Math and Sudoku

January 6, 2006

Welcome to 2006! I hope everyone had a cheery holiday season.

I posed the following query on comp.theory but haven’t gotten any responses at all, so I thought I’d see if I can get any feedback here. (In the past when I’ve posted some really dumb questions on comp.theory, I’ve received lots of replies; there seems to be an inverse relationship between the volume of discussion and the meaningfullness of it. So maybe my current question is not so bad.)

My niece has become interested in sudoku, and this interest has spread to my own children. I was thinking that sudoku would make a nice jumping-off point to introduce topics in discrete math and complexity theory. Are there any books out there that deal with this? I haven’t been able to find anything. Ideally, such a book would be geared toward a teen-aged audience and maybe cover topics like combinatorics, logic, and NP-completeness as they apply to sudoku. A quick Google search reveals lots of web sites that touch on this stuff, so maybe it’s just too new an area to have made its way to print yet.

I’m reminded of some of the discussion following FOCS ‘05 about how to get complexity theory into the public awareness. It seems to me that tying it to a subject that’s already popular with the general public would be one way to achieve this.

Any thoughts? I know David Eppstein has an interest in sudoku; I wonder if he’s ever considered writing something like this. Or maybe I should think about writing this myself? I’m grossly unqualified, of course, but that might actually be an advantage–it could make it easier to understand the point of view of a general audience and anticipate the hard spots when explaining concepts.

posted in Sudoku, pedagogy by Kurt

8 Comments to "Math and Sudoku"

  1. KristinW wrote:

    I’m not aware of any books, but there is an examination of the mathematics of sudoku here:http://theory.tifr.res.in/~sgupta/sudoku/algo.htmlKristinW< HREF="http://www.sudokulinks.com" REL="nofollow">SudokuLinks<>

  2. Kurt wrote:

    Kristin, thanks for that link. I haven’t had a chance to read through all of it yet, but so far it’s very interesting. I was somewhat surprized to see that there are a number of open questions regarding Sudoku mathematics. Even something as seemingly simple as counting the number of possible configurations requires a brute-force enumeration.Your SudokuLinks site is also very nice.

  3. twidjaja wrote:

    Kurt: I think the game is too new, and probably no one has written a book on the mathematics of sudoku. A good account on the subject is probably wikipedia http://en.wikipedia.org/wiki/Mathematics_of_Sudoku.What else? ;-)

  4. Kurt wrote:

    Hi Anthony,Thanks for the link. I should have thought of checking there; one of the things Wikipedia excels at is new or rapidly changing information.By the way, I noticed on Logicomp your pointer to Igor Naverniouk. I really dig his new < HREF="http://trueai.blogspot.com/" REL="nofollow">blog<>’s aesthetics!

  5. twidjaja wrote:

    Kurt: I have let Igor know about your kind words – he will appreciate that.Anyway, I have noticed several postings in the blogsphere (including your blog, Suresh’s, and Lance’s) on how to popularize complexity theory to general audience. I am interested in something related: how to get kids interested in math and science (including computer science, physics, or even cosmology). These days many kids are spoiled by video games, etc. leaving very little room for curiosity about math and science. Since you have kids and are interested in a related issue, I’m sure you have some advice or pointers to useful discussion.

  6. Abednego wrote:

    First of all, I don’t think it’s fair to blame computer games for lack of interest in math, but that’s a topic for a different and very heated discussion.I can tell you how my dad got me interested in math and computer science. Once in a while, he would give me a book and say, “This is cool; see if you like it.” Many of them ended up on my favourites list. Here are a few.H. Dudeney, < HREF="http://www.amazon.com/gp/product/B0006BQK8O/qid=1136995018/sr=8-3/ref=sr_8_xs_ap_i3_xgl14/103-3479146-0640602?n=507846&s=books&v=glance" REL="nofollow">536 puzzles and curious problems<>, a couple of book my Martin Gardner (on was called “Tic Tac Toe”) and a book by Raymond Smullian called “Princess or Tiger”. All of them were Russian translations, so I might be off on the titles.And I wasn’t an avid reader. These books and whatever was assigned to us at school were pretty much the only ones I would read, so even if your kids hate reading, it’s worth a try. I’m certainly glad my dad pointed them out. I must have been 6 or 7 back then.

  7. Anonymous wrote:

    A great site to teach you the various techniques to solve Sudoku puzzles is < HREF="http://www.sudokulearningcenter.com" REL="nofollow">Sudoku Learning Center<>It has great web based online tutorials on the various techniques, a graphical interface to give hints and show the techniques, and specially constructed puzzles to focus on the individual techniques.Try it out and see what you think.

  8. Anonymous wrote:

    I have a neat Sudoku applicationfor Windows, it includes the abilityto create a puzzle to solve on a PC,store, or EMail it. It has featuresincluding HINT and AUTOSOLVE, coloring, etc. Contact me atervnork@excite.com and I’ll Emaila Zip file to you with Demo puzzlesincluded.

 
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