Solving Sudoku – Four Group Intersection

Here we come to the most challenging technique yet for solving Sudoku. This one involves looking at the intersection of two rows and two columns. Look for a situation where you have the same possibility in four unsolved cells, where those four cells are the corners of a rectangle. Consider the following diagram:

Here we have 4 as a possibility in the fours cells marked in green. Examine the other marked cells. If 4 does not occur in any of the red cells, then it must not exist in any of the blue cells.

That is, if 4 is not in any red cells, then there are two possible arrangements for the 4‘s in the green cells: upper-left and lower-right; or upper-right and lower-left. Either way, with just the green cells, the columns will already have their cells with value 4. If there are any 4‘s in any of the blue cells, they can be eliminated as possibilities.

In practice, this situation is rather rare. Sometimes, you’ll find cases where you’ll find the same value in four corner cells. But more often than not, you find that value in both the rows and columns. In those cases, see if it’s possible to eliminate possibilities to get to a state where you can apply this technique.

Note that this technique can also scale up to three columns and three rows. But that’s an even more rare situation.

Well, those are all the techniques I’ve figured out. To summarize, continually use the basic techniques until you reach an impasse. If you’re lucky, and the puzzle author is kind, the basic techniques will be sufficient. But once you find yourself needing to make notes, you’re probably into the realm of the advanced techniques. First look at the groups with lots of solved values, and the cells with few possibilities. And keep plugging away at it. With experience, you’ll find it easier to recognize the situations where you can apply the more advanced techniques.

Hans

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