X Wing
For every Sudoku, a value can exist only once in each row,
column and box. If a value has only 2 possible locations in
a given row (ie it has a candidate in only 2 cells in that row),
then it must be assigned to one of these 2 cells.
Given a particular puzzle that has two rows where a given
candidate 'C' is restricted to exactly the same two columns
(and no more than 2 columns), and since
1) candidate C must be assigned once in each of these two rows, and
2) no column can contain more than one of candidate C
then candidate C must be assigned exactly once in each of
these two columns within these two rows. Therefore,
it's not possible for any other cells in these two columns to contain
candidate C. This same logic applies when a puzzle that has two
columns where candidate C is restricted to exactly the same two rows.
This will be understood more easily by examining the example below.
Filtering has been added so only candidate 6's are visible.
The cells marked with a blue highlight form an "X-Wing" since
rows one and nine both have only two cells with candidate 6's
and these two cells share the same two columns. Therefore,
other candidate 6's in columns six and nine (highlighted yellow)
can safely be removed.
(Note: Candidate C must be assigned to either
1) the top-left and bottom-right corners, or
2) the bottom-left and top-right corners of the
rectangular grid created by these two rows and columns.
The pattern created by these crossed diagonals is the
likely origin to this technique's name.)
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