UR1.1, again

Advanced methods and approaches for solving Sudoku puzzles

Re: UR1.1, again

Postby 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!

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Re: UR1.1, again

Postby 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.
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Re: ONE MORE FLAW in RedED' "PROOF" of UR1.1

Postby 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.
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Re: ONE MORE FLAW in RedED' "PROOF" of UR1.1

Postby denis_berthier » Sun Feb 23, 2020 5:35 pm

loop
eleven wrote:blah blah

end loop
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Re: UR1.1, again

Postby 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.
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Re: UR1.1, again

Postby 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?
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Re: UR1.1, again

Postby 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.
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Re: UR1.1, again

Postby 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.
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Re: UR1.1, again

Postby 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
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 754329186961584273238671549417953628526847931893162754389715462645298317172436895
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.

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Re: UR1.1, again

Postby 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
***********************************************************************************************
*** SudoRules 20.0.s based on CSP-Rules 2.0.s, config = W+SFin
*** using CLIPS 6.40-r761
***********************************************************************************************
.5........6.5.42....8.71...4....36.8..........9.1..7..3...........2.7.1..72.3..9.
hidden-single-in-a-row ==> r9c1 = 1
hidden-single-in-a-row ==> r7c5 = 1
218 candidates, 1409 csp-links and 1409 links. Density = 5.95696106202173%
whip[1]: c2n1{r5 .} ==> r5c3 ≠ 1
whip[1]: r4n9{c5 .} ==> r5c6 ≠ 9, r5c5 ≠ 9, r5c4 ≠ 9
whip[1]: r4n1{c3 .} ==> r5c2 ≠ 1
hidden-single-in-a-column ==> r4c2 = 1
whip[1]: r3n2{c2 .} ==> r1c1 ≠ 2
naked-pairs-in-a-column: c2{r7 r8}{n4 n8} ==> r5c2 ≠ 8
whip[1]: c2n8{r8 .} ==> r8c1 ≠ 8
naked-pairs-in-a-column: c2{r7 r8}{n4 n8} ==> r3c2 ≠ 4
singles ==> r1c3 = 4, r2c3 = 1, r3c2 = 3, r5c2 = 2, r3c1 = 2 r1c4 = 3
whip[1]: c3n7{r5 .} ==> r5c1 ≠ 7
whip[1]: c3n9{r8 .} ==> r8c1 ≠ 9
hidden-pairs-in-a-row: r7{n2 n7}{c8 c9} ==> r7c9 ≠ 6, r7c9 ≠ 5, r7c9 ≠ 4, r7c8 ≠ 8
whip[1]: b9n8{r9c7 .} ==> r1c7 ≠ 8
hidden-pairs-in-a-row: r7{n2 n7}{c8 c9} ==> r7c8 ≠ 6
whip[1]: b9n6{r9c9 .} ==> r1c9 ≠ 6, r3c9 ≠ 6
hidden-pairs-in-a-row: r7{n2 n7}{c8 c9} ==> r7c8 ≠ 5, r7c8 ≠ 4
hidden-pairs-in-a-row: r5{n1 n9}{c7 c9} ==> r5c9 ≠ 5, r5c9 ≠ 4, r5c9 ≠ 3, r5c7 ≠ 5, r5c7 ≠ 4, r5c7 ≠ 3
hidden-single-in-a-column ==> r8c7 = 3
naked-pairs-in-a-column: c7{r1 r5}{n1 n9} ==> r3c7 ≠ 9
naked-triplets-in-a-row: r1{c1 c7 c9}{n7 n9 n1} ==> r1c8 ≠ 7, r1c6 ≠ 9
singles ==> r7c6 = 9, r8c3 = 9
naked-triplets-in-a-row: r1{c1 c7 c9}{n7 n9 n1} ==> r1c5 ≠ 9
biv-chain[3]: c9n6{r9 r8} - r8c1{n6 n5} - b8n5{r8c5 r9c6} ==> r9c6 ≠ 6, r9c9 ≠ 5
whip[3]: r2c5{n8 n9} - r3c4{n9 n6} - b8n6{r7c4 .} ==> r8c5 ≠ 8
singles ==> r8c2 = 8, r7c2 = 4
biv-chain[4]: r4c3{n5 n7} - r4c4{n7 n9} - r3c4{n9 n6} - r7n6{c4 c3} ==> r7c3 ≠ 5
singles ==> r7c3 = 6, r7c4 = 8, r7c7 = 5, r3c7 = 4, r9c7 = 8, r9c6 = 5, r8c1 = 5
whip[1]: c8n4{r6 .} ==> r6c9 ≠ 4
naked-pairs-in-a-row: r5{c1 c6}{n6 n8} ==> r5c5 ≠ 8, r5c5 ≠ 6, r5c4 ≠ 6
biv-chain[3]: b6n4{r6c8 r5c8} - r5n3{c8 c3} - r6c3{n3 n5} ==> r6c8 ≠ 5
biv-chain[4]: r4n9{c5 c4} - r3c4{n9 n6} - r3c8{n6 n5} - r4c8{n5 n2} ==> r4c5 ≠ 2
singles ==> r4c8 = 2, r7c8 = 7, r7c9 = 2
naked-pairs-in-a-row: r6{c3 c9}{n3 n5} ==> r6c8 ≠ 3
naked-single ==> r6c8 = 4
naked-pairs-in-a-row: r6{c3 c9}{n3 n5} ==> r6c5 ≠ 5
biv-chain[4]: b2n9{r2c5 r3c4} - r3c9{n9 n5} - b6n5{r6c9 r5c8} - b5n5{r5c5 r4c5} ==> r4c5 ≠ 9
singles ==> r4c5 = 5, r4c3 = 7, r3c4 = 6, r3c8 = 5, r3c9 = 9, r1c7 = 1, r1c9 = 7, r1c1 = 9, r2c1 = 7, r2c9 = 3, r2c8 = 8, r1c8 = 6, r2c5 = 9, r6c9 = 5, r6c3 = 3, r5c3 = 5, r5c7 = 9, r5c9 = 1, r5c8 = 3, r9c4 = 4, r5c4 = 7, r8c5 = 6, r8c9 = 4, r9c9 = 6, r5c5 = 4


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
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Re: UR1.1, again

Postby 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.
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Re: UR1.1, again

Postby 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
1 954326187761584239238971456415793628627458391893162745349615872586247913172839564
2 954326187761584239238971465415793628627458391893162754349615872586247913172839546
3 954326187761584239238971546415793628627458391893162754349615872586247913172839465
4 954326187761584239238971564415793628627458391893162745349615872586247913172839456
5 954326187761584293238971456415793628627458931893162745349615872586247319172839564
6 954326187761584293238971465415793628627458931893162754346819572589247316172635849
7 954326187761584293238971465415793628627458931893162754349615872586247319172839546
8 954326187761584293238971546415793628627458931893162754349615872586247319172839465
9 954326187761584293238971564415793628627458931893162745349615872586247319172839456
10 954362187761584239238971456415793628627458391893126745349615872586247913172839564
11 954362187761584239238971465415723698627498351893156724349615872586247913172839546
12 954362187761584239238971465415793628627458391893126754349615872586247913172839546
13 954362187761584239238971546415723698627498351893156724349615872586247913172839465
14 954362187761584239238971546415723698627849351893156724349615872586297413172438965
15 954362187761584239238971546415723698627849351893156724389615472546297813172438965
16 954362187761584239238971546415793628627458391893126754349615872586247913172839465
17 954362187761584239238971564415723698627859341893146725349615872586297413172438956
18 954362187761584239238971564415723698627859341893146725389615472546297813172438956
19 954362187761584239238971564415793628627458391893126745349615872586247913172839456
20 954362187761584293238971456415793628627458931893126745349615872586247319172839564
21 954362187761584293238971465415793628627458931893126754346819572589247316172635849
22 954362187761584293238971465415793628627458931893126754349615872586247319172839546
23 954362187761584293238971546415793628627458931893126754349615872586247319172839465
24 954362187761584293238971564415793628627458931893126745349615872586247319172839456
25 954362871761584239238971465415723698627498153893156742346815927589247316172639584
26 954362871761584239238971465415723698627498153893156742346819527589247316172635984
27 954362871761584239238971465415723698627849153893156742349618527586297314172435986
28 954362871761584239238971465415723698627859143893146752349618527586297314172435986
29 954362871761584239238971564415723698627498153893156742346815927589247316172639485
30 954382167761594283238671549415723698627859431893146725346915872589267314172438956
31 954382167761594283238671549415723698627958431893146725346815972589267314172439856
32 954382167761594283238671459417953628625748931893126745346819572589267314172435896
33 954382176761594283238671549415723698627859431893146752346915827589267314172438965
34 954382176761594283238671549415723698627958431893146752346815927589267314172439865
35 954382176761594283238671945415723698627859431893146752346915827589267314172438569
36 954382176761594283238671945415723698627859431893146752346918527589267314172435869
37 954382176761594283238671945415723698627958431893146752346819527589267314172435869
38 954382176761594283238671459415723698627849531893156742346915827589267314172438965
39 954382176761594283238671459415723698627948531893156742346815927589267314172439865
40 954382176761594283238671549417923658523768491896145732345816927689257314172439865
41 954382176761594283238671549417923658623758491895146732346815927589267314172439865
42 954382176761594283238671945417923658623758491895146732346819527589267314172435869
43 954382176761594283238671495417923658623758941895146732346819527589267314172435869
44 954382176761594283238671495417923658625748931893156742346819527589267314172435869
45 754329186961584237238671459415793628627458391893162745349816572586247913172935864
46 754329186961584237238671495417953628523768941896142753349816572685297314172435869
47 754329186961584237238671945417953628523768491896142753349816572685297314172435869
48 754329186961584237238671945417953628526748391893162754349816572685297413172435869
49 754329186961584237238671945417953628526748391893162754389416572645297813172835469
50 754329186961584237238671459417953628526748391893162745389416572645297813172835964
51 754329186961584237238671954417953628526748391893162745349816572685297413172435869
52 754329186961584237238671954417953628526748391893162745389416572645297813172835469
53 754329186961584237238671495417953628623748951895162743349816572586297314172435869
54 754329186961584237238671945417953628625748391893162754349816572586297413172435869
55 754329186961584237238671945417953628625748391893162754389416572546297813172835469
56 754329186961584237238671459417953628625748391893162745389416572546297813172835964
57 754329186961584237238671954417953628625748391893162745349816572586297413172435869
58 754329186961584237238671954417953628625748391893162745389416572546297813172835469
59 754329861961584237238671549415793628627458193893162754346815972589247316172936485
60 754329861961584237238671945415793628627458193893162754349816572586247319172935486
61 754329861961584237238671459415793628627458193893162745346815972589247316172936584
62 754329861961584237238671954415793628627458193893162745349816572586247319172935486
63 754329861961584237238671495417953628523768149896142753349816572685297314172435986
64 754329861961584237238671459417953628526748193893162745349816572685297314172435986
65 754329861961584237238671459417953628623748195895162743349816572586297314172435986
66 754329861961584237238671495417953628623748159895162743349816572586297314172435986
67 754329861961584237238671459417953628625748193893162745349816572586297314172435986
68 754392186961584237238671549415723698627849351893156724346915872589267413172438965
69 754392186961584237238671549415723698627849351893156724386415972549267813172938465
70 754392186961584237238671549415723698627849351893156724386915472549267813172438965
71 754392186961584237238671549415723698627948351893156724346815972589267413172439865
72 754392186961584237238671549415723698627948351893156724386415972549267813172839465
73 754392186961584237238671945415723698627849351893156724346915872589267413172438569
74 754392186961584237238671945415723698627849351893156724346918572589267413172435869
75 754392186961584237238671945415723698627849351893156724386915472549267813172438569
76 754392186961584237238671945415723698627948351893156724346819572589267413172435869
77 754392186961584237238671945415723698627948351893156724386419572549267813172835469
78 754392186961584237238671459415723698627859341893146725386415972549267813172938564
79 754392186961584237238671459415723698627958341893146725386415972549267813172839564
80 754392186961584237238671459415723698627958341893146725386419572549267813172835964
81 754392186961584237238671954415723698627859341893146725346915872589267413172438569
82 754392186961584237238671954415723698627859341893146725346918572589267413172435869
83 754392186961584237238671954415723698627859341893146725386915472549267813172438569
84 754392186961584237238671954415723698627958341893146725346819572589267413172435869
85 754392186961584237238671954415723698627958341893146725386419572549267813172835469
86 754392186961584237238671549417923658523768491896145723345816972689257314172439865
87 754392186961584237238671549417923658526748391893165724345816972689257413172439865
88 754392186961584237238671549417923658526748391893165724385416972649257813172839465
89 754392186961584237238671549417923658623758491895146723346815972589267314172439865
90 754392186961584237238671549417923658625748391893156724346815972589267413172439865
91 754392186961584237238671549417923658625748391893156724386415972549267813172839465
92 754392186961584237238671945417923658623758491895146723346819572589267314172435869
93 754392186961584237238671945417923658625748391893156724346819572589267413172435869
94 754392186961584237238671945417923658625748391893156724386419572549267813172835469
95 754392186961584237238671495417923658623758941895146723346819572589267314172435869
96 754392186961584237238671459417953628623748591895126743346815972589267314172439865
97 754392186961584237238671495417953628623748951895126743346819572589267314172435869
98 754392186961584237238671549417953628625748391893126754346815972589267413172439865
99 754392186961584237238671549417953628625748391893126754386415972549267813172839465
100 754392186961584237238671945417953628625748391893126754346819572589267413172435869
101 754392186961584237238671945417953628625748391893126754386419572549267813172835469
102 754392186961584237238671459417953628625748391893126745386415972549267813172839564
103 754392186961584237238671459417953628625748391893126745386419572549267813172835964
104 754392186961584237238671954417953628625748391893126745346819572589267413172435869
105 754392186961584237238671954417953628625748391893126745386419572549267813172835469
106 754392861961584237238671459415723698627859143893146725346918572589267314172435986
107 754392861961584237238671459415723698627958143893146725346815972589267314172439586
108 754392861961584237238671459415723698627958143893146725346819572589267314172435986
109 754392861961584237238671495417923658523768149896145723345816972689257314172439586
110 754392861961584237238671495417923658623758149895146723346815972589267314172439586
111 754392861961584237238671495417923658623758149895146723346819572589267314172435986
112 754392861961584237238671459417953628623748195895126743346815972589267314172439586
113 754392861961584237238671459417953628623748195895126743346819572589267314172435986
114 754392861961584237238671495417953628623748159895126743346815972589267314172439586
115 754392861961584237238671495417953628623748159895126743346819572589267314172435986
116 754392861961584237238671459417953628625748193893126745346815972589267314172439586
117 754392861961584237238671459417953628625748193893126745346819572589267314172435986
118 754326189961584237238971456415793628627458391893162745349615872586247913172839564
119 754326189961584237238971465415793628627458391893162754349615872586247913172839546
120 754326189961584237238971546415793628627458391893162754349615872586247913172839465
121 754326189961584237238971564415793628627458391893162745349615872586247913172839456
122 754326981961584237238971456415793628627458193893162745349615872586247319172839564
123 754326981961584237238971465415793628627458193893162754346819572589247316172635849
124 754326981961584237238971465415793628627458193893162754349615872586247319172839546
125 754326981961584237238971546415793628627458193893162754349615872586247319172839465
126 754326981961584237238971564415793628627458193893162745349615872586247319172839456
127 754362189961584237238971456415793628627458391893126745349615872586247913172839564
128 754362189961584237238971465415723698627498351893156724349615872586247913172839546
129 754362189961584237238971465415793628627458391893126754349615872586247913172839546
130 754362189961584237238971546415723698627498351893156724349615872586247913172839465
131 754362189961584237238971546415723698627849351893156724349615872586297413172438965
132 754362189961584237238971546415723698627849351893156724389615472546297813172438965
133 754362189961584237238971546415793628627458391893126754349615872586247913172839465
134 754362189961584237238971564415723698627859341893146725349615872586297413172438956
135 754362189961584237238971564415723698627859341893146725389615472546297813172438956
136 754362189961584237238971564415793628627458391893126745349615872586247913172839456
137 754362981961584237238971456415723698627859143893146725349615872586297314172438569
138 754362981961584237238971456415723698627859143893146725349618572586297314172435869
139 754362981961584237238971456415793628627458193893126745349615872586247319172839564
140 754362981961584237238971465415723698627498153893156724346819572589247316172635849
141 754362981961584237238971465415723698627498153893156724349615872586247319172839546
142 754362981961584237238971465415793628627458193893126754346819572589247316172635849
143 754362981961584237238971465415793628627458193893126754349615872586247319172839546
144 754362981961584237238971546415723698627498153893156724349615872586247319172839465
145 754362981961584237238971546415793628627458193893126754349615872586247319172839465
146 754362981961584237238971564415793628627458193893126745349615872586247319172839456
147 754392186961584273238671549415723698627859431893146752346915827589267314172438965
148 754392186961584273238671549415723698627958431893146752346815927589267314172439865
149 754392186961584273238671945415723698627859431893146752346915827589267314172438569
150 754392186961584273238671945415723698627859431893146752346918527589267314172435869
151 754392186961584273238671945415723698627958431893146752346819527589267314172435869
152 754392186961584273238671459415723698627849531893156742346915827589267314172438965
153 754392186961584273238671459415723698627948531893156742346815927589267314172439865
154 754392186961584273238671549417923658523768491896145732345816927689257314172439865
155 754392186961584273238671549417923658623758491895146732346815927589267314172439865
156 754392186961584273238671945417923658623758491895146732346819527589267314172435869
157 754392186961584273238671495417923658623758941895146732346819527589267314172435869
158 754392186961584273238671495417923658625748931893156742346819527589267314172435869
159 754392861961584273238671459415723698627849135893156742346918527589267314172435986
160 754392861961584273238671459415723698627948135893156742346815927589267314172439586
161 754392861961584273238671459415723698627948135893156742346819527589267314172435986
162 754392861961584273238671495417923658523768149896145732345816927689257314172439586
163 754392861961584273238671495417923658526748139893165742345816927689257314172439586
164 754392861961584273238671495417923658623758149895146732346815927589267314172439586
165 754392861961584273238671495417923658623758149895146732346819527589267314172435986
166 754392861961584273238671495417923658625748139893156742346815927589267314172439586
167 754392861961584273238671495417923658625748139893156742346819527589267314172435986
168 754362189961584273238971456415723698627849531893156742349615827586297314172438965
169 754362189961584273238971465415723698627498531893156742346815927589247316172639854
170 754362189961584273238971465415723698627849531893156742349615827586297314172438956
171 754362189961584273238971546415723698627859431893146752349615827586297314172438965
172 754362981961584273238971456415723698627498135893156742349615827586247319172839564
173 754362981961584273238971456415723698627849135893156742349615827586297314172438569
174 754362981961584273238971456415723698627849135893156742349618527586297314172435869
175 754362981961584273238971564415723698627498135893156742349615827586247319172839456

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
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Re: UR1.1, again

Postby 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
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Location: France

Re: UR1.1, again

Postby 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
denis_berthier
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Re: UR1.1, again

Postby 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
Last edited by denis_berthier on Tue Feb 25, 2020 5:08 am, edited 1 time in total.
denis_berthier
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