Solving Sudoku – Two Group Intersection

Let’s continue with a study of the advanced Sudoku solving techniques. In my previous post, I looked at partitioning the cells of a single group. In this epistle, I look at what you can do with two intersecting groups. In this case, it’s a 3×3 square intersecting with either a row or a column. (If you consider the intersection of a row and a column, you can apply one of the basic techniques.)

Consider the groups marked in green in the following:

We have two groups: a row and a 3×3 square. Look at the three cells that belong to both groups, and consider the value 4. Within the row, the value 4 exists only in the intersecting cells. Within the 3×3 square, the value 4 must exist in one of those two cells that also belong to the row. Therefore, the value 4 can be eliminated from the other cells of the square.

With the techniques described up until now, you have the means at your disposal to solve the vast majority of puzzles. But there are still a few tricks left, which will have to wait until later postings. Next up, we look at the corners of a rectangle.


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