Is this a new technique?

Advanced methods and approaches for solving Sudoku puzzles

Postby Lummox JR » Thu Oct 20, 2005 9:24 pm

gsf wrote:
Lummox JR wrote:No indeed. Trial and error has a specific placement to prove true or false; this does not. This method compares possible sets to determine which interfere with each other, and which can never be chosen. Based on that it can look for 1) digits which never appear in a certain position, or even better 2) digits which always appear in a certain position.

are you saying trial and error is limited to "does this move solve the puzzle"?

Absolutely not. I'm saying trial-and-error is limited to:

1) Does this move cause a contradiction?
2) Does this set of moves, one of which must be true, prove another move false?
3) Does this set of moves, one of which must be true, prove another move true?

Clearly Brendan's technique is not T&E, although it may be making deductions with similar results, because it has a pattern. It's analyzing a convergence of two columns or rows, and finding cases that can never work. If you consider that T&E, you could say the same of coloring, X-wing, or any other technique. (Indeed all logical techniques have an if-then factor, but the easier ones are all refined in some way. If the term trial and error is to have meaning at all, you need to draw the line somwhere.)

Another major reason this could not be considered true T&E is that it does not rely on having a specific placement to prove or disprove. It merely applies a pattern and looks for eliminations based on that, as all easier techniques do.
Last edited by Lummox JR on Thu Oct 20, 2005 7:10 pm, edited 1 time in total.
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Postby r.e.s. » Thu Oct 20, 2005 10:24 pm

DanO wrote:I tried it out on the "Toughest Known Puzzle" by enumerating the first two rows and was surprised that the permitted values [12] dropped out of R1C1 and R1C3.
Lummox JR wrote: It's very interesting that you found two eliminations in row 1 for the toughest known puzzle.

Just to set the record straight in this thread ... DanO was mistaken, as was pointed out in a different thread. (For this puzzle, the solution to r1c1 is 2, so it cannot be eliminated as claimed.)
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Postby DanO » Fri Oct 21, 2005 12:11 am

Lummox JR wrote:Given that this test relies on two columns or two rows and on the digits that line up between them, I think it makes sense to call this test Alignment. I'd reserve the term enumeration for cases where you're only testing the possibilities of a single column/row (or box!).

Sudoku itself relies on the alignment of columns and rows. This technique enumerates the possibilities for a set of cells then eliminates the combinations that can't exist. Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth. So an alternate name could be Sherlock.

The technique (or a slight modification of it) can also be extended to any number of rows or columns as long as you have enough paper and patience.

The real use I see for his technique is to determine if there is an unknown rule hidden in the pattern in some set of cells. It can't tell you directly what the rule is but it can be used to find the subset of cells that are involved.

And it would be best to have a computer to do the work because it's too easy to make a mistake:)
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Postby Lummox JR » Fri Oct 21, 2005 4:38 am

Enumeration, though, is the precise definition of what you're doing for just one row: You enumerate the possibilities for it. Your test is checking how those enumerated possibilities can merge, and that is dictated by the alignment of digits between the two rows.

Sherlock does have a nice ring to it, though.:)
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Postby r.e.s. » Fri Oct 21, 2005 4:44 am

Obviously it's Sherlock's Permutation Alignment Method (SPAM).
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Postby Brendan » Fri Oct 21, 2005 4:57 am

I like Sherlock, it gets my vote. Enumeration doesn't really imply a test, just listing possibilities. I thought allignment was good, but then tried the test for rows within a single block, and it is a bit more than simple allignment due to constraints of the block. Perhaps Row Allignment and Block Allignment as two variants of the same approach, but a single word that can be made into a verb is better. You could say "I Sherlocked row 1 with row 5". That sounds quite nice.

Since you pointed me to the Hardest Known Sudoku, I tried it myself. I "Sherlocked" the first three rows in a manner similar to similtaneous equations (row 1 on 2, row 1 on 3, result 1 on result 2) and was able to find the position of the 8 in the top right block, which forced the 8 in the centre. I was also able eliminate one of the 1s in the top left block, but I haven't had much luck elsewhere. Still, I haven't done an exhaustive search yet. By hand it takes so long. Maybe I should write an excel program to do the enumerations.

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Postby Myth Jellies » Mon Oct 24, 2005 5:28 am

killed because of errors
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