My sudoku brain broke

[Fish]

Stuck on LA Times Sudoku page (no registration required), a 5-star puzzle from Friday December 26th. Link. (http://games.latimes.com/index_sudoku.html?uc_feature_code=lasud&uc_full_date=20081226) Given numbers are in green; my inserts are in black.

I always seem to get to this point and get stuck. There's obviously a technique for getting past it, but the techniques (X-wings and swordfish) are hard to grasp. What am I looking for here?

6 2 7 | _ _ _ | 9 _ 5
9 5 _ | _ 2 _ | _ 7 _
8 _ 3 | 9 5 7 | 2 _ _
- - - - - - - - - - -
4 _ _ | 5 _ _ | 7 _ 9
5 _ 9 | 7 1 4 | _ 2 _
7 _ _ | _ 3 9 | _ 5 4
- - - - - - - - - - -
3 _ 5 | _ _ _ | 6 _ 7
2 9 _ | _ 7 5 | _ 8 3
1 7 _ | _ _ _ | 5 _ 2

[Lumpy]

Here's a few clues:

R2C9 cannot be 6, because the only places that can be 6 in the second 3x3 square are in row2. That means that R2C9 can only be 1 or 8.

It is then possible to show by a chain of either/ors that if R6C7 is not 1, then R2C3 has to be 1, and vice-versa. This means that the two squares at R2C7 and R6C3 cannot be 1.

This opens up a chain of either/ors for the 1s that eliminate further candidates from being 1s. Some of the eliminated squares than have only two numbers left and can be scouted for either/or chains for other numbers, etc.

P.S., I couldn't do this without a computer aid that shows me remaining candidates for each square.

[want2know]

In square 3 on the top section, 8 can only go in R2, C7 or 9. That eliminates 8 from R2 in square 2 ; 8 can only go in R1.

[Lumpy]

Actually, the clues I gave above aren't that helpful, since they dead-end. Here's a much better one:

R5C2 cannot be 8, since either R7C2 is 8, or if it's not, then by a chain of either/ors R5C9 has to be 8.

That opens up the rest of the puzzle.

[Oslo Ostragoth]

Since row 5 contains a 1, the only possible 1's in column 9 are in row 2 or 3, so other 1's can be excluded in square 3.

Lumpy - could you explain the either/or thing to me? Also, what calculator are you using? Simple Sudoku got stuck at the same place.

[Oslo Ostragoth]

Ditto square 2 - the one's in row 2 can be excluded and the 6's in row 2 of square 3.

[Lumpy]

Lumpy - could you explain the either/or thing to me? Also, what calculator are you using? Simple Sudoku got stuck at the same place.I was using Simple Sudoku to display the candidates but it doesn't solve it automatically. When I plug in Fish's numbers I get the following results:

R7C2 is either 4 or 8. R3C2 is 1 or 4. R3C9 is 1 or 6. R5C9 is 6 or 8.

R5C2 can't be 8 if R7C2 is 8. If it's 4, then R3C2 has to be 1; R3C9 has to be 6; and R5C9 has to be 8. In which case R5C2 can't be 8 anyway. I believe most Sudoku references call this type of proof "chaining".

[Fish]

Ah, thank you Lumpy. I see where you're going with that.

If only there were a simple way to see such chains without all the "if this, then that" throughout the puzzle.

[Oslo Ostragoth]

Errrm, I'm still not getting it.

[Fish]

The five squares in Lumpy's example make a shape like a P, like this:1 or 4 .... 1 or 6
R5C2 .... 6 or 8
4 or 8
We can test the possibilities 4 and 8 in that one box. If we choose 8, then R5C2 cannot contain 8.

If we choose 4, then you follow the possibilities around the chain and end up with 8 in the "6 or 8" box.

In both cases you have ruled out 8 in R5C2.