## Notice

I am no longer posting new puzzles to this blog. For all of my Sudoku puzzles, old and new, please visit Sudoku in another section of this website. I will still create and offer new puzzles, in batches of a couple of hundred, once a week or so.

## Sudoku #59

Category: Sudoku
Sun, 07 May 2006, 17:09

After doing Sudoku puzzles for about a year, you might think there's nothing left to learn about the puzzle. On the contrary, I never believed for a moment that I knew all there is to know about Sudoku. Actually, I always suspected that there was yet another solving technique to be discovered. And finally, this past week, I came across that technique.

Here's part of my solution and notes to puzzles S72.60 in the Standard Puzzles:

Note that the cells marked with yellow have the possibilities {14}. But the cell to note is the cell marked in blue with possibilities {149}. Let's assume that the blue cell does not have the value 9. All the yellow and blue cells would then have the possibilities {14}. This would mean that the puzzle would have two solutions! Since valid Sudoku puzzles must have unique solutions, our original assumption must be wrong, and the blue cell must have the value 9.

The following diagram illustrates the technique:

Consider the four cells at the intersection of two rows and two columns. If three of the cells have possibilities {ab} and the fourth has {abc}, then possibilities {ab} can be eliminated from the fourth cell. Note that c might be one or more possibilities.

Also note that, unlike the other advanced techniques described in How to Solve Sudoku, this one can result in the direct determination of the value of a cell.

Anyways, what does this new technique mean to my puzzles? Clearly, none of my 150,000 puzzles require this technique. I said I wasn't going to post any more new puzzles. But I may have to reconsider that decision. I'll add this new technique to my program, and then I'll see if it's possible to generate puzzles that do require this technique. If so, then I may have to add some more puzzles.

Hans