Advanced Techniques

If two cells in the same row, column, or block contain only the exact same two candidates, you can safely eliminate those two candidates from all other cells in that same row, column, or block.

If two candidates appear in exactly the same two cells within a row, column, or block, they must be placed in those two cells. You can eliminate all other candidates from those two cells.

If a candidate only appears in a single row or column within a 3x3 block, it must be placed in that line within the block. Therefore, you can eliminate that candidate from the rest of that row or column outside the block.

If a candidate appears exactly twice in two different rows, and they share the same two columns (forming a rectangle), you can eliminate that candidate from all other cells in those two columns. (This also works vice-versa for columns to rows).

An extension of X-Wing. If a candidate appears in at most three cells in three different rows, and those cells fall into exactly three columns, you can eliminate that candidate from all other cells in those three columns.

Find a cell with exactly two candidates (the "pivot", e.g., XY). Find two other cells (the "pincers") in the same row, column, or block as the pivot, containing candidates XZ and YZ. Any cell that "sees" both pincers cannot contain the candidate Z.

If a candidate in a block forms an "L" shape (an empty rectangle), combined with a strong link in another row or column, you can eliminate the candidate at the intersection.

If four cells form a rectangle across two blocks and contain only the same two candidates, it causes multiple solutions. You must actively break this pattern to eliminate candidates.