When this condition exists, then these four cells are now completely isolated from the rest of the puzzle and whichever legal arrangement of digits is made, it has no influence on the rest of the puzzle. Likewise, whatever happens in the rest of the puzzle has no influence on the four UR cells.

In your example, the bottom two cells are not in the same row, and because of that, you don't get the isolation from the rest of the puzzle that would exist in a real UR. It doesn't meet the definition of a UR, it's not a UR, and the normal UR elimination rules cannot apply.

----------
Edit:
It was pointed out to me that the OP was using the term "Deadly Pattern", not "Unique Rectangle", so my comments in this post may not be applicable.

Now, I'm trying to think of a 4 cell DP that isn't a UR, but that's an area where I haven't done much research.

[kurbads]

Thank you! Finally!