may be one point for partial double exocet having as here 2 digits matching and 2 digits non matching.
In my example with 3 digits matching, I just had to prove that the non matching digit could not occupy the 2 partial exocets.
The same can be tried for the 2 non matching digits in the last example
Exotic patterns a resume
Re: Exotic patterns a resume
by champagne » Sat Jan 12, 2013 4:29 pm
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Re: Exotic patterns a resume
by champagne » Sun Jun 16, 2013 12:05 pm
An interesting situation for an overlapping rank 0 logic
I just updated my current data base of potential hardest for the rank 0 logic, using my fresh code.
When I change my code, I check the data base for non regressive code and I found that old one not seen by the fresh code.
This is clearly not a "non overlapping" rank 0 logic, but as it works, it has not been seen when I tried to solve it.
In my former code, I tried to test some "nearly rank 0 logic" and accepted to look at puzzles where one of the positions of a 2 rows 2 columns set base was occupied.
Here the cell r9c5 is not "empty" for the floors 1367. The new code does not study that sets base.
The old code found a SLG with, in r9c5, digits 1 and 6 attached to 2 truths and 2 links (each of them)
AFAIK, this is not a situation described in Allan Barker site.
As in that case the value assigned to the cell r9c5 is valid for the same number of truths and links, I think that it works exactly as a non overlapping rank 0 logic.
I just updated my current data base of potential hardest for the rank 0 logic, using my fresh code.
When I change my code, I check the data base for non regressive code and I found that old one not seen by the fresh code.
Hidden Text: Show
This is clearly not a "non overlapping" rank 0 logic, but as it works, it has not been seen when I tried to solve it.
In my former code, I tried to test some "nearly rank 0 logic" and accepted to look at puzzles where one of the positions of a 2 rows 2 columns set base was occupied.
Here the cell r9c5 is not "empty" for the floors 1367. The new code does not study that sets base.
The old code found a SLG with, in r9c5, digits 1 and 6 attached to 2 truths and 2 links (each of them)
AFAIK, this is not a situation described in Allan Barker site.
As in that case the value assigned to the cell r9c5 is valid for the same number of truths and links, I think that it works exactly as a non overlapping rank 0 logic.
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Re: Exotic patterns a resume
by blue » Sun Jun 16, 2013 2:49 pm
Hi champagne,
It does work "exactly as a non overlapping rank 0 logic".
The way I would describe it is that the candidates that are in 'n' truths, also in (at least) 'n' links (n=2 here), and the overall truth and link counts match, and so candidates that are in more links than truths can be elimnated.
This is Obi-Wahn's principle, with "fin sector" count = 0, extended to non-single-digit cases.
It's what I consider to be the proper definition for "rank 0" logic.
Here is a non-overlapping SLG (only slightly different) that accomplishes the same eliminations.
18 Truths = {1367R3 1367R9 37C5 1367C9 456N2 1B5}
18 Links = {1367c2 1c6 3n1 9n3 469n5 46n9 1b3 3b29 6b3 7b29}
It can be obtained from your SLG, by doing a kind of transformation that Obi-Wahn discusses:
Blue.
champagne wrote:As in that case the value assigned to the cell r9c5 is valid for the same number of truths and links, I think that it works exactly as a non overlapping rank 0 logic.
It does work "exactly as a non overlapping rank 0 logic".
The way I would describe it is that the candidates that are in 'n' truths, also in (at least) 'n' links (n=2 here), and the overall truth and link counts match, and so candidates that are in more links than truths can be elimnated.
This is Obi-Wahn's principle, with "fin sector" count = 0, extended to non-single-digit cases.
It's what I consider to be the proper definition for "rank 0" logic.
Here is a non-overlapping SLG (only slightly different) that accomplishes the same eliminations.
18 Truths = {1367R3 1367R9 37C5 1367C9 456N2 1B5}
18 Links = {1367c2 1c6 3n1 9n3 469n5 46n9 1b3 3b29 6b3 7b29}
It can be obtained from your SLG, by doing a kind of transformation that Obi-Wahn discusses:
- add box truths covered by column links, in stack 2, for digits 1 and 6 -- total of 3 truths and 3 links added.
- allow the box truths added in b8, to cancel with the box links were are already present -- 2 truths canceling 2 links
- allow the column links added in c5, to cancel with the column truths that were already present -- 2 links canceling 2 truths
Blue.
Last edited by blue on Fri Jun 21, 2013 2:22 am, edited 1 time in total.
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Re: Exotic patterns a resume
by champagne » Sun Jun 16, 2013 6:00 pm
blue wrote:Hi champagne,champagne wrote:As in that case the value assigned to the cell r9c5 is valid for the same number of truths and links, I think that it works exactly as a non overlapping rank 0 logic.
It does work "exactly as a non overlapping rank 0 logic".
...
Hi blue,
To be frank, I had no doubt, but it's good to have it checked.
I am short in time to digest all your stuff but several remarks after a quick overview.
1) your alternative SLGs show again, (I am thinking of ronk's various examples of rank 0 equivalent SLGs) that the rank 0 space is still widely open.
2) I have several examples very similar to that one, but I am convinced that we can find other examples with 2 crossing occupied, and why not more. May be you have already a theoretical approach of that.
3) this is a relatively old puzzle (eleven did not work in the potential hardest area for 2 or 3 years), but it's specific properties have not be pointed out before (AFAIK)
4) your "non overlapping" SLGs are outside the field of the patterns searched by my program. I am far from having a general process and I work on a limited number of identified patterns.
Last edited by champagne on Mon Jun 17, 2013 7:17 am, edited 1 time in total.
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Re: Exotic patterns a resume
by JC Van Hay » Sun Jun 16, 2013 6:45 pm
Why not translating into cell truths 
.....67...5.1...3...9.2...42..........8.4...29.46..........7.6....3..1..8.......5;1426;elev;318
21 Links = {58r3 249r9 1367c2 7c4 13c6 89c9 16b3 589b5 37b9}
24 Eliminations --> r6c6<>1358, r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89, r1c2<>3, r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9
.....67...5.1...3...9.2...42..........8.4...29.46..........7.6....3..1..8.......5;1426;elev;318
- Code: Select all
+--------------------------+--------------------------+-------------------------+
| 134 248-13 123 | 4589 3589 6 | 7 2589-1 (189) |
| 467 5 267 | 1 789 489 | 289-6 3 (689) |
| 1367 (13678) 9 | (578) 2 (358) | (568) (158) 4 |
+--------------------------+--------------------------+-------------------------+
| 2 (1367) 13567 | (5789) 137-589 (13589) | 345689 145789 1367-89 |
| 13567 (1367) 8 | (579) 4 (1359) | 3569 1579 2 |
| 9 (137) 4 | 6 137-58 2-1358 | 358 1578 137-8 |
+--------------------------+--------------------------+-------------------------+
| 1345 249-13 1235 | 24589 1589 7 | 2489-3 6 (389) |
| 4567 249-67 2567 | 3 5689 24589 | 1 2489-7 (789) |
| 8 (1234679) 1367-2 | (249) 16-9 (1249) | (2349) (2479) 5 |
+--------------------------+--------------------------+-------------------------+
21 Links = {58r3 249r9 1367c2 7c4 13c6 89c9 16b3 589b5 37b9}
24 Eliminations --> r6c6<>1358, r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89, r1c2<>3, r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9
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Re: Exotic patterns a resume
by ronk » Sun Jun 16, 2013 9:33 pm
blue wrote:Here is a non-overlapping SLG (only slightly different) that accomplishes the same eliminations.
18 Truths = {1367R3 1367R9 37C5 1367C9 456N2 1B5}
18 Links = {1367c2 1c6 3n1 9n3 469n5 46n9 1b3 3b29 6b3 7b29}
Replacing all the truths in c5 by truths in b5 has more appeal IMO. I didn't attempt an Obi-Wahn transformation though.
18 Truths = {1367R39 1367C9 456N2 137B5}
18 Links = {1367c2 7c4 13c6 3n1 9n3 469n5 46n9 16b3 37b9}
20 Eliminations --> r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89, r1c2<>3,
r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9
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Re: Exotic patterns a resume
by blue » Mon Jun 17, 2013 4:08 am
Hi ronk,
It makes a prettier picture, yes.
Your SLG is what you would get if you did what I did (ala Obi-Wahn) , but for all of the digits with column truths in c5.
I did only the minimum necessary to remove the "overlapping truths" issue/non-issue.
JC Van Hay's SLG is almost what you would get by applying an Obi-Wahn transformation to your SLG -- adding cell truths covered by box links, in b5, and letting the existing box truths and cell links, cancel with added box links and cell truths.
The result of that, would be:
22 Truths = {34569N2 3459N4 34569N6 39N7 39N8 1278N9}
22 Links = {58r3 249r9 1367c2 7c4 13c6 89c9 16b3 2589b5 37b9}
24 Eliminations, 1 Assignment --> r6c6<>1358, r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89,
r1c2<>3, r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9,
r6c6=2
It has 4 (XSudo) "cannibal" eliminations and one (resulting) assignment ... all in r6c6.
Obi-Wahn's Exclusion Rule, applied to the 22/22 problem, wouldn't say that the cannibal eliminations are justified.
The eliminations that it grants, are always the same before and after applying an Obi-Wahn transformation.
Removing the r6c6 cell truth and the 2b5 box link from the 22/22 SLG, though, leaves JC Van Hay's 21/21 SLG, where the 4 new eliminations are justified (by the usual rank 0 rule).
Regards,
Blue.
ronk wrote:Replacing all the truths in c5 by truths in b5 has more appeal IMO. I didn't attempt an Obi-Wahn transformation though.
It makes a prettier picture, yes.
Your SLG is what you would get if you did what I did (ala Obi-Wahn) , but for all of the digits with column truths in c5.
I did only the minimum necessary to remove the "overlapping truths" issue/non-issue.
JC Van Hay's SLG is almost what you would get by applying an Obi-Wahn transformation to your SLG -- adding cell truths covered by box links, in b5, and letting the existing box truths and cell links, cancel with added box links and cell truths.
The result of that, would be:
22 Truths = {34569N2 3459N4 34569N6 39N7 39N8 1278N9}
22 Links = {58r3 249r9 1367c2 7c4 13c6 89c9 16b3 2589b5 37b9}
24 Eliminations, 1 Assignment --> r6c6<>1358, r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89,
r1c2<>3, r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9,
r6c6=2
It has 4 (XSudo) "cannibal" eliminations and one (resulting) assignment ... all in r6c6.
Obi-Wahn's Exclusion Rule, applied to the 22/22 problem, wouldn't say that the cannibal eliminations are justified.
The eliminations that it grants, are always the same before and after applying an Obi-Wahn transformation.
Removing the r6c6 cell truth and the 2b5 box link from the 22/22 SLG, though, leaves JC Van Hay's 21/21 SLG, where the 4 new eliminations are justified (by the usual rank 0 rule).
Regards,
Blue.
Last edited by blue on Fri Jun 21, 2013 2:23 am, edited 1 time in total.
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Re: Exotic patterns a resume
by champagne » Mon Jun 17, 2013 6:06 am
impressive work. I don't see clearly after that in which direction to go to improve my rank0 logic detection, but there is a lot to do.
here a list of puzzles having a good chance to have similar properties
I only had a look to the head of the file
here a list of puzzles having a good chance to have similar properties
I only had a look to the head of the file
Hidden Text: Show
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Re: Exotic patterns a resume
by David P Bird » Mon Jun 17, 2013 6:55 am
Blue,
Using only strong sets for a (1367) set for selected rows and a complementary (24589) for selected columns this almost pattern can be found
Multi-Sector ANS (13)r1,(67)r2,(137)r6,(13)r7,(67)r8,(45)c1,(25)c3,(589)c5,(89)c9 20 candidates in 19 available cells
Where a digit in a set is known within the row or column, it's been removed from the set.
The PEs are shown but there are one too many of them as one of the digits must be false in the AHS, and therefore true in one peer cell outside it.
This can be confined to (5)b4 where there is a strong link between the two eliminated candidates, so the other 20 PEs are valid.
Now this can be converted to a Multi-Sector LS by removing (5) from the c13 covers and adding (5)b7
Multi-Sector LS (13)r1,(67)r2,(137)r6,(13)r7,(67)r8,(4)c1,(2)c3,(589)c5,(89)c9,(5)b7 19 candidates in 19 available cells
This method still requires combinations of rows and columns to be found by experimentation, but the search is much more restricted and doesn't involve any individual cell covers. In practice any set which doesn't reduce to 3 or less digits when the knowns are removed can be ignored.
Champagne, this could possibly be a process that you could explore. There are always two ways to get a balance like this depending on which way round the sets are used for the rows & columns, and I use the one that completely covers the fewest cells.
David
[Added] I've been testing my method on Champagne's list and find my points in the last 4 lines aren't always accurate. I've found sets that may need 4 of the 5 digits in the complementary sets, and also that the balances with the sets swapped over between the rows and columns don't work out the way I described. I'll play some more with the examples to try to get a better picture.
[Edit] Typos
Using only strong sets for a (1367) set for selected rows and a complementary (24589) for selected columns this almost pattern can be found
- Code: Select all
*-------------------------*-------------------------*-------------------------*
13 | 134 248-13 123 | 4589 3589 <6> | <7> 2589-1 189 |
67 | 467 <5> 267 | <1> 789 489 | 289-6 <3> 689 |
| 1367 13678 <9> | 578 <2> 358 | 568 158 <4> |
*-------------------------*-------------------------*-------------------------*
| <2> 1367 1367-5 | 5789 137-589 13589 | 345689 145789 1367-89 |
| 1367-5 1367 <8> | 579 <4> 1359 | 3569 1579 <2> |
137 | <9> 137 <4> | <6> 13578 2 | 58-3 58-17 1378 |
*-------------------------*-------------------------*-------------------------*
13 | 1345 249-13 1235 | 24589 1589 <7> | 2489-3 <6> 389 |
67 | 4567 249-67 2567 | <3> 5689 4589 | <1> 2489-7 789 |
| <8> 1234679 1367-2 | 249 16-9 149 | 2349 2479 <5> |
*-------------------------*-------------------------*-------------------------*
45 25 589 89
Multi-Sector ANS (13)r1,(67)r2,(137)r6,(13)r7,(67)r8,(45)c1,(25)c3,(589)c5,(89)c9 20 candidates in 19 available cells
Where a digit in a set is known within the row or column, it's been removed from the set.
The PEs are shown but there are one too many of them as one of the digits must be false in the AHS, and therefore true in one peer cell outside it.
This can be confined to (5)b4 where there is a strong link between the two eliminated candidates, so the other 20 PEs are valid.
Now this can be converted to a Multi-Sector LS by removing (5) from the c13 covers and adding (5)b7
Multi-Sector LS (13)r1,(67)r2,(137)r6,(13)r7,(67)r8,(4)c1,(2)c3,(589)c5,(89)c9,(5)b7 19 candidates in 19 available cells
This method still requires combinations of rows and columns to be found by experimentation, but the search is much more restricted and doesn't involve any individual cell covers. In practice any set which doesn't reduce to 3 or less digits when the knowns are removed can be ignored.
Champagne, this could possibly be a process that you could explore. There are always two ways to get a balance like this depending on which way round the sets are used for the rows & columns, and I use the one that completely covers the fewest cells.
David
[Added] I've been testing my method on Champagne's list and find my points in the last 4 lines aren't always accurate. I've found sets that may need 4 of the 5 digits in the complementary sets, and also that the balances with the sets swapped over between the rows and columns don't work out the way I described. I'll play some more with the examples to try to get a better picture.
[Edit] Typos
Last edited by David P Bird on Mon Jun 17, 2013 9:14 pm, edited 1 time in total.
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Re: Exotic patterns a resume
by David P Bird » Mon Jun 17, 2013 12:08 pm
Champagne, here are my results for 5 grids picked at random from your list
They seem to have strong family resemblances, so all I can say it that my method works for these samples. It may not work for the ones that you can already resolve. I'd need to try those out and several more from this set before I could attempt to write a standard procedure. (What I wrote before was from a clearly incomplete memory.)
David
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Re: Exotic patterns a resume
by JC Van Hay » Mon Jun 17, 2013 4:59 pm
Further comments on the following puzzle :
.....67...5.1...3...9.2...42..........8.4...29.46..........7.6....3..1..8.......5;1426;elev;318
After r6c6=2, the following 'All Cells' Rank 0 Logic admits an easy interpretation ...
21 Links = {58r3 249r9 1367c2 7c4 13c6 89c9 16b3 589b5 37b9}
20 Eliminations --> r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89, r1c2<>3,
r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9
...
Loop[21] : (37=89)r78c9-(89=16)r12c9-(16=58)r3c78-[(8=1367)r3456c2-1367r9c2 and (58=37)r3c46-(37=1589)r45c46-1r9c6]=NT(249)r9c246-(249=37)r9c78 @
[Note that the loop begins like an 'sk-loop' ... ]
or
as the following less awkward representation by a 'condensed' 21*21 Pigeonhole Matrix where the weak links that will become strong are more easily seen :
.....67...5.1...3...9.2...42..........8.4...29.46..........7.6....3..1..8.......5;1426;elev;318
After r6c6=2, the following 'All Cells' Rank 0 Logic admits an easy interpretation ...
- Code: Select all
+--------------------------+--------------------------+-------------------------+
| 134 248-13 123 | 4589 3589 6 | 7 2589-1 (189) |
| 467 5 267 | 1 789 489 | 289-6 3 (689) |
| 1367 (13678) 9 | (578) 2 (358) | (568) (158) 4 |
+--------------------------+--------------------------+-------------------------+
| 2 (1367) 13567 | (5789) 137-589 (13589) | 345689 145789 1367-89 |
| 13567 (1367) 8 | (579) 4 (1359) | 3569 1579 2 |
| 9 (137) 4 | 6 137-58 2 | 358 1578 137-8 |
+--------------------------+--------------------------+-------------------------+
| 1345 249-13 1235 | 24589 1589 7 | 2489-3 6 (389) |
| 4567 249-67 2567 | 3 5689 4589 | 1 2489-7 (789) |
| 8 (1234679) 1367-2 | (249) 16-9 (149) | (2349) (2479) 5 |
+--------------------------+--------------------------+-------------------------+
21 Links = {58r3 249r9 1367c2 7c4 13c6 89c9 16b3 589b5 37b9}
20 Eliminations --> r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89, r1c2<>3,
r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9
...
Loop[21] : (37=89)r78c9-(89=16)r12c9-(16=58)r3c78-[(8=1367)r3456c2-1367r9c2 and (58=37)r3c46-(37=1589)r45c46-1r9c6]=NT(249)r9c246-(249=37)r9c78 @
[Note that the loop begins like an 'sk-loop' ... ]
or
as the following less awkward representation by a 'condensed' 21*21 Pigeonhole Matrix where the weak links that will become strong are more easily seen :
- Code: Select all
3r7c9=======8r7c9=9r7c9
7r8c9=8r8c9=9r8c9
8r1c9=9r1c9=1r1c9
8r2c9=9r2c9=======6r2c9
1r3c8=======5r3c8=8r3c8
6r3c7=5r3c7=8r3c7
8r3c2=NQ(1367)r3456c2
5r3c6=8r3c6=================3r3c6
5r3c4=8r3c4=======================7r3c4
3r4c6=======5r4c6=8r4c6=9r4c6=1r4c6
3r5c6=======5r5c6=======9r5c6=1r5c6
7r4c4=5r4c4=8r4c4=9r4c4
7r5c6=5r5c6=======9r5c6
(1367)r9c2====================================1r9c6=NT(249)r9c246
3r9c7===============================================================================================(249)r9c7
7r9c8=========================================================================================(249)r9c8
.................................................................................................................
:=> 20 Eliminations : ...
3r7c7 7r8c8 8r4c9 9r4c9 1r1c8 6r2c7 13r17c2 5r4c5 8r4c5 9r4c5 2r9c3
8r6c9 67r8c2 5r6c5 8r5c5 9r9c5
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Re: Exotic patterns a resume
by ronk » Mon Jun 17, 2013 5:39 pm
David P Bird wrote:Champagne, here are my results for 5 grids picked at random from your list
...
They seem to have strong family resemblances ...
In terms of champagne's 2-row/2-col search pattern, if these five almost-sk-loop grids were normalized to place the two rows in r2 and r8 and place the two columns in c2 and c8, there appears to be one truth overlap in one of b1379 and one unwanted sk-loop digit in one of b2468.
After normalizing the first puzzle for example, overlap is due to 9r8c8 being a member of both 9r8 and 9c8 truths. Moreover, the truths in r8 are reduced to three from (the normal) four due to r9c5=8. As in a recent puzzle, the overlap may be removed by replacing the truths in r8 by truths in b8 (not done in the grid below).
1.........5.....36....3.5.4.1..6.3....82.....9....7....629.8...7.......8....4.6..;3988;elev;2839
- Code: Select all
002000008060003010700000900000000100030045000000360050809000062040006000000080700
+--------------------------+------------------------------+-------------------------+
| 1345-9 15(9) 2 | 145679 15-79 1479 | 3456 34(7) 8 |
| 45(9) 6 45(8) | -45(2789) -5(279) 3 | 45(2) 1 45(7) |
| 7 15(8) 1345-8 | 124568 15-2 1248 | 9 34(2) 3456 |
+--------------------------+------------------------------+-------------------------+
| 456-29 5(2789) 456-78 | (2789) (279) (2789) | 1 34(2789) 346-79 |
| 1269 3 1678 | 12789 4 5 | 268 (2789) 679 |
| 1249 -1(2789) 1478 | 3 6 12789 | 248 5 479 |
+--------------------------+------------------------------+-------------------------+
| 8 15(7) 9 | 1457 135-7 147 | 345 6 2 |
| 135(2) 4 135(7) | -15(279) -135(279) 6 | 358 -3(89) 135(9) |
| 1356-2 15(2) 1356 | 12459 8 1249 | 7 34(9) 1345-9 |
+--------------------------+------------------------------+-------------------------+
18 Truths = {2789R2 279R8 2789C2 2789C8 4N456}
18 Links = {2789r4 2n45 5n8 6n2 8n458 2b37 7b37 8b1 9b19}
20 Eliminations --> r8c5<>135, r2c45<>5, r4c39<>7, r4c19<>9, r49c1<>2, r34c3<>8, r8c4<>15,
r1c1<>9, r2c4<>4, r6c2<>1, r8c8<>3, r9c9<>9
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Re: Exotic patterns a resume
by blue » Mon Jun 17, 2013 7:04 pm
Hi David,
A few things to address in this post ...
First, it's a Multi-Sector ANS, not AHS -- "cell truths" in 19 cells, with candidates covered by 20 "row/column/box links".
Second, the items that you list ... (13)r1, ets ... are cover sets, not base sets as your first line would indicate.
If you want to use strong links for digits 1367, then you need to have them either in c1357 (your "selected columns"), or r3459 (your "unselected rows").
No issues with this, except that it's an ANS again, candidates in 19 cells, covered by 19 row/column links ... the ones that you mention.
Side note (not important): Another way to deal with the "5's", is to add a box truth for digit 5 in b4, leading to a 20/20 problem -- one box and 19 cell truths, covered by the original 20 row/column links.
Item three: When you present these kinds of things, I would be grateful if you would list the cells as well. It was 19 in this case, and one of them (r6c2, containing candidates for digits 137, only) wasn't in the intersection of your "selected row" and "selected column" sets -- it was sort of a "special case", just like the 5 in b5. Actually I'ld be happiest if you'ld list the cells first (the base sets), and then the cover sets.
Item four -- not so important: I mentioned something about this to you in a PM. In this example, viewed as a base/cover problem, you can remove the 3 cell truths and row links in r6, and have a perfectly fine base/cover problem, with 16 cell truths, covered by 16 row/column/box links. You don't get the eliminations for 3r6c7 and 17r6c8 directly. Instead, you get eliminations for 58r6c5 and 8r6c9, leaving is a naked set for 137 in r6 that eliminates 3r6c7 and 17r6c8. Note: If you're using XSudo, and you plug the 19 cell truths and 19 cover sets (using 5b7, rather than 5c1 and 5c3), then it shows all 6 eliminations, but the ones for 58r6c5 and 8r6c9 are shown as "cannibal eliminations".
Best Regards,
Blue.
P.S. For XSudo users (and David as well), here are a couple more takes on things, inspired by David's post:
This one has row truths for 1367 in r3459 (an option mentioned above), and highlights the special situations for 5b5 and r6c2.
18 Truths = {1R3459 3R3459 6R3459 7R3459 6N2 5B4}
18 Links = {1367c2 7c4 13c6 36c7 17c8 3n1 4n359 5n1 9n35}
20 Eliminations --> r4c5<>589, r1c28<>1, r7c27<>3, r8c28<>7, r4c9<>89, r6c8<>17, r1c2<>3,
r2c7<>6, r6c7<>3, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9,
This one has row truths for 1367 in r34569 (one more row).
The special circumstance for r6c2, has gone away.
The eliminations are different too -- with differences confined to r6.
20 Truths = {1R34569 3R34569 6R3459 7R34569 5B4}
20 Links = {1367c2 7c4 13c6 36c7 17c8 35n1 49n3 469n5 46n9}
20 Eliminations --> r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89, r1c2<>3,
r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9,
David P Bird wrote:Blue,
Using only strong sets for a (1367) set for selected rows and a complementary (24589) for selected columns this almost pattern can be found
- Code: Select all
*-------------------------*-------------------------*-------------------------*
13 | 134 248-13 123 | 4589 3589 <6> | <7> 2589-1 189 |
67 | 467 <5> 267 | <1> 789 489 | 289-6 <3> 689 |
| 1367 13678 <9> | 578 <2> 358 | 568 158 <4> |
*-------------------------*-------------------------*-------------------------*
| <2> 1367 1367-5 | 5789 137-589 13589 | 345689 145789 1367-89 |
| 1367-5 1367 <8> | 579 <4> 1359 | 3569 1579 <2> |
137 | <9> 137 <4> | <6> 13578 2 | 58-3 58-17 1378 |
*-------------------------*-------------------------*-------------------------*
13 | 1345 249-13 1235 | 24589 1589 <7> | 2489-3 <6> 389 |
67 | 4567 249-67 2567 | <3> 5689 4589 | <1> 2489-7 789 |
| <8> 1234679 1367-2 | 249 16-9 149 | 2349 2479 <5> |
*-------------------------*-------------------------*-------------------------*
45 25 589 89
Multi-Sector AHS (13)r1,(67)r2,(137)r6,(13)r7,(67)r8,(45)c1,(25)c3,(589)c5,(89)c9 20 candidates in 19 available cells
A few things to address in this post ...
First, it's a Multi-Sector ANS, not AHS -- "cell truths" in 19 cells, with candidates covered by 20 "row/column/box links".
Second, the items that you list ... (13)r1, ets ... are cover sets, not base sets as your first line would indicate.
If you want to use strong links for digits 1367, then you need to have them either in c1357 (your "selected columns"), or r3459 (your "unselected rows").
The PEs are shown but there are one too many of them as one of the digits must be false in the AHS, and therefore true in one peer cell outside it.
This can be confined to (5)b4 where there is a strong link between the two eliminated candidates, so the other 20 PEs are valid.
Now this can be converted to a Multi-Sector LS by removing (5) from the c13 covers and adding (5)b7
Multi-Sector AHS (13)r1,(67)r2,(137)r6,(13)r7,(67)r8,(4)c1,(2)c3,(589)c5,(89)c9,(5)b7 19 candidates in 19 available cells
No issues with this, except that it's an ANS again, candidates in 19 cells, covered by 19 row/column links ... the ones that you mention.
Side note (not important): Another way to deal with the "5's", is to add a box truth for digit 5 in b4, leading to a 20/20 problem -- one box and 19 cell truths, covered by the original 20 row/column links.
Item three: When you present these kinds of things, I would be grateful if you would list the cells as well. It was 19 in this case, and one of them (r6c2, containing candidates for digits 137, only) wasn't in the intersection of your "selected row" and "selected column" sets -- it was sort of a "special case", just like the 5 in b5. Actually I'ld be happiest if you'ld list the cells first (the base sets), and then the cover sets.
Item four -- not so important: I mentioned something about this to you in a PM. In this example, viewed as a base/cover problem, you can remove the 3 cell truths and row links in r6, and have a perfectly fine base/cover problem, with 16 cell truths, covered by 16 row/column/box links. You don't get the eliminations for 3r6c7 and 17r6c8 directly. Instead, you get eliminations for 58r6c5 and 8r6c9, leaving is a naked set for 137 in r6 that eliminates 3r6c7 and 17r6c8. Note: If you're using XSudo, and you plug the 19 cell truths and 19 cover sets (using 5b7, rather than 5c1 and 5c3), then it shows all 6 eliminations, but the ones for 58r6c5 and 8r6c9 are shown as "cannibal eliminations".
Best Regards,
Blue.
P.S. For XSudo users (and David as well), here are a couple more takes on things, inspired by David's post:
This one has row truths for 1367 in r3459 (an option mentioned above), and highlights the special situations for 5b5 and r6c2.
18 Truths = {1R3459 3R3459 6R3459 7R3459 6N2 5B4}
18 Links = {1367c2 7c4 13c6 36c7 17c8 3n1 4n359 5n1 9n35}
20 Eliminations --> r4c5<>589, r1c28<>1, r7c27<>3, r8c28<>7, r4c9<>89, r6c8<>17, r1c2<>3,
r2c7<>6, r6c7<>3, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9,
This one has row truths for 1367 in r34569 (one more row).
The special circumstance for r6c2, has gone away.
The eliminations are different too -- with differences confined to r6.
20 Truths = {1R34569 3R34569 6R3459 7R34569 5B4}
20 Links = {1367c2 7c4 13c6 36c7 17c8 35n1 49n3 469n5 46n9}
20 Eliminations --> r4c5<>589, r1c28<>1, r6c59<>8, r7c27<>3, r8c28<>7, r4c9<>89, r1c2<>3,
r2c7<>6, r6c5<>5, r7c2<>1, r8c2<>6, r9c3<>2, r9c5<>9,
Last edited by blue on Tue Jun 18, 2013 6:48 am, edited 2 times in total.
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Re: Exotic patterns a resume
by David P Bird » Mon Jun 17, 2013 10:20 pm
Blue, thanks for your critique.
You're the expert on truth and links sets so I accept I've been reversing the base and cover terms, but they're all the same to me the way I'm working. I enter the digits alongside the rows columns and boxes and my PM shows me three main types of cell: those with no digits covered, those with some digit covered, and those with all digits covered. A fourth type is an alarm indicating one or more digits have been covered twice in the cell.
If the total digit count equals the fully covered cell count it's a Locked Set, otherwise it will be some sort of ANS or AHS (when the count of all the fully or partially covered cells is used for comparison). I then have flags indicating if the eliminations will leave any house without a digit to allow me to modify my selections. That's a lot simpler than XSudo (which I can't run on my computer) and a lot quicker, albeit less powerful.
I took it that as I didn't show any of the PM grids, anyone checking my solutions would run them on their own computer and get the PM grid I see translated into red and blue candidates. I don't appreciate why a cell that has all it's candidates covered by one set is a problem to you though.
Now you disregard that I don’t use any truth or link sets for individual cells, so the Xsudo breakdowns you gave each with 9 such sets don't translate.
By concentrating on all the mistakes I've made, you seem to have overlooked that Champagne could possibly have a relatively easy job coding my schoolboy approach into his solver, compared with trying to replicate Xsudo. Whether or not this
a) will solve all his problem cases
b) will match all his future ambitions
is another matter though which remains to be seen.
David
You're the expert on truth and links sets so I accept I've been reversing the base and cover terms, but they're all the same to me the way I'm working. I enter the digits alongside the rows columns and boxes and my PM shows me three main types of cell: those with no digits covered, those with some digit covered, and those with all digits covered. A fourth type is an alarm indicating one or more digits have been covered twice in the cell.
If the total digit count equals the fully covered cell count it's a Locked Set, otherwise it will be some sort of ANS or AHS (when the count of all the fully or partially covered cells is used for comparison). I then have flags indicating if the eliminations will leave any house without a digit to allow me to modify my selections. That's a lot simpler than XSudo (which I can't run on my computer) and a lot quicker, albeit less powerful.
I took it that as I didn't show any of the PM grids, anyone checking my solutions would run them on their own computer and get the PM grid I see translated into red and blue candidates. I don't appreciate why a cell that has all it's candidates covered by one set is a problem to you though.
Now you disregard that I don’t use any truth or link sets for individual cells, so the Xsudo breakdowns you gave each with 9 such sets don't translate.
By concentrating on all the mistakes I've made, you seem to have overlooked that Champagne could possibly have a relatively easy job coding my schoolboy approach into his solver, compared with trying to replicate Xsudo. Whether or not this
a) will solve all his problem cases
b) will match all his future ambitions
is another matter though which remains to be seen.
David
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Re: Exotic patterns a resume
by champagne » Tue Jun 18, 2013 7:31 am
David P Bird wrote:By concentrating on all the mistakes I've made, you seem to have overlooked that Champagne could possibly have a relatively easy job coding my schoolboy approach into his solver, compared with trying to replicate Xsudo. Whether or not this
a) will solve all his problem cases
b) will match all his future ambitions
is another matter though which remains to be seen.
David
Hi David,
It's too early to draw any conclusion, but this is where I am.
I would express what I am doing not as "copying XSUDO", but more working on a "SET/COVER" issue. Allan Barker used the expression rank 0 logic, but we know that others made similar work with another vocabulary as pointed blue.
As far as I can see, your multi sector view is not so far from the set/cover logic.
My target is not to become expert in set/cover construction and I am impressed by the skills I see. I just try to qualify puzzles towards some solving techniques. When I have found one rank0 logic, the job is done.
I am so far extracting puzzles with one of the following patterns, all in a multi floor view :
- rows as main base for sets, columns as main base for links and reverse
- "X" (2 rows, 2 columns, 4 boxes) set base with no floor digit at the crossing.
with an optimised search of the minimal rank, this seems to work pretty well and could cover the majority of the puzzles having a rank0 potential., but it's risky to draw any conclusion from the silence.
I have several examples of rank0 logic with non empty crossings in the 'X' pattern, I'll restart the corresponding code.
I have seen here many variations around the SLG proposed by my previous code. This remind me that puzzle
98.7.....7.6...8...54......6..8..3......9..2......4..1.3.6..7......5..9......1..4 # GP;H1521
where ronk found 5 or 6 different SLGs
I coded at that time one pattern shown by ronk, but I found no other example so I trashed the corresponding code.
What could help me is an idea to extract missing puzzles. All I see here is highly creative, but starting from an existing SLG. I need a process starting from scratch and not too expensive. On top of it, if it just cover the same puzzles that I find with the current code, it is of no interest (unless it can be much faster).
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