The New Sudoku Players' Forum

[ArkieTech]

From the One Trick Pony of 4/6/08 I located "what I call and empty rectangle". I don't know how to display my logic

Code: Select all

 *-----------*
 |...|86.|..7|
 |7..|...|.59|
 |...|...|6.4|
 |---+---+---|
 |..3|4..|7..|
 |9..|.3.|..6|
 |..7|..8|2..|
 |---+---+---|
 |3.1|...|...|
 |42.|...|..1|
 |5..|.94|...|
 *-----------*
 *-----------------------------------------------------------------------------*
 | 12      459     459     | 8       6       59      | 13      23      7       |
 | 7       1368    268     | 23      4       123     | 18      5       9       |
 | 128     13589   589     | 23579   1257    123579  | 6       28      4       |
 |-------------------------+-------------------------+-------------------------|
 | 1268    158     3       | 4       125     69      | 7       189     58      |
 | 9       1458    2458    | 257     3       1257    | 45      148     6       |
 | 16      145     7       | 69      15      8       | 2       149     3       |
 |-------------------------+-------------------------+-------------------------|
 | 3       6789    1       | 2567    2578    2567    | 459     4678    58      |
 | 4       2       689     | 3567    578     3567    | 59      678     1       |
 | 5       678     68      | 1       9       4       | 38      3678    2       |
 *-----------------------------------------------------------------------------*
xyz-wing 2-r1c1-1-r3c1-8-r3c8-2=>r3c3<>2 no help
empty rectangle r3c1|r4c1=8
                r3c1=8=>r3c8<>8
                r4c1=8=>r4c89<>8=>r5c8=8=>r3c8<>8


What is the proper notation to show the logic of the empty rectangle?
Is the xyz-wing notation correct?

dan

[daj95376]

My solver's output after SSTS. The Empty Rectangle elimination can always be represented as a Sashimi finned Franken X-Wing, but I often (manually) abbreviate it to just the base sectors -- as added below.

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         XYZ-Wing [r3c1]/[r1c1]+[r3c8]   <> 2    [r3c3]

2-Fish c1b6\r34              fF 011\200  <> 8    [r3c8] -or-
  c1b6   Empty Rectangle                 <> 8    [r3c8] (manually added)


I sometimes think of an Empty Rectangle as grouped Multiple Colors.

P(ink) and G(reen) see each other, so anything that sees B(lue) and A(mber) can be eliminated.

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+-----------------------------------+
|  .  .  .  |  8  .  .  |  .  .  .  |
|  .  8  8  |  .  .  .  |  8  .  .  |
| B8  8  8  |  .  .  .  |  . -8  .  |
|-----------+-----------+-----------|
| G8  8  .  |  .  .  .  |  . P8 P8  |
|  .  8  8  |  .  .  .  |  . A8  .  |
|  .  .  .  |  .  .  8  |  .  .  .  |
|-----------+-----------+-----------|
|  .  8  .  |  .  8  .  |  .  8  8  |
|  .  .  8  |  .  8  .  |  .  8  .  |
|  .  8  8  |  .  .  .  |  8  8  .  |
+-----------------------------------+


[ArkieTech]

daj95376,

Thanks, I am amazed at the number of differing ways to get at the same result in Sudoku

dan

[Mike Barker]

There actually is a notation standard, which is pretty good except that I usually also follow Jeff's modification to keep the ALS together (instead of using a 1|2) and Ron's modification to lose the square braces. The resulting nice loop notation for the empty rectangle would be something like:
r3c8 -8- r3c1=8=r4c1 -8- r4c89=8=r45c8 -8- r3c8 => r3c8<>8

Although I usually shorten it to:
r3c1=8=r4c1 -8- r4c89=8=r45c8 -8- => r3c8<>8

The xy-wing can be notated as:
r3c3 -2- r1c1 -1- ALS:r3c18 -2- r3c3 => r3c3<>2

which I again shorten to:
r1c1 -1- ALS:r3c18 -2- => r3c3<>2

The "ALS:" isn't necessary. Also, it would be nice to show all of the candidates in the ALS (only necessary for continuous loops), but there is not standard for this. I might propose something like:
r1c1 -1- ALS:r3c18n8 -2- => r3c3<>2

[ArkieTech]

Mike Barker,

Thanks, that is exactly what I was looking for. I want a way to record solutions both by solver and manually. I thought doing it the right way might be refreshing.

dan

[daj95376]

There is a notation standard that many have agreed to use in this forum. If you try to use Nice Loop notation in the Eureka forum, they'll run you out of there. So, notation standards are relative!

Note: I fully admit that I have recently chosen contradictory implication chains (CIC) over Nice Loops. I use an abbreviated version of (basic) Eureka notation offline that's almost identical to CICs.

[Mike Barker]

Not only are notation standards relative between forums, but they are not (and should not be) strictly enforced within the forum. To me the idea is to be able to communicate what you are doing. If you want to reach the widest audience then its good to use their languange. Notation standards make this easier for newbies.

I will post with different notation depending on where I am. Here I use nice loop notation, because it is the most common here. On Eureka, I'll use Eureka notation. If someone is new I'll go out of my way to translate what they are saying into the lingua franca. On the other hand, I'll probably skip posts which continue to use a non-standard notation - its just generally not worth the time to do the translation. The choice is up to the submitter.

[Pat]

I have recently chosen contradictory implication chains (CIC) over Nice Loops

hey daj95376, you know i just looked again at Mike Barker's great list of methods -- and i still see no mention of contradictory implication chains

indeed the word "contradict" doesn't appear there at all---

would you care to provide a link?

thanks!

~ Pat

[daj95376]

I have recently chosen contradictory implication chains (CIC) over Nice Loops

hey daj95376, you know i just looked again at Mike Barker's great list of methods -- and i still see no mention of contradictory implication chains

indeed the word "contradict" doesn't appear there at all---

would you care to provide a link?

thanks!

~ Pat

[Edit: Not sure what my point was back then, but I believe that Pat's assessment is correct.]

[Pat]

my use of contradictory was redundant and should have been placed in parentheses. I wanted to emphasise that the initial assertion of my implication-chains would always lead to a contradiction. Thus, any assertion in my implication-chain should always be assumed [?] false ... and save me the => at the end to explicitly say so.

hey daj95376,

i'm not quite sure here but i
think you're referring to a single implication-stream
which loops back to bite its head with a contradiction
-- i.e. a type of "single implication network"

we had a recent discussion on this,
where ronk kindly helped me understand that the single implication-stream
could also be viewed as two implication-streams
( thus making it a forcing chain )

i hope i finally got it straight---