The New Sudoku Players' Forum

[aeb]

A type 4 UR destroys the unique rectangle

The validity of the Uniqueness Argument does not depend on your current solving state. Hence a "unique rectangle" cannot be destroyed.

[ronk]

I can't even find ones that need type 2.
......................
can anyone give me one ?

If I understand the type definitions, a good example is #655 of the top1465.

Code: Select all

 ..8|..5|...
 ...|23.|...
 9.2|4..|...
 ---+---+---
 .6.|...|...
 ..9|.4.|.57
 8.3|.7.|.1.
 ---+---+---
 3..|...|.7.
 ...|5..|.26
 ...|..8|4..


 1467   1347   8      | 1679   169    5      | 12379  3469   1239
 14567  147    14567  | 2      3      1679   | 1789   4689   189
 9      137    2      | 4      8      167    | 1357   36     135
----------------------+----------------------+--------------------
*47     6     *47     | 1389   5      1239   | 2389   389    2389
 12     12     9      | 368    4      36     | 368    5      7
 8      5      3      | 69     7      269    | 269    1      4
----------------------+----------------------+--------------------
 3      12489  1456   | 169    1269   4      | 1589   7      1589
*147    14789 *147    | 5      19     347    | 1389   2      6
 12567  1279   1567   | 37     1269   8      | 4      39     1359


Eight 1s may be eliminated in box 7 and row 8.

Ron

[eclark]

Great thanks it seems I had bug in my solver that was missing the type 2. Now its time to fix it thanks.

[flip]

A type 4 UR destroys the unique rectangle

The validity of the Uniqueness Argument does not depend on your current solving state. Hence a "unique rectangle" cannot be destroyed.

Sorry. it should read that a type 4 reduction destroys the unique rectangle (post edited).

[aeb]

The validity of the Uniqueness Argument does not depend on your current solving state. Hence a "unique rectangle" cannot be destroyed.

Sorry. it should read that a type 4 reduction destroys the unique rectangle.

But a unique rectangle cannot be destroyed. Even when you solve a corner it still applies. Somewhere else I already pointed at http://homepages.cwi.nl/~aeb/games/sudoku/solving15.html - let me do it again. What is needed for the Local BUG Principle that this forum seems to be in the process of rediscovering is a collection of positions not fixed by having one of the original clues, and a collection of candidate values at those positions, two candidate values at each, where each row, column and box contains 0 or 2 candidates with any given value. Those candidates may be freely invented, they need not have any relation with the current list of candidates that some solver maintains. And the conclusion is that if the total number of solutions is odd, for example 1, then there is a solution and a position such that that solution there differs from both candidates at that position.

[Jeff]

Somewhere else I already pointed at http://homepages.cwi.nl/~aeb/games/sudoku/solving15.html - let me do it again. What is needed for the Local BUG Principle that this forum seems to be in the process of rediscovering is a collection of positions not fixed by having one of the original clues, and a collection of candidate values at those positions, two candidate values at each, where each row, column and box contains 0 or 2 candidates with any given value. Those candidates may be freely invented, they need not have any relation with the current list of candidates that some solver maintains. And the conclusion is that if the total number of solutions is odd, for example 1, then there is a solution and a position such that that solution there differs from both candidates at that position.

Hi Aeb, I can understand the description of the local BUG principle in your web page. But, I have problem with the statements highlighted in the description above. Could you shed some more light on these statements? I suppose "position" means "cell" and "solution" means "true digit in a cell". Thanks in advance.

[aeb]

Somewhere else I already pointed at http://homepages.cwi.nl/~aeb/games/sudoku/solving15.html - let me do it again. What is needed for the Local BUG Principle that this forum seems to be in the process of rediscovering is a collection of positions not fixed by having one of the original clues, and a collection of candidate values at those positions, two candidate values at each, where each row, column and box contains 0 or 2 candidates with any given value. Those candidates may be freely invented, they need not have any relation with the current list of candidates that some solver maintains. And the conclusion is that if the total number of solutions is odd, for example 1, then there is a solution and a position such that that solution there differs from both candidates at that position.

Hi Aeb, I can understand the description of the local BUG principle in your web page. But, I have problem with the statements highlighted in the description above. Could you shed some more light on these statements? I suppose "position" means "cell" and "solution" means "true digit in a cell". Thanks in advance.

I edited the web page and merged BUG principle and Local BUG principle, so that latter term no longer occurs. Don't know what to answer to your question/request - all seems so clear that nothing more need to be said. Perhaps I should stress that "candidates" is unrelated to what you are doing: completely regardless of how much you have found out about the final solution, if you point at a rectangle meeting two boxes, with four initially open corners and label the four corners with candidates 1,2 then the conclusion is that the solution will have some number different from both 1 and 2 at at least one of the corners.
You highlight "odd, for example 1". One can reason about proper grids, where proper means that there is a unique solution, or about arbitrary grids as one finds in real life, where the number of solutions may be zero or larger than one (by mistake). The theorem holds in the general situation and then says that an even number of solutions agrees with a given choice of positions (cells) and candidates. When the grid has a unique solution, that even number can only be zero.

[eclark]

I can't even find ones that need type 2.
......................
can anyone give me one ?

If I understand the type definitions, a good example is #655 of the top1465.

Code: Select all

 ..8|..5|...
 ...|23.|...
 9.2|4..|...
 ---+---+---
 .6.|...|...
 ..9|.4.|.57
 8.3|.7.|.1.
 ---+---+---
 3..|...|.7.
 ...|5..|.26
 ...|..8|4..


 1467   1347   8      | 1679   169    5      | 12379  3469   1239
 14567  147    14567  | 2      3      1679   | 1789   4689   189
 9      137    2      | 4      8      167    | 1357   36     135
----------------------+----------------------+--------------------
*47     6     *47     | 1389   5      1239   | 2389   389    2389
 12     12     9      | 368    4      36     | 368    5      7
 8      5      3      | 69     7      269    | 269    1      4
----------------------+----------------------+--------------------
 3      12489  1456   | 169    1269   4      | 1589   7      1589
*147    14789 *147    | 5      19     347    | 1389   2      6
 12567  1279   1567   | 37     1269   8      | 4      39     1359


Eight 1s may be eliminated in box 7 and row 8.

Ron

Thanks now my solver is making the appropriate redustions

[ronk]

now give me a sudoku that requires type 3! (and can not be solved with 1,2 and 4 instead)

Wolfgang has already posted a type 3, but you may wish to look at others posted here.

[edit: Link was to an invalid type 3.]

[Havard]

ronk:

I don't know if you read the posts in reverse order or simply don't read them at all, but I saw Wolfang's post:

Hi Havard,

thanks for your explanations, together with MadOverlord's definitions i hope, i understood it now. Then this Angus' unlimited021 should be a "pure" type 3:

and thanked him for it:

That puzzle is great! just what I wanted. Thank you!

[flip]

Here are my solver results for UR with the top95.
The UR reductions are only attempted after all simpler reductions,
and also after all xwing/swordfish/jellyfish, conjugate coloring, bug and xy-wing. No implication chains, tabling, nishio, T/E before the UR..
(edited) When everything else fails, elementary discontinous nice loops implying an assertion of a candidate is tried.

Code: Select all

 #  1  2  2B  3  3B  4  4B
 4  x
 5                   x
11                   x
13  x
14            x
25         x
32  x         x
39            x
41                   x
45            x
52                   x
56            x      x
61            x
71            x          x
82     x
91                       x
92                   x
94                   x


I hope you will find this interesting, and would appreciate feedback.
I would like to know that the players on the forum agree with this.
If required I can post the candidates matrix for any of the solutions. If there is sufficient interest, we can do this also for top 870, top 520, ...

[ronk]

I don't know if you read the posts in reverse order or simply don't read them at all, but I saw Wolfang's post

My comment was intended to let you know that I was aware of Wolfgang's post ... *not* that you were unaware.

And since you brought up comprehension, or lack thereof, it'a apparent you didn't observe my link to another UR type 3 puzzle.

Ron

[Havard]

flip:

That is really cool! I have to go through them at some stage, but for now I have some questions:

In what order do you check the uniqeness in? The order listed? (1, 2, 2b etc)

Because if it is done in that order I would be very interested to know how many of the 3's that could have been done with a 4, and also:

By swapping the order of the two methods would you be able to find a puzzle where you indeed find a 4, but finding that will lead you to a dead end, as opposed to first finding the 3 and then solving it. (to prove your point in a previous post)

hope you can answer this!

havard

[Havard]

Ronk:

I am sorry man! Completly misread it. It was not my intention of being bitchy about it though, which I hope my little smily at the bottom indicated... Thanks for your link!

[ronk]

Here are my solver results for UR with the top95.
The UR reductions are only attempted after all simpler reductions, and also after all xwing/swordfish/jellyfish, conjugate coloring, bug and xy-wing. No implication chains, tabling, nishio, T/E before the UR..

Does that mean "implication chains, tabling, nishio, T/E", etc. are totally disabled? Or do these advanced techniques make reductions when req'd ... then giving simpler techniques additional opportunity to advance the puzzles?

TIA, Ron

P.S I observe little correlation to your results. For example, my solver finds type 4 in puzzle numbers 11, 14, 39, 56, 61 and 92. But then I haven't implemented type 3 yet, and I suppose that would alter results significantly.