This is the fourth posting in the series of techniques for solving Sudoku puzzles. First, I discussed the basic techniques. Then, I discussed single-group partitioning and two group intersection. Those techniques are enough for the vast majority of puzzles. Here, I discuss another technique that might be useful.
This technique takes advantage of an important characteristic of Sudoku puzzles. All puzzles have (or should have) one unique solution. Consider the cells at the four corners of a rectangle, for example:
Consider the cell at the lower right. If values 6 and 7 were eliminated, we would be left with an ambiguous state. That is, these four cells would all have the same two possibilities. There would be two possible solutions. But we can’t have that. We must have a unique solution.
Therefore, the possibilities 6 and 7 must remain, and we can eliminate the possibilities 4 and 5 from that cell:
And of course, once possibilities are eliminated, other opportunities to proceed will open up. In this particular example, if there were only three possibilities instead of four, we could write that in directly.
Next up, four group intersection.