| Mathematician, puzzle designer explores
Sudoku’s mathematical roots MATT GETTY Math department guest speaker Laura Taalman recently had some shocking news for the masses of Sudoku junkies out there. Though the now ubiquitous puzzle rose to fame because of its supposed math-free pleasures, hunching over the newspaper and scribbling numbers into that nine-by-nine grid, she argued, is actually math in its purest form. “People always say that Sudoku doesn’t involve any math because you don’t have to add or subtract any of the numbers,” said the James Madison University professor and puzzle designer during her “Beaucoup Sudoku: The Sudoku Mystique” lecture. “What they really mean is that there’s no arithmetic—because that’s what they think [mathematicians] do all day, just add different numbers together. But there’s lots of math in Sudoku. There’s logic, there’s reasoning . . . That’s what math really is.” Throughout her talk, Taalman, dove deeply enough into that math to cross the eyes of most Sudoku enthusiasts. She detailed dozens of puzzle variations, explained their ties to such complex math concepts as polyominos, Latin squares, and permutation group theory, and explored the research questions they raise for mathematicians. Among those head-scratchers were seemingly innocent queries like how many different Sudoku boards are possible, and what’s the lowest number of clues needed to create a solvable Sudoku puzzle? Before you start counting, two mathematicians already used a computer algorithm to prove that there are
6,670,903,752,021,072,936,960 possible Sudoku boards out there. The second question, however, remains a bit more open. Though no one has created a Sudoku puzzle that can be solved with less than 17 clues (blocks prefilled with numbers), Taalman said, mathematicians have yet to prove that 17 is the definitive minimum. What’s also unknown, Taalman’s talk proved, is how many Sudoku variations you can create. From mini 4-by-4 Shidoku squares, to hexagonal Hexaguko boards, to a three-dimensional Sudoku cube featuring numbers 1 through 64, Taalman discussed the subtle theoretical differences between puzzles that, though they embrace the same concepts as classic Sudoku, wouldn’t necessarily be a great way to pass the time on your next commute. “You wouldn’t ever want to do a puzzle like that,” she warned, pointing at one of the more intricate examples and noting that it would take the better part of a week just to complete a single row. “That wouldn’t be any fun—unless you were a computer.” Still, according to Taalman, the implications of Sudoku’s math roots sometimes reach beyond computers and mathematicians. In 2005, she explained, a life-sized Sudoku puzzle in England showed that not understanding the math behind the puzzles can cause real problems. Constructed as a publicity stunt by an English TV network, the 275-foot puzzle promised 5,000 pounds to the first person who could solve it. Though a true Sudoku puzzle only has one solution, she explained, this one had 1,905 winning solutions, which—at 5,000 pounds a piece—made for a rather costly math mistake. 
In honor of the math department’s annual “Fool’s Feast,” which followed the Sudoku lecture, Taalman created this “Fool’s Feast Sudoku” puzzle. To solve it, fill each column, row, and bolded region with each of the letters from “Fool’s Feast.” Note: because that phrase contains two Fs and two Os, those letters will appear twice in each column, row, and region, while the others will appear only once. Good luck.
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