Is there a super technic that solvs any puzzle?

Advanced methods and approaches for solving Sudoku puzzles

Is there a super technic that solvs any puzzle?

Postby inventor » Mon May 08, 2006 9:43 pm

Hi evryone!

I think anyone who are puzling with sudoku whish there were a simple technic of solving any sudoku. And I am convinced that some of those posting here also think that there should be such a techic.

By looking at all these technics presented here, like X-wing, Swordfish, Coloring etc, I am very impressed and think these are efforts to come closer to a super technic. But as far as I know, none is found.

After having worked with this problem since christmas, I finaly and luckily discovered a technic 2 days ago (may 6, 2006). Astonishing it is an "All catch technic" that replaces all the advanced technics previously presented, and may even replace the "naked pair" (or triples) as well! And it also solves with ease puzzels that the sudoku program calls "unfair", as they cannot be solved unless using gessing. I have used the whole weekend solving all the "unfair" or "impossible" sudokus I have gathered over time, and anyone was solved. And it is not more difficult to use than most of the advanced tecnics presented here. On the contrary, as it require only a few "pencilmarks" in some selected cells.

It is obious that the sudoku ekspert programmer of "sudoku" has not found this technic, and as far as I have searched the net, no one else have. Or does anyone know? Or is it a silent agreement not to publish or present this technic?

I am currently constucing a computer program that I hope will be ready for released in june this summer, presenting this technic. You will be informed by me later on:)
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Postby ravel » Mon May 08, 2006 10:43 pm

I would be pleased to see a solution to one of the 4 hardest puzzles collected here with your technique.
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Postby dudzcom » Wed May 17, 2006 8:21 pm

presented are 3 techniques that may help you in your goal. these are generalizations of several established 'named' techniques.

99.9% of random standard-sized sudoku can b solved using these three techniques, however not all.

take a look, and see if you can reduce the 3 reduction rules on this website to a single rule. then you might be on to something.
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Postby Jeff » Fri May 19, 2006 2:45 pm

dudzcom wrote:99.9% of random standard-sized sudoku can b solved using these three techniques, however not all

Hi Dudzcom, Using the 3 reduction rules (which doesn't cover any nice loops), you will be very lucky to solve 90% of random 9x9 puzzles. Refer page 16 of Eppstein's paper here.
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Postby tso » Mon May 29, 2006 2:16 pm

It may depend on what you mean by "puzzle". The puzzles generated and tested in Eppstein's experiment were all minimal and limited to those with 180 degree rotational symmetry.

It also may depend on what you mean be "randomly generated". There are two main ways to create a puzzle -- start with a completed grid and remove clues, start with an empty grid and add clues -- each of which has room for much variation.

It's very likely that insisting on the puzzle being minimal or having a particular symmetry will change the percentages of puzzles solved by a set of rules. I'd be surprised if the method of creation didn't have as much an effect as well. (The way a completed grid is generated in the first method might have an effect also.)

Another way to generate puzzles starts with a mask -- a set of cells that will hold the clues. Different masks give widely different results. The method by which these masks are picked and used will change your results. Some masks might be unlikely -- maybe even unable -- to contain a puzzle that need anything but simple tactics, while others might give opposite results.

Further -- and I'm just speculating here -- if I were to create a puzzle by starting from a completed grid, and then, instead of removing a number at random and testing what's left for solvability, if I were to choose a solving tactic and apply it in reverse -- might I be able to create an unlimited number of puzzles, all of which could be solved by any particular set of tactics I chose? As long as the tactics were chosen at random and the cell or cells on which they were applied were as well, wouldn't I still be able to call them random sudokus? Is it possible that other methods typically used to create puzzles by hand are more likely to be solvable by simpler tactics than those generated at random? Might this be the reason that 100% of the hand made puzzles published by Nikoli before Sudoku reached the UK and the rest of the world were solvable by simple tactics rarely reaching the level of an x-wing?

Still, 99.9% seems too high for nearly any reasonable definition of random computer generated puzzle.
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Postby Binarius » Thu Feb 15, 2007 2:05 pm

Hi Dudzcom,

Regarding the website you refer to, reductions 1 and 3 are equivalent under the exchange of digits and rows/columns. It may be helpful to visualize the grid as a 9x9x9 cube (with digits changing along the third axis) -- you will see that Naked Pairs, Hidden Pairs, and X-Wings are exactly the same shape, just rotated through the three dimensions. The same goes for Naked/Hidden Triples and Swordfish, and Naked/Hidden Quads and Jellyfish. Note that we don't actually care about Squirmbags or n-Gronks for the same reason we don't care about naked or hidden subsets for n>4 (i.e., they each have a complementary subset of order <=4). Finally, I think the site may be mistaken in the statement that "Symbol Reduction is only valid when applied directly after Subset Reduction"; the way I see it, that would only be true if one updated one's candidates only after applying the Symbol Reduction rule -- a forgivable lapse of thoroughness on the part of a human player, perhaps, but less so on the part of a computer.

As for reduction 2, it is also equivalent to reduction 1 under the exchange of boxes and rows/columns. This situation is not as straightforward to visualize, since the intersection of a box and a row/column consists of either 0 or 3 coordinates for each digit, compared with the simpler value of 1 coordinate for each digit for the intersection of a row and a column; equivalently, any consideration of the effects of box constraints will break the three-fold symmetry we enjoyed with our 9x9x9 cube from above.

One more thing to note. While it is true enough that these rules will be sufficient to solve the vast majority of puzzles (specifically, those with ratings lower than "Hard", "Tough", "Fiendish", etc.), it is also true that they constitute a subset of the Simple Sudoku Technique Set, which has become standardized by convention in the advanced solving community as the realm of complexity only beyond which it becomes useful to formulate the "dozens of solution strategies" I presume the website is referring to. (It is true that many of these strategies are themselves special cases of more comprehensively overarching rules on which work remains ongoing, but this only becomes clear on levels that, while not necessarily higher, strike the solving community as more complex. We're only human, after all.)
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Postby sirdave » Thu Feb 15, 2007 8:43 pm

I'm glad to see Jeff responded above.

Above, we have 2 different posters presenting what are purported, in so many words, to be 'one-size-fits-all' methods that will make all the others unnecessary. I, for one, won't be holding my breath.

All the 'regular' methods, up to and including, nice loops have been fully described and tested with several puzzle examples over a period of several months to 1 to 2 years. In the case of the first poster, we have nothing but his say-so and judging from the name 'inventor', he may see this as something that must be kept under careful wraps because if I had developed a new earth-shaking method, I would be regailing everyone with nice examples.

In the second case, we have some nice theorems/formulas, but no examples. From what I can tell, as Jeff also concluded, they describe methods that will solve basic puzzles but not the category of puzzles that are usually discussed in this section of the forum.
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