Math in Madison
Some of you may be surprised at this, but even mathematicians get together for conferences. I just returned from a math conference in Madison, WI, sponsored by the Mathematical Association of America (MAA). There were probably over 500 mathematicians there. Now you might be asking yourself what mathematicians could sit around and talk about for three or four days. Well, believe it or not, the frontiers of mathematics are ever expanding.
One of my favorite talks was given by Dr. Laura Taalman of James Madison University on sudoku puzzles. She described the variants of sudoku (for instance, a 4×4 version that is known as shidoku), and the mathematics behind the puzzles. Here are some example questions that you could ask that naturally involve a lot of math:
- How many possible sudoku boards are there? (The answer turns out to be a LOT.)
- How many of these are essentially the same?
- What is the minimum number of clues needed for a sudoku puzzle to have a unique solution? (This is currently not known, though it’s guessed to be around 17.)
Much of the answers to these and other questions involve group theory and/or combinatorics. (One note: I can’t get by without saying that newspaper introductions to sudoku that say something like, “This puzzle isn’t about math at all” really don’t know what they’re talking about!)
You can check out Dr. Taalman’s website here: http://www.math.jmu.edu/~taal/mainpage.html
If you’re interested in sudoku variants, check out this website: