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Last Issue:
Tuesday,
December
18
2007
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When Sudoku Meets Math and Creative Minds
By Michelle Williams
Published on 05-Dec-06
More than 70 Sudoku enthusiasts came out Wednesday evening to learn about the many variations and mathematical analysis of the latest puzzle craze. The event, hosted by the Math Club, attracted faculty and former faculty members, staff and students who did the puzzle up to at least three times a day.
"I generally do one a day," says Frank McDonald, a research scientist at the Institute for Physical Science and Technology. "They're strangely addictive."
Although the definite origin of Sudoku remains unclear, it was introduced in Japan in 1984 as Suujii wa dokushin ni kagiru meaning "the numbers are to remain single." The common Sudoku puzzle is a 9 x 9 board. The general rule for solving the puzzle is not to repeat the digits 1-9 in any row, column or block. A true Sudoku puzzle only has one unique solution; however, the world's biggest Sudoku puzzle, a 275 ft by 275 ft grid, in the United Kingdom had 1,905 solutions--a sizable Sudoku blunder.
The guest speaker of the presentation was Laura Taalman, an associate professor at James Madison University's Math Department. Wearing a black shirt with "puzzle geek" printed across the front, she explained how mathematics could give new perspectives to the puzzles' nuances. For example, two European professors, Bertram Felgenhauer and Frazer Jarvis, estimated that there are 6.67 sextillion or 6.67 X 1021 completed solutions boards of a 9 x 9 Sudoku grid. Felgenhauer and Jarvis came up with the number using permutations, combinatorics and what they called "brute force."
Another way to look at the puzzle mathematically is to use certain math problems to solve the puzzle. This is good for someone who wants to solve the puzzle in a more methodical way instead of the ol' stab in the dark approach.
"You can think about Sudoku puzzles as Latin squares with additional constraints," says Taalman. She added that treating the puzzle as an integer solutions problem is another possible avenue to solving the logic-based puzzle. With that, you take a system of equations, "solve the system of equations," and take that answer and translate it into Sudoku language.
For the ones who become bored very easily, Taalman also revealed many variations of Sudoku. There are puzzles with extra restrictions such as Four Pyramids where no number is repeated in a shaded pyramid. There are puzzles containing multiple Sudoku puzzles such as Twodoku or the Samurai X where the puzzles' solutions hinge on parts of the other(s). There is even the Dion cube for the hardcore enthusiasts.
"The Dion cube had 27 interlocking Sudoku puzzles," says Taalman of the three-dimensional puzzle resembling a Rubik's Cube. A man from Scotland solved the puzzle and only won a bottle of champagne for his effort.
From puzzles using alphabets to mini Sudokus with 4 x 4 boards, the creators of the puzzles are doing it all. Some of the creators even throw witticisms into the puzzles such as in the Size 8 whose clues form an eight in the middle of the board. The variety of Sudoku puzzles was entertaining to the audience.
"I thought [the presentation] was wonderfully done," says Douglas Gill, a professor in the Department of Biology who plays the puzzle when he wakes up and before he goes to bed. "I would love to take a class with her."
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