Solving Sudoku – Single-Group Partitioning

Okay, so you’ve mastered the basic techniques to solve Sudoku puzzles, and you’re still stuck on a puzzle. At this point, you’ll need to make notes, writing in small print the possible values at the top of each cell. There are a number of “advanced” techniques that can help you progress. At no time should you have to guess at a possibility. All puzzles should be solvable using analytical methods. However, note that most of the advanced techniques only help you to eliminate possibilities. You’ll still need to basic techniques to finish the puzzle. But eliminating possibilities should provide more opportunities to apply the basic techniques.

The technique I describe here involves looking at the cells of one group. Consider the following group with possibilities listed:

Before continuing, have a look to see if you can spot any possibilities can be eliminated.

Note that the values 1 and 2 exist in only two cells in that row, and not in any other cells. Since those two values can only be in those two cells, all other possibilities can be eliminated:

At this point, with those values eliminated, you may find opportunities for applying the basic techniques, allowing you to move forward.

One more note on this particular example: The full 3×3 square at the left is not shown. However, now that we know that two cells of the square only contain the values 1 and 2, we can now eliminate those values from the rest of the cells of that square.

Note that the technique can also be applied with three values. Look for a set of three values that exist in only three cells. All other values in those three cells can be ruled out. Likewise for four or more cells.

In the next installment, I look at an advanced technique involving two intersecting groups.

Hans

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