## On the UR+3U/2SL

Advanced methods and approaches for solving Sudoku puzzles

### On the UR+3U/2SL

Hi,

Inpired by discussion in the UR+2B/2SL thread,
I have implemented something like the an incomplete UR deadly pattern.
Where I complete an almost deadly pattern like
Code: Select all
`   ab   abX   abY  aZ`

by the missing b, apply the zoo of UR methods and take b off again.
Endless loops by virtually inserting the 'missing' b into the
grid and eliminate the same b by one of the cannibalistic URs again and again are prevented.

Up to know I found only cases for the UR+3U/2SL, which looked rather suspiceous to me;
either my UR+3U/2SL code misses an elimation, or the UR+3U/2SL pattern provides
more elimations, than given by Mike Barker:

--- UR+3U/2SL: the strong links are disjoint with different labels => "a" can be removed from "abY"

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`     ab-----abX         a         b    abY-----abZ`

I think there are more eliminations available:
Because of the symmetry of the UR+3U/2SL pattern (exchange of labels a and b)
b can be removed from "abY" as well.
surbier
2012 Supporter

Posts: 54
Joined: 06 June 2008

### Re: On the UR+3U/2SL

What I said on the UR+3U/2SL is complete nonsense,
sorry for the noise

Code: Select all
`+--------------------+--------------------+--------------------+|   1     7  #25     |#235     6   23     |   9     4     8    ||   6     3     9    |   7     8     4    | 15      2   15     || 45      8  #24-5   |#25      1     9    |   7     3     6    | +--------------------+--------------------+--------------------+| 479   49    48     | 138     5   37     |   6   18      2    || 57      6     1    | 28      4   27     |   3   58      9    ||   3     2   58     | 18      9     6    |   4     7   15     |+--------------------+--------------------+--------------------+|   2     1     7    |   6     3     5    |   8     9     4    || 48    45      6    |   9     7   18     |   2   15      3    || 89    59      3    |   4     2   18     | 15      6     7    |+--------------------+--------------------+--------------------+UR+3U/2SL (25)[r1c3|r3c4] r3c3<>5but 2 in r3c3 cannot be eliminated`

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`+--------------------+--------------------+--------------------+                  -5-|   1     7  #25     |#235     6   23     |   9     4     8    |              |         |              2         5              |         ||   6     3     9    |   7     8     4    | 15      2   15     || 45      8  #245    |#25      1     9    |   7     3     6    |                  -2-+--------------------+--------------------+--------------------+| 479   49    48     | 138     5   37     |   6   18      2    || 57      6     1    | 28      4   27     |   3   58      9    ||   3     2   58     | 18      9     6    |   4     7   15     |+--------------------+--------------------+--------------------+|   2     1     7    |   6     3     5    |   8     9     4    || 48    45      6    |   9     7   18     |   2   15      3    || 89    59      3    |   4     2   18     | 15      6     7    |+--------------------+--------------------+--------------------+            UR+3U/2SL (25)[r1c3|r3c4]  r3c3<>5 incomplete UR+3U/2SL (25)[r1c3|r3c4]  r1c4<>2`

The second elimination (after re-inserting 5 in 33) is
based on the rotated pattern using the other two strong links.

Nothing actually new
surbier
2012 Supporter

Posts: 54
Joined: 06 June 2008

### Re: On the UR+3U/2SL

Since two of your cells are bivalues <25>, I don't see your example as a UR+3U scenario.

--- UR+2D/1SL: cells with extra candidates diagonal to each other => strong link on "a" removes "a" from "abY" - repeat for each strong link

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` ab     abY | |a |abX     ab`

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` <25> UR+2D/1SL w/SL 5r1  =>  r3c3<>5 <25> UR+2D/1SL w/SL 2r3  =>  r1c4<>2 +-----------------------------------------------------+ |  1    7   *25   | *235  6    23   |  9    4    8    | < SL:5 |  6    3    9    |  7    8    4    |  15   2    15   | |  45   8   *245  | *25   1    9    |  7    3    6    | < SL:2 |-----------------+-----------------+-----------------| |  479  49   48   |  138  5    37   |  6    18   2    | |  57   6    1    |  28   4    27   |  3    58   9    | |  3    2    58   |  18   9    6    |  4    7    15   | |-----------------+-----------------+-----------------| |  2    1    7    |  6    3    5    |  8    9    4    | |  48   45   6    |  9    7    18   |  2    15   3    | |  89   59   3    |  4    2    18   |  15   6    7    | +-----------------------------------------------------+ # 33 eliminations remain`

Using SLs 2c3 and 5r1 :

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` (2)r1c3 = (2-4)r3c3 =UR= (3-5)r1c4 = (5)r1c3 - loop  =>  r1c4<>2; r3c3<>5`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: On the UR+3U/2SL

Since two of your cells are bivalues <25>, I don't see your example as a UR+3U scenario.

Z is optional, It's a UR+3U with Z being {}

UR+2D/1SL: cells with extra candidates diagonal to each other => strong link on "a" removes "a" from "abY" - repeat for each strong link

I fully agree
surbier
2012 Supporter

Posts: 54
Joined: 06 June 2008

### Re: On the UR+3U/2SL

surbier wrote:
Since two of your cells are bivalues <25>, I don't see your example as a UR+3U scenario.

Z is optional, It's a UR+3U with Z being {}

Sorry, but I think the "optional" concept is a bad one. An AUR, and UR for that matter, either has "extra candidates" in one, two, three or all four cells. That's the primary classification property in Mike Barker's name assignments.
ronk
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Joined: 02 November 2005
Location: Southeastern USA

### Re: On the UR+3U/2SL

I didn't like the optional reply either, but I didn't say so because it leaves open for discussion the concept of optional UR values in the UR cells -- as in Myth Jellies' (?) UR Type 1.1 . In Mike Barker's scenarios, "ab" is present in all four UR cells.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: On the UR+3U/2SL

daj95376 wrote:I didn't like the optional reply either, but I didn't say so because it leaves open for discussion the concept of optional UR values in the UR cells -- as in Myth Jellies' (?) UR Type 1.1 . In Mike Barker's scenarios, "ab" is present in all four UR cells.

The UR1.1 and it's brethren have been around a while. Does anyone now use the "optional" term in that context?
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: On the UR+3U/2SL

Z is optional, It's a UR+3U with Z being {}

I will not defend this.

My understanding is, that the zoo of URs is complete in coverage.
In so far it is not necessary to consider the labels for the additional
candidates as optional. Nevertheless, when coding, I allowed for the
'optional' since I was curious. It was not intended to compensate for
missed URs like the UR+2D/2SL which I implemented later and forgot
to activate.
surbier
2012 Supporter

Posts: 54
Joined: 06 June 2008