The New Sudoku Players' Forum

by **Serg** » Sun Feb 23, 2020 5:04 pm

Hi, tarek!

tarek wrote:
Serg wrote:If there exists pair of candidate digits (a,b) such, that solutions of given puzzle may contain the next fragment (candidate sets of A, B, C, D permit such configuration)
but any solution must not contain the next fragment (candidate sets of A, B, C, D prohibit such configuration)
then any solution of the puzzle must not contain fragment
End of definition.

Why don't we use: "Then (Candidates + Fragments) would prevent a single solution to the puzzle" which is then used as definition of DP. We can then move to say: "In a single solution puzzle, therefore, the extra candidates must be true"

You propose definition of some uniqness technique, assuming that any puzzle must have a single solution. But UR1.1 is not uniqness, but universal technique, not assuming that given puzzle must have a single solution. This is the originality of the RW's idea - in some configurations the rule being very close to uniqness technique UR1 can work as universal technique, not assuming that the puzzle must have a single solution. It's beautiful paradox!

Serg

Website · by **denis_berthier** » Sun Feb 23, 2020 5:06 pm

Serg wrote:
denis_berthier wrote:... it should be a priority for the believers in the UR1.1 rule to exhibit an example.

I see the opposite situation - there are just examples, but no strict definition - what is "UR1.1 rule"?

What was discussed here IS a precise pattern:

Code: Select all: a b b ac

And what was debated is whether it requires some extra-logical assumption (e.g. uniqueness)

What you propose is a much more general definition. It may be interesting per se or not. I haven't yet read the details. But I fear it can only dilute the current question.

by **eleven** » Sun Feb 23, 2020 5:23 pm

denis_berthier wrote:As I already answered to champagne, this flaw is nor exactly in the proof (my bad for negligent writing), it is in writing a "theorem" when there is no example for the conditions.
...
Unless I've become suddenly unable to read, the pattern in this example is not the pattern discussed here. It is:
Code: Select all
ab ab ab ac

Ah sorry, the 4 samples with the UR1.1 pattern are 2 posts down. However you should have realized in the meantime, that also the more general rule works with the same proof, as RW had it formulated - and which you doubt with the same (non) arguments.

eleven wrote:Concerning your other flaw claim i can only repeat, that it is your limited sudoku model, which cannot do trivial things like to find out, which cells have no givens, that prevents you from following this simple proof.

I'm disappointed. I thought you were smarter than repeating indefinitely the same absurdities (which I already answered), instead of finding counter-arguments or flaws in my proof (which depends only on basic logic, not on any particular model, as I already told you). But I guess you didn't even care to read my proof or my answers.

I'm disappointed. I thought you were smarter than repeating indefinitely the same absurdities. Tell me where the flaw is in the proof with another argument than, that your model is not able to describe it. Anyone else with very basic logical skills can simply verify it.

Website · by **denis_berthier** » Sun Feb 23, 2020 5:35 pm

loop

eleven wrote:blah blah

end loop

by **eleven** » Sun Feb 23, 2020 6:35 pm

DON'T quote with "blah blah", after i did the work for you to provide you with special examples !!!!
Yes, this is not, what you wanted to see, but you should keep a last rest of politeness, also when you realize, that you are wrong.

And now IT IS UP TO YOU TO GIVE a CORRECT COUNTER-EXAMPLE, if you really still think, that the rule is not valid.

Website · by **denis_berthier** » Sun Feb 23, 2020 6:54 pm

eleven wrote:DON'T quote with "blah blah", after i did the work for you to provide you with special examples !!!!

Thanks for the examples. Nobodies knows examples of what they are, but they are definitely examples of something.
Did you realise they are all for single-solution puzzles?

by **eleven** » Sun Feb 23, 2020 7:00 pm

Not RW's and the other 2 more general ones, as well as Leren's.

As i have said, the rule is of no practical worth for people like me, who use uniqueness techniques, but for purists it can help in rare cases.

Website · by **denis_berthier** » Mon Feb 24, 2020 7:39 am

I've added a few lines to my introductory post for clarity.

I've also fixed my negligent writing in this post: http://forum.enjoysudoku.com/ur1-1-again-t37404-76.html. The first version caused some unnecessary turmoil. I still have to check some more suggested examples.

by **Leren** » Mon Feb 24, 2020 9:07 am

I'm not sure what you are looking for this might fit the bill.

Took the original UR1.1 puzzle from Hodoku : .5........6.5.42....8.71...4....36.8.........89.1..7..3...........2.7.1..72.3..9. and removed the 8 from r6c1 : .5........6.5.42....8.71...4....36.8..........9.1..7..3...........2.7.1..72.3..9.

The resulting puzzle has just 3 solutions :

954328167761594283238671459417953628825746931693182745346819572589267314172435896
954382167761594283238671459417953628625748931893126745346819572589267314172435896
954382167761594283238671459417953628825746931693128745346819572589267314172435896

The UR1.1 cells are always the same, so it would appear to work.

If you remove the 7 from r8c6 : .5........6.5.42....8.71...4....36.8.........89.1..7..3...........2...1..72.3..9. The resulting puzzle has 27 solutions :

Hidden Text: Show

The UR1.1 cells have the right values for the 12th solution but not for the others.

Leren

Website · by **denis_berthier** » Mon Feb 24, 2020 10:53 am

Hi Leren, you found an interesting example

Leren wrote:Took the original UR1.1 puzzle from Hodoku : .5........6.5.42....8.71...4....36.8.........89.1..7..3...........2.7.1..72.3..9. and removed the 8 from r6c1 : .5........6.5.42....8.71...4....36.8..........9.1..7..3...........2.7.1..72.3..9.
The resulting puzzle has just 3 solutions :
954328167761594283238671459417953628825746931693182745346819572589267314172435896
954382167761594283238671459417953628625748931893126745346819572589267314172435896
954382167761594283238671459417953628825746931693128745346819572589267314172435896
The UR1.1 cells are always the same, so it would appear to work but maybe that is just a fluke.

What exactly do you mean: "the UR1.1 cells have the right values?" Do you mean that all the possible solutions have a partial resolution paths where the a/b/b/ac pattern is reached (and how did you check this? I don't know how to do.)
Or do you only mean that, in the 3 solutions, the 4 cells have the values implied by the UR1.1 rule? (This is my most likely interpretation.)

Leren wrote:If you remove the 7 from r8c6 : .5........6.5.42....8.71...4....36.8.........89.1..7..3...........2...1..72.3..9. The resulting puzzle has 27 solutions
1 954328176761594283238671549417953628526487931893162754345719862689245317172836495
2 954328176761594283238671549417953628526487931893162754349715862685249317172836495
3 954328176761594283238671549417953628526847931893162754385719462649285317172436895
4 954328176761594283238671549417953628526847931893162754389715462645289317172436895
5 954328176761594283238671549417953628623487951895162734349715862586249317172836495
6 954328176761594283238671549417953628623847951895162734389715462546289317172436895
7 954328176761594283238671549417953628625487931893162754349715862586249317172836495
8 954328176761594283238671549417953628625847931893162754389715462546289317172436895
9 954328176761594283238671459417953628526487931893162745345719862689245317172836594
10 954328176761594283238671459417953628526487931893162745349715862685249317172836594
11 954328176761594283238671459417953628625487931893162745349715862586249317172836594
12 954382167761594283238671459417953628625748931893126745346819572589267314172435896
13 954382176761594283238671549417923658526847931893165724385719462649258317172436895
14 754329861961584273238671945415793628627458139893162754346917582589246317172835496
15 754329861961584273238671954415793628627458139893162745346917582589246317172835496
16 754329188661584273238671549417953628526847931893162754389715462645298317172436895
17 754329186961584273238671549417953628623847951895162734389715462546298317172436895
18 754329186961584273238671549417953628625847931893162754389715462546298317172436895
19 754392186961584273238671549417923658526847931893165724385719462649258317172436895
20 754326189961584273238971456415793628627458931893162745349817562586249317172635894
21 754326189961584273238971564415793628627458931893162745349617852586249317172835496
22 754362189961584273238971456415793628627458931893126745349817562586249317172635894
23 754362189961584273238971564415793628627458931893126745349617852586249317172835496
24 754326981961584273238971456415793628627458139893162745349817562586249317172635894
25 754326981961584273238971564415793628627458139893162745349617852586249317172835496
26 754362981961584273238971456415793628627458139893126745349817562586249317172635894
27 754362981961584273238971564415793628627458139893126745349617852586249317172835496
The UR1.1 cells have the right values for the 12th solution but not for the others.

As one of the solutions has a different behaviour from the others, this example seems much more promising.
For ease of reading, I've marked red the 4 UR cells in your post (I hope I haven't introduced errors). Now, it seems that several solutions have right values in the 4 UR cells: #12 and #20 to 23
In all the solutions, r2c9 is always 3 (as in the previous case), as predicted by UR1.1. Now, as the conditions of some UR1.1 are clearly not satisfied by all of the solutions, the question is, is r2c9=3 due to UR1.1 or to something else?

I fed SudokuExplainer with this example and it says there are multiple solutions. So I tried SE's hints one by one, until I reached a resolution state common to all the possible solutions, where SE finds a UR4 on r15c79 and would apply it if I chose to "apply hint". Quite surprisingly, SE first said it's a multi-sol puzzle but it suggests a rule based on uniqueness.

Finally, I gave it to SudoRules:

Hidden Text: Show

The point is not the details of the resolution path.
Remember that in case of multi-solution puzzles, SudoRules can only find values and eliminations common to all the solutions.
What's noticeable here is:
- r2c9=3 is found by SudoRules
- this is done with rules using at most 4 CSP-variables, like UR1.1 - i.e. nothing more complex than UR1.1

To be more explicit about my conclusion: there seems to be a good reason to think that UR1.1 is irrelevant to the value r2c9=3

by **ghfick** » Mon Feb 24, 2020 4:43 pm

I tried Philip Beeby's solver. Using only steps up to 'Advanced Set' but not 'Deadly' takes one to :

Code: Select all: 79 5 4 | 3 2689 2689 | 189 678 1679 79 6 1 | 5 89 4 | 2 78 3 2 3 8 | 69 7 1 | 459 456 4569 ------------------------+----------------------+--------------------- 4 1 57 | 79 259 3 | 6 25 8 56 2 3567 | 478 4568 78 | 19 345 19 8 9 356 | 1 2456 256 | 7 2345 45 ------------------------+----------------------+--------------------- 3 48 569 | 6789 1 56789 | 458 45678 2 56 48 569 | 2 45689 56789 | 3 1 467 1 7 2 | 468 3 568 | 458 9 456

so r2c9 is 3.
Gordon

by **Leren** » Mon Feb 24, 2020 8:16 pm

Hi denis,

Yes, by the "right" values, all I meant was that they had the "same" values as in Red Ed's post (ie with suitable relabelling).

Here is a better example : this time I removed the 9 from r9c8 : .5........6.5.42....8.71...4....36.8.........89.1..7..3...........2.7.1..72.3.... and there were the following 175 solutions:

Hidden Text: Show

Checking through all these, you'll find many with the deadly pattern 9XXXXXXX77XXXXXXX9 for instance the first four have this pattern, but there are others eg solutions 10 - 19.

You will find others that have the other version 7XXXXXXX99XXXXXXX7 for instance there are some starting at no 127 that I've spotted.

As far as I can see, the only other value that r2c9 can have is 3.

I haven't actually checked, but I'm sure you'll find exactly the same number of each version of the DP and you should be able to pair them up so that all the other cells have the same values in each position outside of the DP.

Leren

by **Mauriès Robert** » Mon Feb 24, 2020 9:23 pm

Hi all,
About the UR1.1 configuration below

Code: Select all: a b b ac

I did not follow all the exchanges on this subject because many were sterile and boring on a subject that does not deserve so much.
My opinion is that without the hypothesis of a single solution of a puzzle where such a configuration appears, nothing allows to draw any conclusion from the configuration as such, i.e. the validation of c, except to verify directly that the elimination of c leads to a contradiction.
Indeed, there are puzzles with multiple solutions where c is common to all the solutions of the puzzle (see the example proposed by Denis Berthier) and puzzles with multiple solutions where at least one solution does not contain c (I can propose some).
It seems to me that this should close the debate and put everyone in agreement!
Robert

Website · by **denis_berthier** » Tue Feb 25, 2020 4:19 am

ghfick wrote:I tried Philip Beeby's solver. Using only steps up to 'Advanced Set' but not 'Deadly' takes one to :
[...]
so r2c9 is 3.

So, we reach the same conclusion: it doesn't result from some UR1.1

Website · by **denis_berthier** » Tue Feb 25, 2020 4:45 am

Leren wrote:Here is a better example : this time I removed the 9 from r9c8 : .5........6.5.42....8.71...4....36.8.........89.1..7..3...........2.7.1..72.3.... and there were the following 175 solutions:[...]
Checking through all these, you'll find many with the deadly pattern 9XXXXXXX77XXXXXXX9 for instance the first four have this pattern, but there are others eg solutions 10 - 19.
You will find others that have the other version 7XXXXXXX99XXXXXXX7 for instance there are some starting at no 127 that I've spotted.
As far as I can see, the only other value that r2c9 can have is 3.

Now, we have a problem interpreting the results. Considering the values in the UR cells, it's likely there is a UR1 pattern (not UR1.1). But as there is no uniqueness, the UR1 rule cannot be applied.
For the UR1.1 rule itself, it is clear from the different solutions that the a/b/b/ac pattern cannot appear in the resolution path of the puzzle itself. It might appear in some sub-puzzle obtained by adding more clues, but not in the puzzle itself.

Leren wrote:I haven't actually checked, but I'm sure you'll find exactly the same number of each version of the DP and you should be able to pair them up so that all the other cells have the same values in each position outside of the DP.

Actually, no. There are more solution with 7/9/9/7 than with 9/7/7/9. It is likely that the puzzle has several independent near-DP.s

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