## Future Pairs

Advanced methods and approaches for solving Sudoku puzzles

### Future Pairs

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
reallyjoel

Posts: 8
Joined: 14 July 2005

### Re: Future Pairs

Joel, I think what you're describing is what I call a "naked triple".
angusj

Posts: 306
Joined: 12 June 2005

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.
reallyjoel

Posts: 8
Joined: 14 July 2005

### IT'S SOLID!

Why not dub it the 'incomplete triple'?
normxxx

Posts: 11
Joined: 12 July 2005

### Re: Future Pairs

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 - - - - - - - - - - AfterA: (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.
tso

Posts: 798
Joined: 22 June 2005

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
reallyjoel

Posts: 8
Joined: 14 July 2005