Future Pairs

Advanced methods and approaches for solving Sudoku puzzles

Future Pairs

Postby reallyjoel » Sat Jul 23, 2005 2:29 am

This is a pretty obvious one, but it's not mentioned on http://www.angusj.com/sudoku/hints.php, so i thought I'd throw it out there.

If you have three cells with candidates 1 and 2, and 2 of them have candidates 3 also, and candidate 3 is ONLY in those two cells in that box/row, then you can eliminate all other cells 1's and 2's, because wether the 3 goes in one or the other, the other one will make a pair with the third cell.

I can only guess this is very common knowledge.

/Joel
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Re: Future Pairs

Postby angusj » Sat Jul 23, 2005 2:35 am

Joel, I think what you're describing is what I call a "naked triple".
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Postby reallyjoel » Sat Jul 23, 2005 2:59 am

No, I dont..

In a row, two cells has for example 1,2 and 3 for candidates. 3 can only be in those two cells in that row. A third cell has only 1 and 2. No matter where the 3 ends up, there will eventually be a pair with the other cell. Thus, you can remove 1 and 2 from the other 6 cells.
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IT'S SOLID!

Postby normxxx » Sat Jul 23, 2005 4:49 am

Why not dub it the 'incomplete triple'?
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Re: Future Pairs

Postby tso » Sat Jul 23, 2005 6:35 am

reallyjoel wrote:This is a pretty obvious one, but it's not mentioned on http://www.angusj.com/sudoku/hints.php, so i thought I'd throw it out there.

If you have three cells with candidates 1 and 2, and 2 of them have candidates 3 also, and candidate 3 is ONLY in those two cells in that box/row, then you can eliminate all other cells 1's and 2's, because wether the 3 goes in one or the other, the other one will make a pair with the third cell.

I can only guess this is very common knowledge.

/Joel


Really realyjoel, you *are* describing a specific case of naked triples. A through D below are all basically the same structure. In each case, the first three cells must be 1, 2 and 3 in some order, so the 4th through 9th cells must not be 1, 2 or 3. You've described B -- but they're all basically the same thing:
Code: Select all
     Before - - - - - - - - - - After
A: (123) (123) (123) (1234) => (123) (123) (123) (---4)

B: (123) (123) (12-) (124)  => (123) (123) (12-) (--4) 

C: (123) (1-3) (12-) (1234)  => (123) (1-3) (12-) (---4)

D: (-23) (1-3) (12-) (1234)  => (-23) (1-3) (12-) (---4) 



Even this line below qualifies as a triplet, though it includes a pair within which could be processed first:
Code: Select all
(-23) (-23) (1-3) (1234) => (-23) (-23) (1-3) (---4) => (-23) (-23) (1--) (---4)
or
(-23) (-23) (1-3) (1234) => (-23) (-23) (1--) (12-4) =>  (-23) (-23) (1--) (---4)




This idea extends to quads, quints, etc. N cells with N values:

Code: Select all
E: (12345)(12345)(12345)(12345)(12345)(123456)

F: (1---5)(-23--)(-2-4-)(---45)(12--5)(123456)


In both E and F, the first 5 cells must be 1 through 5 in some order, so the 6th cell is 6. Read Argusj again.
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Postby reallyjoel » Sat Jul 23, 2005 3:37 pm

OK, I got it now.. I thought naked triples only was the same three candidates in three cells and nothing else. But ofcourse it doesnt matter if one of the three cells are missing one candidate.

Cheers
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