## UR+2B/2SL

Advanced methods and approaches for solving Sudoku puzzles

### Re: UR+2B/2SL

Ron, Have a good trip. In the meanwhile it's obvious that we have different ideas of what the purpose of the notated chain actually is. For me it's a proof that a sequence of known theorems can be applied that allows a conclusion to be drawn. Being a proof, the facts it uses must be open to scrutiny which requires the pencil marked grid to be available. For example without the grid, readers can't confirm that every strong inference in a chain is actually sound.

OK so the chain must provide an unambiguous statement when it is read in conjunction with the grid, but how this is done is merely a question of style.

You criticised my chain (6=23)r56c6 -[UR]- (23=9)r56c8 - (9=3)r6c7 => r6c6 <> 3

saying (6)r56c6 was ambiguous. But using the chain and grid in combination that's not so â€“ the chain asserts that the 6 in r56c6 and (3)r6c7 can't both be false. It takes a millisecond or so to see from the grid that the 6 is in r6c6 which therefore can't hold 3.

You then wrote a preferred chain: r3c9 =4= r3c7 -4- r7c7 =4= r7c1 -4- als:[r34569c1 =4|5= r3c1] = r3c9 => r3c9<>5

which I criticised because it didn't list the locked candidates in the ALS that you consider unimportant. But, in comparison, the reader must count the 5 cells listed and then mentally identify and accumulate the 4 locked candidates to confirm the strong inference between 4 and 5 in those cells â€“ a considerably longer mental check than the one you objected to, and which would have been easier if a checklist the locked candidates was provided.

The fact is that with the grid both chains provide sufficient information, and without it neither of them does. What is important or not in the chain notation are consequently matters of personal preference. (In fact when there are options regarding the particular instances of a candidate in a group node being used I do split them out as you would like.)

The Eureka notation was developed to try to gain a uniformity of style between different authors as a time saving measure in absorbing each others work. Every one of its components is a compromise â€“ for example it would be far more concise to use letters and numbers to index the cells. Consequently every new author has their own personal way of improving it (including stripping out all white space).

As our community is composed of a number of strong minded individuals who believe that the rest of the regiment should fall in step with them, chaos reigns. All I can say is there must be a prospect of some major benefit to me before I'm prepared to invest time understanding yet another notation system and I suspect others feel the same way.

Aran when our reading is interrupted we know roughly whereabouts along the length of a line we were and use the spaces as milestones to quickly return there. (There's been a mass of work done on how our brains - rather than your program - process written material.)
David P Bird
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### Re: UR+2B/2SL

David
If as you say there are good pedagogical reasons for the spacing that you suggest, then why not restrict the spacing to articles, solutions etc intended to be educational ?
The experienced solver will usually be seeking to maximally streamline his thought and presentation and these extra spaces will run counter to that.
In passing, such streamlining involves elimination of any symbols which make no useful contribution such as unnecessary brackets, and pointless colons (eg als:).
The experienced reader can read a chain without having to consult the grid ; if he chose, he could read the chain sans grid, then look at the grid to validate the elimination. I agree that he probably would consult the grid en route, but that consultation would not be systematic at each "white space". So those spaces won't reflect reality, and to the extent may be dys-informational.
aran

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### Re: UR+2B/2SL

Aran wrote: If as you say there are good pedagogical reasons for the spacing that you suggest, then why not restrict the spacing to articles, solutions etc intended to be educational ?

Words flail me. If you had read this thread from the beginning you'd appreciate why I think we should avoid elitist attitudes and consider all our contributions to be educational.
David P Bird
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### Re: UR+2B/2SL

David P Bird wrote:Words flail me.

Good heavens...I hadn't imagined that my-not-intended-to-be-elitist remarks would have such an effect.
aran

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### Re: UR+2B/2SL

David P Bird wrote:
ronk wrote:
David P Bird wrote:But the same type of ambiguity often exists regarding the location of linking candidates in an ALS where it seems to be generally acceptable.

I can't believe you're telling me the "Ambiguity in one place justifies ambiguity elsewhere."

I thought I made myself clear â€“ using the chain and the grid in combination there is no ambiguity.

I reject the notion that I should have a grid to understand a chain, especially a simple chain, and the AUR chain that triggered this discussion is certainly simple.

Davd P Bird wrote:(6=23)r56c6 -[UR]- (23=9)r56c8 - (9=3)r6c7 => r6c6 <> 3

In my mind's eye, this looks like ...
Code: Select all
` .  .  .  | .  .  .  | .   .   .   .  .  .  | .  .  .  | .   .   .   .  .  .  | .  .  .  | .   .   .  ----------+----------+------------  .  .  .  | .  .  .  | .   .   .   .  .  .  | .  . 23+6| .  23+9 .   .  .  .  | .  . 23+6| 39 23+9 .  ----------+----------+------------  .  .  .  | .  .  .  | .   .   .   .  .  .  | .  .  .  | .   .    .   .  .  .  | .  .  .  | .   .   .  `

... for which the stated exclusion r6c6<>3 is obviously invalid. So your chain above is not just ambiguous, it's erroneous IMO. And this in order to include the weak link in the notation? The "strong inference notation" ...

(6)r6c6 =[however you wish to write the causal UR]= (9)r6c8 - (9=3)r6c7 => r6c6 <> 3

... doesn't have this problem.

David P Bird wrote:Now take your preferred chain:

r3c9 =4= r3c7 -4- r7c7 =4= r7c1 -4- als:[r34569c1 =4|5= r3c1] = r3c9 => r3c9<>5

It still doesn't stand alone. How does this indicate which digits are locked in the ALS? How can readers confirm that the ALS is good without consulting the grid?

ronk wrote:When there is no continuous loop,there is ultimately no locked set ... and the other digits of the ALS are unimportant.

My reply was apparently too vague, even for two experienced sudokuists, so I'll clarify.

From the notation, the 5-cell ALS holds digits <abcd45>. If the loop is continuous, the cells of the ALS will ultimately contain either <abcd4> or <abcd5>, and digits <abcd> must be known to identify potential exclusions.

However, if the loop is not continuous, the cells of the ALS will ultimately contain <bcd45>, <acd45>, <abd45>, <abc45>, <abcd4> or <abcd5>. No digit is present in all the possibilities, so no exclusions are possible. Hence, the values of <abcd> are unimportant to understanding and using the notation.
ronk
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### Re: UR+2B/2SL

ronk wrote:
Davd P Bird wrote:(6=23)r56c6 -[UR]- (23=9)r56c8 - (9=3)r6c7 => r6c6 <> 3

In my mind's eye, this looks like ...
Code: Select all
`----------+----------+------------  .  .  .  | .  .  .  | .   .   .   .  .  .  | .  . 23+6| .  23+9 .   .  .  .  | .  . 23+6| 39 23+9 .  ----------+----------+------------ `

Ron: I disagree. For your pattern, I would have expected:

(66=23)r56c6 -[UR]- (23=99)r56c8 - (9=3)r6c7 ...

For David's UR, (6=23)r56c6 -[UR]- (23=9)r56c8, I would have expected:

Code: Select all
`----------+----------+------------ .  .  .  | .  .  .  | .   .   . .  .  .  | .  . 23+6| .  23   . .  .  .  | .  . 23  | 39 23+9 .----------+----------+------------`

I would consider: (6=23)r65c6 -[UR]- (23=9)r56c8 - (9=3)r6c7

Code: Select all
`----------+----------+------------ .  .  .  | .  .  .  | .   .   . .  .  .  | .  . 23  | .  23   . .  .  .  | .  . 23+6| 39 23+9 .----------+----------+------------`
daj95376
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### Re: UR+2B/2SL

daj95376 wrote:
ronk wrote:
Code: Select all
`----------+----------+------------  .  .  .  | .  .  .  | .   .   .   .  .  .  | .  . 23+6| .  23+9 .   .  .  .  | .  . 23+6| 39 23+9 .  ----------+----------+------------ `

For your pattern, I would have expected:

(66=23)r56c6 -[UR]- (23=99)r56c8 - (9=3)r6c7 ...

(the closest that I could find to "passed out and fell down")
ronk
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### Re: UR+2B/2SL

Ron, I have been considering the purpose of the notated chain to provide proof that the conclusion drawn is valid. You seem to ignore this role and just concentrate on it being a description of the path taken.

This may be fair enough if you are using a solver which has been thoroughly stress tested and debugged. In that case the locked candidates are unimportant in the ALS as we can rely on the solver to have checked them. But don't you see that in that case we can equally well rely on the solver to have ensured that the linking involving candidates in group nodes are valid. Thatâ€™s the reason I said if one is unimportant so is the other.

ronk wrote:
David P Bird wrote:(6=23)r56c6 -[UR]- (23=9)r56c8 - (9=3)r6c7 => r6c6 <> 3

In my mind's eye, this looks like ...
Code: Select all
` .  .  .  | .  .  .  | .   .   .   .  .  .  | .  .  .  | .   .   .   .  .  .  | .  .  .  | .   .   .  ----------+----------+------------  .  .  .  | .  .  .  | .   .   .   .  .  .  | .  . 23+6| .  23+9 .   .  .  .  | .  . 23+6| 39 23+9 .  ----------+----------+------------  .  .  .  | .  .  .  | .   .   .   .  .  .  | .  .  .  | .   .    .   .  .  .  | .  .  .  | .   .   .  `

... for which the stated exclusion r6c6<>3 is obviously invalid.

Now it appears you want the chain to provide a proof that r6c7 sees each 6 in r56c6. But why? You'll be accepting on trust a heap of strong inferences and ALSs that must have the right number of locked candidates, and yet you pick up on a point that is of no greater or lesser importance to scrutinise. If we trust the solver we know the only 6 in r56c6 must be in r6 otherwise, as you say, the deduction would be erroneous.

My point about the ALS is whether we're sure that abcd are all locked in the five cells. If they aren't these cells can contain both 4 and 5. To validate that we need sight of the grid, when it would be helpful to have the list of the candidates involved.

I beginning to think that this is yet another topic on which we'll never agree.
David P Bird
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### Re: UR+2B/2SL

Ronk
I don't see that your argument stands up :
continuous/discontinuous caracterisation can only be determined at the end of the logical sequence. You appear to say that how you write out a chain reflecting this logic is dependent on the conclusion.
Feedback has its place, just not in sudoku.
aran

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Joined: 02 March 2007

### Re: UR+2B/2SL

David P Bird wrote:I beginning to think that this is yet another topic on which we'll never agree.

Agreed ... so my counterpoints to your last post will remain unsaid.
ronk
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### Re: UR+2B/2SL

I have an answer to that, but I'm not telling you what it is...
aran

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### Re: UR+2B/2SL

surbier wrote:I have coded all URs from this post (Mike Barker, Sat Apr 22, 2006 10:27 pm) and I have been
looking for examples.

Apparently, Mike Barker derived additional patterns to those in the post you referenced. I found these among those in his "zoo" post:

Code: Select all
`#19 UR+2rd67.5.8.9.............3...2.5.......9....4.2...4...1.8...147...3.2...31..49....5...........24..5193.9..4..........3.7..8..7.421....1...5.5..94....28...6..36...2........8.1...51..7.....92........6.....73...94....8..6.742...5....3..4.16...1....5.14..3...........6....845....2.....9..18......9.6....78.5.7..9..372.1...4..4.....2#20 UR+2kx1239........1...5...7........83..64...9..8..5.1..65.3.8...9...3....21.....5...8.412.3..4.87.3....5.8..49.3....6.34..1...1..56......2........6.......8.9........745.2...8.....5...2..7...1...6.......2.938.2......74.58.....1.97....95..6..6...83..4`

There may be others.
daj95376
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### Re: UR+2B/2SL

daj95376 wrote:Apparently, Mike Barker derived additional patterns to those in the post you referenced.

In May 2006, Mike Barker posted an "addendum" here.
ronk
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### Re: UR+2B/2SL

ronk wrote:In May 2006, Mike Barker posted an "addendum".

Thanks Ron for the link. It is very informative!!!
daj95376
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### Re: UR+2B/2SL

surbier wrote:I have coded all URs from (Mike Barker, Sat Apr 22, 2006 10:27 pm) and I have been looking for examples.

In case you aren't aware, Mike posted a number of puzzles in the "zoo" thread. Supposedly, each example in the "zoo" needs only one advanced technique to crack each puzzle. I guess MB doesn't consider an XY-Wing as an advanced technique because some of his puzzles need it along with the use of other basics.

Anyway, I've been running his UR puzzles through my solver. When I reached these puzzles:

--- UR+3C/2SL: both strong links share a node, do not include the bivalue cell and have equal labels => "b" can be removed from "abZ"

Code: Select all
` ab     abX         |        a|     a   |abY-----abZ#22 UR+3C/2SL........8.....863..9.13.4...473........51..9..........62.8...1..78.....5...6258....2.9......46.7....9...43..7.8.....9.4..2.8...5..3.1.....5.......6..89.........37....3..4....2.6.3.1.2.9.........389...3....27.54......5...872....16.....4.......52.1.....8.....3..........626.3..7....52.947..7..3..1..4....6.519..5...4...7.1....`

I was able to duplicate the UR pattern, but I wasn't able to get it to crack the puzzles. Do you get any better results?
daj95376
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