Type 3 Unique Rectangles - Hidden Subsets?

Advanced methods and approaches for solving Sudoku puzzles

Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby daj95376 » Fri Apr 01, 2011 1:17 am

ronk wrote:Before I continue with the others in that post, would someone please confirm? daj95376?

Ron,

I don't have a problem with your examples for UR+2kx. Everything seems in line with Mike Barker's statement.

Before you continue with the other definitions, would you please tell me where the UR+2kx pattern exists in Mike Barker's first "zoo" entry for this elimination pattern? Remember, it must crack the puzzle.

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

 +--------------------------------------------------------------+
 |  1     2     3     |  9     5     67    |  4     8     67    |
 |  69    468   46    |  1     378   2367  |  237   5     679   |
 |  569   568   7     |  4     38    236   |  23    269   1     |
 |--------------------+--------------------+--------------------|
 |  57    57    8     |  3     1     9     |  6     4     2     |
 |  36    36    9     |  2     4     8     |  1     7     5     |
 |  4     1     2     |  7     6     5     |  9     3     8     |
 |--------------------+--------------------+--------------------|
 |  8     67    1     |  5     9     4     |  27    26    3     |
 |  367   3467  46    |  8     2     1     |  5     69    679   |
 |  2     9     5     |  6     37    37    |  8     1     4     |
 +--------------------------------------------------------------+
 # 43 eliminations remain

Regards, Danny
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Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby ronk » Fri Apr 01, 2011 1:49 am

daj95376 wrote:Before you continue with the other definitions, would you please tell me where the UR+2kx pattern exists in Mike Barker's first "zoo" entry for this elimination pattern? Remember, it must crack the puzzle.

Code: Select all
 +--------------------------------------------------------------+
 |  1     2     3     |  9     5     67    |  4     8     67    |
 |  69    468   46    |  1     378   2367  |  237   5     679   |
 |  569   568   7     |  4     38    236   |  23    269   1     |
 |--------------------+--------------------+--------------------|
 |  57    57    8     |  3     1     9     |  6     4     2     |
 |  36    36    9     |  2     4     8     |  1     7     5     |
 |  4     1     2     |  7     6     5     |  9     3     8     |
 |--------------------+--------------------+--------------------|
 |  8     67    1     |  5     9     4     |  27    26    3     |
 |  367   3467  46    |  8     2     1     |  5     69    679   |
 |  2     9     5     |  6     37    37    |  8     1     4     |
 +--------------------------------------------------------------+
 # 43 eliminations remain

Thanks for the response. As to your question, UR(36)r58c12 sis: (4)r8c2, (7)r8c2, (7)r8c1

(4|7)r8c2 =UR= (7)r8c1 - (7=36)als:r75c2 ==> r8c2<>36, singles follow

Note the ALS still works with r7c2=367.
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Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby keith » Fri Apr 01, 2011 4:16 am

Wow! A zombie thread comes back to life. I had forgotten how much good stuff is here.

I sent Jason a donation for preserving this.

The downside is, you all still have to put up with me.

Keith :P
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Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby daj95376 » Fri Apr 01, 2011 2:59 pm

ronk wrote:
Code: Select all
 +--------------------------------------------------------------+
 |  1     2     3     |  9     5     67    |  4     8     67    |
 |  69    468   46    |  1     378   2367  |  237   5     679   |
 |  569   568   7     |  4     38    236   |  23    269   1     |
 |--------------------+--------------------+--------------------|
 |  57    57    8     |  3     1     9     |  6     4     2     |
 |  36    36    9     |  2     4     8     |  1     7     5     |
 |  4     1     2     |  7     6     5     |  9     3     8     |
 |--------------------+--------------------+--------------------|
 |  8     67    1     |  5     9     4     |  27    26    3     |
 |  367   3467  46    |  8     2     1     |  5     69    679   |
 |  2     9     5     |  6     37    37    |  8     1     4     |
 +--------------------------------------------------------------+
 # 43 eliminations remain

Thanks for the response. As to your question, UR(36)r58c12 sis: (4)r8c2, (7)r8c2, (7)r8c1

(4|7)r8c2 =UR= (7)r8c1 - (7=36)als:r75c2 ==> r8c2<>36, singles follow

Note the ALS still works with r7c2=367.

Thanks for your UR interpretation. I agree that it works. It just didn't work with my interpretation of Mike's definition.

The point being, I gave up on trying to interpret/use Mike Barker's UR types and definitions a long time ago.

Regards, Danny

This reminds me of a thread a long time ago where the topic of URs was revived. I (basically) asked "What's allowed and not allowed when working with a UR". Ruud's reply was (basically), "Everything is allowed". Later, and after seeing many URs used in solutions by others, I've come to accept Ruud's statement!
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Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby daj95376 » Fri Apr 01, 2011 6:51 pm

Sometimes, I need to work out what's really happening.

Code: Select all
 |-----------+-----------+-----------|
 |  . ab  .  |  . ab  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  | one possible UR+2kx configuration
 |  ? abx ?  |  ? abY ?  |  ?  ?  ?  | "Y" contains at least one candidate other than "x"
 |-----------+-----------+-----------|

Code: Select all
 |-----------+-----------+-----------|
 |  . a   .  |  .  b  .  |  .  .  .  |
 |  %  %  %  |  .  .  .  |  .  .  .  | after "abY" set to "a"
 |  *  bx *  |  # a   #  |  *  *  *  |
 |-----------+-----------+-----------|

In order to force a UR, "x" must be eliminated in cell "bx". If a (#) cell contain "ax|bx|abx", then "ab" can be eliminated from "abY". Otherwise, if a (*) cell contains "ax", then "a" can be eliminated from "abY". What's not addressed is the possibility of "ax" in a (%) cell.

Regards, Danny
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Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby ronk » Sat Apr 02, 2011 4:09 pm

daj95376 wrote:
Code: Select all
 |-----------+-----------+-----------|
 |  . a   .  |  .  b  .  |  .  .  .  |
 |  %  %  %  |  .  .  .  |  .  .  .  | after "abY" set to "a"
 |  *  bx *  |  # a   #  |  *  *  *  |
 |-----------+-----------+-----------|

In order to force a UR, "x" must be eliminated in cell "bx". If a (#) cell contain "ax|bx|abx", then "ab" can be eliminated from "abY". Otherwise, if a (*) cell contains "ax", then "a" can be eliminated from "abY". What's not addressed is the possibility of "ax" in a (%) cell.

Agreed. Backtesting to see what produces an unavoidable set is a great way to make sure all "bases are covered." I'll adopt your illustration method to reduce my [edit: twelve] non-isomorphic illustrations to two: 1) with the two "ab" cells in the same line, and 2) with the "ab" cells in the same box ... and then revise my earlier post.

After that? Well, now that I've read more of this 5-yr old thread, I think we may mostly be rehashing old stuff, so not sure I'll continue.
Last edited by ronk on Mon Apr 04, 2011 1:40 pm, edited 1 time in total.
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Postby ronk » Mon Apr 04, 2011 1:39 pm

OK, one more time, and hopefully the last for "UR+2kx" and "UR+2kd".

In May 2006, Mike Barker here wrote:Obviously the definitions can apply with "a" and "b" switched or with "x", "Y", etc switched.

--- UR+2kx: two cells in a line, one with an extra candidate, "x", and one with at least one other extra different candidate, "Y", plus "(b)(a)x" common to "abx" which can contain “a” and which can also contain "b" if common to the "ab" which is in line with "abY" => "a" can be removed from "abY".
Code: Select all
ab     ab         
abx    abY  (b)(a)x

--- UR+2kd: two diagonal cells one with an extra candidate, "x", and one with at least one other extra different candidate, "Y", plus "(a)(b)x" common to "abx" which can contain “b” and which can also contain "a" if common to "abY" => "a" can be removed "abY".
Code: Select all
ab     abY       
abx    ab   (a)(b)x


Adopting daj95376's illustration style above, I ended up with the three illustrations below that paint a much clearer picture IMO.

Code: Select all
In the following:
 "a", "b" and "x" represent a single candidate, and
 "Y" represents at least one candidate other than "x", but may include "x"
 "a" and "b" may be swapped.

Code: Select all

 --- UR+2kx Fig. 1 of 2:
 . ab  . | . ab  .  | .  .  .
 *  *  * | .  .  .  | .  .  .
 * abx * | # abY #  | *  *  *
---------+----------+---------
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
---------+----------+---------
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
With "ax" in any of the "*" cells, candidate "a" may be eliminated from the "abY" cell.
With "ax" or "bx" or "abx" in either of the "#" cells, both candidates "a" and "b" may be eliminated from the "abY" cell.


 --- UR+2kx Fig. 2 of 2:
 . ab  . | * abx *  | *  *  *
 .  .  . | *  *  *  | .  .  .
 . ab  . | # abY #  | .  .  .
---------+----------+---------
 .  .  . | .  *  .  | .  .  .
 .  .  . | .  *  .  | .  .  .
 .  .  . | .  *  .  | .  .  .
---------+----------+---------
 .  .  . | .  *  .  | .  .  .
 .  .  . | .  *  .  | .  .  .
 .  .  . | .  *  .  | .  .  .
With "ax" in any of the "*" cells, candidate "a" may be eliminated from the "abY" cell.
With "ax" or "bx" or "abx" in either of the "#" cells, both candidates "a" and "b" may be eliminated from the "abY" cell.

Code: Select all
 --- UR+2kd:
 * abx * | # ab  #  | *  *  *
 *  *  * | .  .  .  | .  .  .
 # ab  # | . abY .  | .  .  .
---------+----------+---------
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
---------+----------+---------
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
 .  *  . | .  .  .  | .  .  .
With "bx" in any of the "*" cells, candidate "a" may be eliminated from the "abY" cell.
With "ax" or "bx" or "abx" in any of the "#" cells, both candidates "a" and "b" may be eliminated from the "abY" cell.
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Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby daj95376 » Sun Apr 10, 2011 7:44 pm

An interesting use of the UR+2kx logic -- 2x applications using the same "abY" but different cells for "ax" and "bx".

Second of Mike Barker's "zoo" puzzles for UR+2kx:

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

 r8c2=1  r9c3=8  r9c2=3  =>  DP
 r8c2=3  r5c2=8  r9c2=1  =>  DP
 +------------------------------------------------------+
 |  1    2     9    |  3    6    5    |  4    7    8    |
 |  7    4     3    |  2    1    8    |  6    5    9    |
 |  8    6     5    |  4    9    7    |  3    1    2    |
 |------------------+-----------------+-----------------|
 |  5    7     6    |  8    3    4    |  2    9    1    |
 |  23  @38    28   |  1    7    9    |  5    6    4    |
 |  49   19    14   |  6    5    2    |  8    3    7    |
 |------------------+-----------------+-----------------|
 |  29   59    27   |  57   4    6    |  1    8    3    |
 |  34  *13+5  147  |  57   8   *13   |  9    2    6    |
 |  6   *13+8 $18   |  9    2   *13   |  7    4    5    |
 +------------------------------------------------------+
 # 21 eliminations remain
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Re: Type 3 Unique Rectangles - Hidden Subsets?

Postby ronk » Mon Apr 11, 2011 12:48 am

daj95376 wrote:An interesting use of the UR+2kx logic -- 2x applications using the same "abY" but different cells for "ax" and "bx".

Yes, it is interesting. My solver finds r8c2<>1 because of strong link tests (3r9) that are made first, and then the AUR is destroyed. I could alter the order of some uniqueness techniques or introduce "batch solving", I suppose, but I'm doing very little coding these days.
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