Reverse BUG
In a 9 by 9 sudoku, a Reverse BUG is a state of the grid where every solved cell of two particular digits form an unavoidable set of less than 18 cells, without the presence of hidden singles.
If we assume that a valid sudoku must contain a unique solution, then a Reverse BUG cannot occur. Thus, as a solving technique, we can eliminate candidates from cells that cause a Reverse BUG to appear.
Proof
For any two digits, we have an unavoidable set of 2n cells involving these two digits if and only if these cells occupy exactly n rows, n columns, and n boxes. Suppose we have a Reverse BUG of 2n cells with n < 9, then we have an unavoidable set occupying n rows, n columns, and n boxes. Now, the remaining 9 - n rows, 9 - n columns, and 9 - n boxes will contain another unavoidable set of 18 - 2n cells. As this latter unavoidable set contains no placements, it is a deadly pattern which implies that this sudoku puzzle does not have a unique solution. Therefore, a Reverse BUG cannot occur in a valid sudoku puzzle.
Example
This example is taken from the at Sudoku Players' forums.
*-----------------------------------------------------------* | 189 7 -18 |*2 4 5 | 3 19 6 | | 6 3 *2 |*1 8 9 | 4 5 7 | | 19 5 4 | 3 7 6 | 129 129 8 | |-------------------+-------------------+-------------------| | 1238 1289 1378 | 5 6 12 | 129 78 4 | | 124 1249 6 | 8 12 7 | 5 1239 39 | | 5 128 178 | 9 3 4 | 6 78 12 | |-------------------+-------------------+-------------------| | 7 128 138 | 6 5 12 | 1289 4 39 | | 123 6 9 | 4 12 8 | 7 123 5 | | 1248 1248 5 | 7 9 3 | 128 6 12 | *-----------------------------------------------------------*
If R1C3 = 1, then R12C34 forms a Reverse BUG on the digits 1 and 2. Therefore, 1 can be eliminated from R1C3.
