Because I am a puzzle enthusiast, many a person has naturally assumed that I am also a sudoku enthusiast. Not so. Sure, sudoku is a puzzle of sorts, but I have standards. I am somewhat picky about puzzles, in fact. It is a consequence of seeing so many of them--I have a fairly good conception of what constitutes a "good" puzzle and a "bad" puzzle.

Have I ever told the story about why I dislike Mensa? I was once deeply unimpressed by a set of puzzles that they had published... Deeply unimpressed. But I digress.

As for sudoku, sudoku has no soul.

Forgive me. I forgot to explain what sudoku is. It's an enormously popular puzzle that has been replacing crossword puzzles in newspapers everywhere. It looks like this:

You must fill each of the blank squares with a digit 1 through 9 such that no column, row, or 3x3 square contains two of the same digit. (This one was taken from Wikipedia)

As I was saying, sudoku has no soul. Okay, I'll concede that it has a soul, but only one, and it's fragmented among all of the many many sudoku puzzles that have ever been created. Sudoku is the Lord Voldemort of puzzles.

The sudoku puzzle is one of those puzzles that is easily manufactured. There's software out there that can simply create these puzzles with no real human input. Just tell the computer what difficulty you want, and it will generate a brand new puzzle with different numbers filled in the squares. It's sort of like those factory-made hamburgers that everyone loves to hate (but in practice are very popular). If you like human ingenuity in your puzzles, you won't find it in sudoku. Even if you have one of those hand-made sudoku puzzles, it's only marginally better. The point is that it could have been made by a computer.

To solve pretty much any sudoku puzzle, you just have to learn three or four elementary steps. The rest of the puzzle is just learning to use them more efficiently. Learning to do it more quickly. But never, in all the sudoku puzzles you ever see, will you ever encounter anything truly different. It's always the same. Not exactly the same, but the same on some level of abstraction. I don't like crossword puzzles either, but at least they have new trivia questions every day.

It's sort of like giving a daily Rubik's cube puzzle. There are only a few tricks you have to learn to solve any Rubik's cube arrangement. Thus, one Rubik's cube arrangement is about the same as any other. The Rubik's cube cannot be a daily puzzle, because it is only one puzzle, not many. Likewise, sudoku is only one puzzle, with one soul. Its soul is fragmented once more every time a computer produces another sudoku puzzle.

As far as puzzles with fragmented souls go, sudoku isn't even a particularly interesting one. Yes, there are a whole bunch of other pencil-grid puzzles, each with different rules. The Japanese puzzle magazine Nikoli has created and popularized many of these puzzles. There are also a bunch of examples here, and more unusual examples here. Yes, I have lots of sites like these bookmarked, because for all my griping, I still like to do these puzzles on occasion. But not sudoku; I skip over those. Sudoku has got to be the most boring of them all. Most of the ones besides sudoku require more than 4 different elementary steps, or at least more interesting elementary steps. Some of the more difficult puzzles even require that you look at the puzzle hollistically rather than using elementary steps.

The general population has managed to pick out the driest puzzle of the bunch. For some reason, I do not think this is a coincidence.

## Sunday, October 19, 2008

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## 5 comments:

I agree with you on this, except that there are times when all I want to do is mindlessly follow an algorithm. My puzzle of choice for these times is Paint by Numbers, but it's the same idea.

I am interested in Sudoku from the standpoint of the usual mathematical questions that one always asks of a new puzzle. For instance, given any (solved) Sudoku grid, I can generate a new grid by:

1) permuting the groups of three: the first three columns, second three columns, last three columns, the three blocks of columns, etc., and

2) permuting the numbers 1, …, 9 that fill in the grid.

Given a single solved grid, can we generate ALL other solved grids in this way? That is, is there a unique solution up to these types of permutations?

Basically, it's a nice framework on which to hang some interesting combinatorics.

There are known to be 6*10^21 sudoku solutions, and 5472730538 "essentially" different solutions. I would expect the problem to be highly nontrivial, because a sudoku solution is like a constrained version of a 9x9 latin square. There is no known formula for the number of latin squares, and the extra constraint only makes it harder.

Sorry about that broken link. Here it is:

http://en.wikipedia.org/w/index.php?title=Sudoku&oldid=246318203#Mathematics_of_Sudoku

I once wrote a computer program that would solve any Sudoku puzzle I believe. It was written in Excel, using the Visual Basic that comes with Excel, because that is what was available on the computer that I was using. After entering a few Sudoku puzzles from the newspaper that were said to be the most difficult, I lost all interest in Sudoku and never did one of those puzzles again. I hope I don't lose credibility here, but if anyone asks for the program, unfortunately I lost it in a disk crash. But the point is that it wasn't even a very difficult program.

It's not too surprising that it's easy to write a program to solve sudoku. As I said, there are programs out there that generate Sudoku puzzles. Mechanically generating puzzles would be much harder than mechanically solving them.

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