Mathematical or not?

Last year we talked about Sudoku (Great new way to waste time catches on fast), and followed that up with a blog about Kakuro (Do you do or do you don't 'doku?). There, we said that: “We at Dewey Manor don't think Sudoku really counts as a mathematical game, since it doesn't require players to carry out any mathematical operations,” and “[Kakuro] is really a test of logic, not of arithmetic.” So we assigned Sudoku and Kakuro the Dewey number 793.73 Puzzles and puzzle games, and not 793.74 Mathematical games and recreations.

However, in the comments on the first blog, Thom Hickey and Dennis McGovern disagreed with us.  Dennis (writing under the handle of “LCDennis”) said:

I disagree with the other residents of Dewey Manor in that I think Sudoku really counts as a mathematical game, even though it doesn't require players to carry out any mathematical operations. The popular version of Sudoku (i.e., the one described in the 1st 20 Google results) is played using numbers (mathematical symbols). I think of number games as mathematical recreations, and I agree with the LC subject heading (sh85082131) which has Number games as a 450 ref. to Mathematical recreations. To my way of thinking Guardian's Godoku (which doesn't have much literary warrant) is another game: a logical game using letters that should also class in 793.74.

He also pointed us to the Wikipedia article on Sudoku and to web pages on Sudoku and related puzzles by the Australian mathematicians Anne Street and Diane Donovan.

These things have way of coming back to bite you, and we have just dealt with assigning Dewey numbers to the LCSH Weekly List containing “Sudoku.”  (Weekly List 2005 no. 37 -- the list with “Kakuro” is still in our future).  And we’ve had a change of heart: we’ve decided that Sudoku is a game involving Latin squares, a topic within 511.64 Permutations and combinations, while Kakuro involves 519.77 Integer programming.  The Wikipedia even has an article on the Mathematics of Sudoku.

510 Mathematics is a large topic, and now includes a lot more than traditional topics like algebra, calculus, geometry and statistics: it includes many other formalized and axiomatised systems, such as 511.3 Mathematical logic, 511.6 Combinatorics, and 519.7 Programming (which is not the same topic as the mathematics of computer programming, but includes linear programming and nonlinear programming).  Both Sudoku and Kakuro fit within this broader concept of mathematics, and belong in 793.74 Mathematical games and recreations.

Comments

[Thom]

The links to the previous posts aren't quite right. Here's the first: http://ddc.typepad.com/025431/2005/08/great_new_way_t.html
--Th

[Giles Martin]

Thom -- Thanks, I got a bit confused in setting up the links, but I've corrected them in the article, and I think they are right now.

[Jonathan]

Thanks for the shoutout to NCFC the other day, Giles! But of course it was always going to be The Sudoku Question that would finally wake me from post-Manor reverie. Here's my take on the latest news: Noooooooooo! Don't believe the hype! Sure, some people write about "the mathematics of sudoku" just as you can imagine other people writing about "the mathematics of chess." That doesn't make either sudoku or chess mathematical recreations. The class number in question is not being assigned to works on this "mathematics of sudoku"; it's being assigned largely to works that comprise lots of suduko puzzles. And the bottom line is: When you solve a sudoku puzzle in the normal way, you don't do anything that would normally be construed as mathematical. Sure, you can analyze the setting or solving of sudoku (or chess) puzzles mathematically. That doesn't make the act of solving sudoku (or chess puzzles) in the normal way a mathematical recreation. Sudoku is a logic puzzle, and logic puzzles go in 793.73. To cite "Mathematical logic" as part of mathematics is a red herring. Mathematical logic does not approximate the whole of logic. If it did, then presumably we would be want to class all logic puzzles in 793.74. But it doesn't and we don't! The distinction between logic and mathematics may well be a "fine line" (as Thom says), but so long as it's a line that Dewey continues to draw (in this case between logic puzzles and mathematical puzzles), then how can we possibly class sudoku -- a puzzle which requires no knowledge of any mathematical concepts to solve -- as a mathematical rather than a logical recreation?

[Kaffinator]

Agreed. I've been playing Sudoku almost non-stop ever since a friend introduced it to me last Christmas. The game would play just as easily if you used sets of letters, shapes, or colors instead of numbers. It's a logic game.

[kakuro]

I think that Kakuro is much more interesting than sudoku beacuse that shapes change all the time!

[Free Jigsaw]

I disagree because to do Sudoku you have to use addition to complete each square. That means its a mathmatical problem!

[Domo Sudoku]

I don't think sudoku is a real math game. You just place numbers in a logical sequence.