Monday, July 30, 2007

Easy is relative in Sudoku

The DC Examiner now appears to carry two Sudoku puzzles a day, instead of just one. What's interesting to me, is that even though both puzzles are labeled as one out of five stars in their difficult rating, I found one of the puzzles far more diffficult and time consuming to solve than the other.

The "Pacific Sudoku" was truly easy and I was able to solve it in less than ten minutes, while the "Sudoku classic" was much more difficult for me to crack and took the better part of an hour.

You would think that an easy puzzle is an easy puzzle, wouldn't you?

Except, the more I think about it, the more I think this is a fallacy.

Let's say there are (just for the sake of argument) ten methods a person can use to solve a sudoku puzzle. There isn't one single method that can solve an entire puzzle all by itself; you have to combine at least two methods in order completely solve a puzzle. If all methods worked equally well on all puzzles, then it would be possible to come up with an "objective" difficulty rating.

The problem is that different techniques work on different puzzles with varying degrees of effectiveness. In other words, methods 1 and 3 might work fantastic on one puzzle, but leave significant gaps on a second puzzle.

If you happen to know the two (or three, or however many) techniques that are particularly effective on that specific puzzle, then the puzzle might be easy in the truest sense of the word. But, if you are missing one of the techniques that is particularly effective on that puzzle, and have to "fall back" and rely upon a lesser technique, then you must expend more effort to crack the puzzle's structure.

So, unless you know ALL of the sudoku puzzle cracking techniques, the ratings will appear uneven. (This begs the question, can Sudoku puzzles be crafted in such a way to favor certain solving techniques? I don't know, nor can I think of a way to test that hypothesis at this time.)

The only thing I've managed to learn today is that, from a subjective standpoint, the difficulty ratings on a Sudoku puzzle appear relative to the number of techniques that a person knows. Until you know all the solving techniques, the ratings will seem radically uneven.

Naturally, this begs the question-- how can you learn all of the Sudoku solving techniques?

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