Advanced techniques to solve Sudoku puzzles

X-wing

If a candidate appears only in 2 cells of a row, and the same candidate appears only in 2 cell of another row as well, and these 4 cells are located in the same 2 columns forming a hypothetical rectangle, we can reject that candidate from the rest of cells of the 2 columns. We can proceed with columns as well.

Observing row 2 we see that there are only 2 cells with the candidate 2, A2 and B2, now observing row 7 we see that there are only 2 cells with the candidate 2 as well, A7 and B7. As A2 and A7, and B2 and B7 share the same column respectively, we can reject candidate 2 from the rest of cells from both columns, removing the candidate from the cells A4, A8, B3 and B9.

Sword-fish

Using the same technique from X-Wing but extending the concept to 3 rows, and the candidate appearing only in 2 or 3 cells per row, and these cells located in the same 3 columns, always matching up at least 2 cells per column.

Observing row 1 we see that the candidate 1 appears only in 3 cells, A1, C1 and G1. In row 2 the candidate is repeated in the cells A2 and G2, while in row 8 the cells that contain the candidate 1 are A1 and C1. As all of these cells are distributed only in 3 columns, A, C and G, and there are always at least 2 cells per column, we can reject number 1 as a candidate from the rest of cells from these 3 columns. So we can remove the candidate from the cells A7 and G6.

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