UR+2B/2SL

Advanced methods and approaches for solving Sudoku puzzles

Re: UR+2B/2SL

Postby David P Bird » Wed Mar 02, 2011 10:56 am

daj95376 wrote:
David P Bird wrote:Thinking about the way to notate URs in AICs, ...

I give the reader credit for finding the UR once I identify the strongly linked candidates and cells.

Code: Select all
<23>UR(6=9)r6c68 - (9=3)r6c7 => r6c6 <> 3

This raises the issue about what level of reader are we writing for. I remember only too well how difficult I found it to penetrate the jargon in the Sudoku forums when I first started. In fact I still have difficulties when I try to follow someone else's methods with terms that have been defined in some far off post. Taken to extremes we end up with posts (such as Carcul's) that only a few can follow.

Verbose notations won't hold up the knowledgeable unduly but will help others follow the implications without having to spend time trying to work them out. If we want to attract new blood, the more crutches we supply to help them make a connection to some half-remembered item the better, but obviously without taking it to extremes.

Looking at the number of times posts are viewed on this forum, there about 10 people who will read a post on the day it's made. After that the numbers crawl up as newcomers and improving players try to pick up on a subject. I think we should try to write and notate for both types of reader. That explains why my posts might appear patronising, and why I often use a term in full first before I switch to its abbreviation.
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Re: UR+2B/2SL

Postby ronk » Wed Mar 02, 2011 12:21 pm

David P Bird wrote:Thinking about the way to notate URs in AICs, perhaps it's better to use the complementary weak inference that opposite sides of the UR can't hold the same digit pair.

Strong (6)r6c6 =[(23)UR:r56c68]= (9)r6c8 - (9=3)r6c7 => r6c6 <> 3

Weak (6=23)r56c6 -[UR]- (23=9)r56c8 - (9=3)r6c7 => r6c6 <> 3

daj95376 wrote:I give the reader credit for finding the UR once I identify the strongly linked candidates and cells.

Code: Select all
<23>UR(6=9)r6c68 - (9=3)r6c7 => r6c6 <> 3

If both strong inferences were "native", the AIC would be ... (6)r6c6 = (9)r6c8 - (9=3)r6c7 => r6c6 <> 3. Including the source of a "derived" strong inference should not change the basic elements of this AIC.
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Re: UR+2B/2SL

Postby David P Bird » Wed Mar 02, 2011 3:05 pm

ronk wrote:
David P Bird wrote:Thinking about the way to notate URs in AICs, perhaps it's better to use the complementary weak inference that opposite sides of the UR can't hold the same digit pair.

Strong (6)r6c6 =[(23)UR:r56c68]= (9)r6c8 - (9=3)r6c7 => r6c6 <> 3

Weak (6=23)r56c6 -[UR]- (23=9)r56c8 - (9=3)r6c7 => r6c6 <> 3

daj95376 wrote:I give the reader credit for finding the UR once I identify the strongly linked candidates and cells.

Code: Select all
<23>UR(6=9)r6c68 - (9=3)r6c7 => r6c6 <> 3

If both strong inferences were "native", the AIC would be ... (6)r6c6 = (9)r6c8 - (9=3)r6c7 => r6c6 <> 3. Including the source of a "derived" strong inference should not change the basic elements of this AIC.

What you say is absolutely right, but I don't get your point. The three chains you quote all notate the source of the derived inferences they use either as
    a) a strong inference that at least one of the UR's disrupting digits must be true
    b) a weak inference that the opposite sides of the rectangle can't hold the same digit pair
The issue is just one of style.
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Re: UR+2B/2SL

Postby ronk » Wed Mar 02, 2011 4:51 pm

David P Bird wrote:What you say is absolutely right, but I don't get your point.
...
The issue is just one of style.

The issue is more than just style. One end of the strong link is, e.g., (6)r6c6 not (6)r56c6. With the latter, the location of digit <6> is ambiguous.

And for daj's (6=9)r6c68 notation, the location of the digits is also ambiguous.
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Re: UR+2B/2SL

Postby David P Bird » Wed Mar 02, 2011 5:42 pm

Ronk, ah now I see what you mean! But the same type of ambiguity often exists regarding the location of linking candidates in an ALS where it seems to be generally acceptable. Our chains can't be read in isolation but need the grid in sight. The grid contents then resolve which cells out of the notated group hold the linking candidate(s).

So to me it does boil back to being a question of style, where I favour what I consider to be easiest on the reader.
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Re: UR+2B/2SL

Postby daj95376 » Wed Mar 02, 2011 6:14 pm

ronk wrote:And for daj's (6=9)r6c68 notation, the location of the digits is also ambiguous.

I take exception to your implication!!! Everone else feels that they must list cells in sequential order. ***I*** list cells in the order they are needed/implied.

In this case, I indicated a strong link between <6> and <9>, and I also indicated cells r6c6 and r6c8, in that order. So, since I wrote the chain, you can be guaranteed that it's (6)r6c6 = (9)r6c8 due to the <23> UR.

If the location of the candidates were reversed, I would have written (6=9)r6c86.

Maybe you recall this post of mine from the DailySudoku Forum (where I missed the <15> hidden pair link in [c1]):

Code: Select all
 (4)r3c9 = r3c7|r8c9 - r7c7 = r7c1 - (4=5)r54693c1  =>  r3c9<>5
 +-----------------------------------------------------------------------------------------+
 |  8        345      1        |  235      2345     9        |  6        235      7        |
 |  9        345      2        |  3567     34567    356      |  1        35       8        |
 | e356      7        36       |  8        1235     1235     | b234      9       a24-5     |
 |-----------------------------+-----------------------------+-----------------------------|
 | e2367     1        5        |  236      236      4        |  23789    78       269      |
 | e2346     239      3469     |  12356    8        7        |  23       235      1256     |
 | e2367     8        367      |  9        12356    12356    |  237      4        1256     |
 |-----------------------------+-----------------------------+-----------------------------|
 | d12457    259      8        |  1257     12579    125      | c2479     6        3        |
 |  123457   2359     3479     |  123567   1235679  12356    |  24789    78      b249      |
 | e237      6        379      |  4        2379     8        |  5        1        29       |
 +-----------------------------------------------------------------------------------------+
 # 143 eliminations remain

Basics complete the puzzle.

Where the ALS represents your "native" statement of (4)r5c1 = (5)r3c1.

Regards, Danny
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Re: UR+2B/2SL

Postby ronk » Thu Mar 03, 2011 11:49 am

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."

daj95376 wrote:Everone else feels that they must list cells in sequential order. ***I*** list cells in the order they are needed/implied.

In this case, I indicated a strong link between <6> and <9>, and I also indicated cells r6c6 and r6c8, in that order. So, since I wrote the chain, you can be guaranteed that it's (6)r6c6 = (9)r6c8 due to the <23> UR.

If the location of the candidates were reversed, I would have written (6=9)r6c86.

I considered that possibility, but thought it was consicion gone too far. Still do.

daj95376 wrote:Maybe you recall this post of mine from the DailySudoku Forum (where I missed the <15> hidden pair link in [c1]):

(4)r3c9 = r3c7|r8c9 - r7c7 = r7c1 - (4=5)r54693c1 => r3c9<>5
...
Where the ALS represents your "native" statement of (4)r5c1 = (5)r3c1.

I would rather read ...

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

That's only half true. I'd actually rather read ...

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

[edit: correct last weak link in nice loop]
Last edited by ronk on Wed Mar 09, 2011 10:55 am, edited 1 time in total.
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Re: UR+2B/2SL

Postby daj95376 » Thu Mar 03, 2011 12:02 pm

ronk wrote:I considered that possibility, but thought it was concision gone too far.

Or its cousin ... OCD. _ :) _
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Re: UR+2B/2SL

Postby David P Bird » Thu Mar 03, 2011 12:48 pm

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 – using the chain and the grid in combination there is no ambiguity. Consequently we should consider the processes that readers have to follow to understand the inferences, and pick the notation style that makes it as easy as possible for them. Of course we then get differences of opinion on how to do this, but we don't need over-kill just to make the chain as unambiguous as possible.

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?

On the more positive side it seems that we both agree that there should be white space in the notation to help readers to come back to the right place after they've diverted their glance to the grid.
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Re: UR+2B/2SL

Postby aran » Thu Mar 03, 2011 2:40 pm

Ronk
wrote :
I would rather read ...
(4)r3c9 = r3c7 - r7c7 = r7c1 - als:[(4)r34569c1 = (5)r3c1] => r3c9<>5

I don't see this as a step in the direction of clarity :
"- als" is somewhat unsatisfactory, since als=ls does not hold. You just mean that when you write -als, then the reader must assume you mean ls which he must then go look for, since you omit to supply him with the constituent elements.

There are simpler ways :
4r3c9=r3c7-r7c7=(HP14-5)r78c1=5r3c1
4r3c9=r3c7-r7c7=r3c7-(4=NQ2367)r4569-(23=5)r3c1
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Re: UR+2B/2SL

Postby daj95376 » Thu Mar 03, 2011 4:48 pm

Since my example helped fuel this discussion, I will admit that my notation:

Code: Select all
(4)r3c9 = r3c7|r8c9 - r7c7 = r7c1 - (4=5)r54693c1  =>  r3c9<>5

was not my first choice. Here's how I originally visualized the elimination:

Code: Select all
(4)r3c9 = r3c7|r8c9 - r7c7 = r7c1 - (4=2367)r5469c1 - (36=5)r3c1  =>  r3c9<>5

(Which is aran's second suggestion -- after correcting typos.) I used the smaller ALS because it seemed customary to condense such statements.
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Re: UR+2B/2SL

Postby ronk » Sat Mar 05, 2011 12:58 pm

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?

aran wrote:You just mean that when you write -als, then the reader must assume you mean ls which he must then go look for, since you omit to supply him with the constituent elements.

When there is no continuous loop,there is ultimately no locked set ... and the other digits of the ALS are unimportant.
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Re: UR+2B/2SL

Postby David P Bird » Sat Mar 05, 2011 2:23 pm

ronk wrote:... and the other digits of the ALS are unimportant.

In which case the precise location of the linking candidates in the nodes is unimportant too. - You're just having a laugh.

Aran,Itsnicetoseeyoucontributingagainevenifyoudon'tapproveofwastingspacetoimprovereadability.
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Re: UR+2B/2SL

Postby aran » Sat Mar 05, 2011 10:07 pm

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

That falls somewhere between the sibylline and the meaningless.

David P Bird wrote:Aran,Itsnicetoseeyoucontributingagainevenifyoudon'tapproveofwastingspacetoimprovereadability.

ThankyouDavidforthosekindwords.
David P Bird wrote:On the more positive side it seems that we both agree that there should be white space in the notation to help readers to come back to the right place after they've diverted their glance to the grid.

How does the reader remember which white space he just left ?
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Re: UR+2B/2SL

Postby ronk » Sat Mar 05, 2011 10:22 pm

David P Bird wrote:
ronk wrote:... and the other digits of the ALS are unimportant.

In which case the precise location of the linking candidates in the nodes is unimportant too. - You're just having a laugh.

David, there is apparently a bigger difference between the King's English and American English than I thought. I'm out of town ... and will get back to this when back home.
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