University Times

Do you Sudoku? If the ever-rising number of pencil-clutching ponderers poring over the 81-square game grids is any indication, it seems as though nearly everyone does.

Sudoku is turning up in some unusual places on campus, not just with those who have some time to spare or in the hands of bored students in the back of a lecture hall.

The concept is simple: The Sudoku grid consists of three columns and three rows of three-by-three boxes. Every row, column and box contains the digits 1 through 9 without repeating. (The name “Sudoku” is abbreviated from the Japanese phrase that means “the numbers must be single.”) The difficulty of the puzzle can be adjusted based on which and how many numbers already are filled in for the solver, who must use logic to complete the grid.

Everywhere, it seems, people are working the logic puzzles that appear in newspapers, on page-a-day calendars and in puzzle books with an enthusiasm that can border on addiction. Some are calling the Sudoku craze the Rubik’s Cube of the 21st century.

Earlier this year, the Washington Post — one of about 140 daily newspapers that feature Sudoku puzzles — drew more than 7,000 entries for 200 seats at a Sudoku tournament in which the grand prize was a trip to London and a Union Station shopping spree.

And, capitalizing on the trend, Florida-based Challenge Me LLC is setting up 32 regional tournaments (including a stop in Pittsburgh July 22 and 23) each with 2,048 registration slots, in which organizers hope participants will pay $29.99 for a chance to go on to a national Sudoku tournament in Las Vegas next January.

For a better idea about the puzzle’s popularity, a Google search on the term “Sudoku” yields 68.9 million results. In comparison, a search on “University of Pittsburgh” returned 38.4 million results and “Pittsburgh Steelers” turned up only 15.1 million.

Although Alexandros Labrinidis doesn’t work the puzzles himself, the Pitt assistant professor of computer science jumped on the bandwagon last semester with a Sudoku assignment for his mid-level web programming class. Rather than opting for a tic-tac-toe game assignment he said could be boring, “I kind of rode the wave,” he said. “It’s very popular.”

Students didn’t have to program the game itself, but needed to build a user interface that would allow moves to be made and to be undone on a modified Sudoku grid.

“The rules are easy, but the game is quite complicated to play,” he said. Labrinidis modified the nine-by-nine Sudoku grid to a four-by-four square to prevent savvy students from simply copying an existing on-line Sudoku game.

“I know many of them played this,” he said, adding that the assignment was well received.

Because they had to test the assignment to ensure the solution worked, some could claim they had to play Sudoku for their classwork. “I forced them into playing it,” he said with a laugh.

Mathematics professor Bard Ermentrout pointed out that the puzzles don’t really require numbers or mathematical concepts, but are a special case of what’s known as a Latin Square that adds the requirement that each 3-by-3 box within the puzzle use the numbers 1 through 9 once. (A Latin Square is a square matrix made up of a number of rows and columns in which the same number of different symbols are arranged so each appears only once in each row or column.)

“You could put anything in (the squares),” he said, noting the famous example of a Sudoku predecessor containing the Latin words sator, arepo, tenet, opera and rotas, which, when aligned in a column, spell each word both horizontally and vertically.

Some such grids once were thought to have magical properties, hence the alternate name “magic squares.”

Ermentrout said one key to making a popular puzzle is keeping the rules simple. “Nothing is simpler than these rules,” he said of Sudoku. He said the nearly infinite variety —there are more than 6,670,903,752,021,072,936,960 possible combinations, according to figures quoted by puzzle expert Will Shorts — ensures that players at varying skill levels can enjoy Sudoku without being frustrated and without fear of running out of challenges.

Ermentrout said he typically does not work the puzzles. “I do math all day. It’s not what I want to do for fun,” he said, adding that he’s upset that Sudoku has stolen his former crossword puzzle partner’s attention. “My wife does (Sudoku); I suck at them,” he said with a laugh, lamenting the loss of her help with the crosswords.

Ermentrout said the use of computers to generate Sudoku puzzles allows them to be created quickly and ranked in degree of difficulty, letting players have a bit of advance warning about what they’re getting into at the start.

Rather than working the puzzles for fun, Ermentrout has pondered other questions the puzzle raises:

What is the most number of hints one could give such that if you’d take one number away you could no longer solve the puzzle uniquely? Or, what’s the minimum number of hints one could give and still have a unique, solvable Sudoku puzzle?

Ermentrout notes that the degree of difficulty in each puzzle isn’t based solely on the number of clues, but on their location as well, pointing out that Sudoku design purists, like good crossword puzzle designers, lay out their grid in a symmetrical manner.

“It’s the degree of look-ahead that determines the difficulty,” he said, likening the process to the foresight needed to do well in chess.

Ermentrout also has tinkered with finding alternate ways to make solutions to the puzzle arise without using logic at all, but by thinking about ideas related to oscillation theory — the concepts of repulsion or minimizing an energy landscape to yield a workable solution.

On-line encyclopedia Wiki-pedia.org attributes the advent of today’s Sudoku to “Number Place” puzzles found in a 1969 Dell puzzle book, although the concept of Latin Squares can be traced back several millennia. The Dell version of the puzzle didn’t catch on in America, but became a hit in Japan in the early 1980s, where it soon got the name Sudoku.

Wikipedia.org states that in 1997 Wayne Gould saw the puzzle in a Japanese bookshop. Gould developed a computer program to produce the puzzles quickly and pitched the idea to British newspapers, where the puzzle began appearing late in 2004 before spreading to America and beyond. Ermentrout, who spent spring break in Switzerland, noted he saw Sudoku in the daily papers there, as well as in the airline magazines.

It’s too soon to tell whether the puzzle will spark an increased interest in logic as an academic pursuit, said Distinguished Professor of Philosophy Anil K. Gupta, who teaches undergraduate- and graduate-level logic classes.

The list of logicians who also are puzzlemasters is lengthy, he said. Lewis Carroll, author of the “Alice in Wonderland” stories, is a familiar example from the past; mathematician and author Raymond Smullyan is a modern-day example.

The logic puzzles Gupta gives in class to illustrate logical deduction typically are word problems, but he is considering adding Sudoku puzzles as well.

And while Sudoku isn’t among the deep logic puzzles pondered by logicians through the ages, it is a satisfying pastime, said Gupta, who said he occasionally picks up a Sudoku puzzle.

Why is Sudoku so popular? Gupta said the puzzle has many attractive aspects. “It’s a challenge, but it’s meetable,” he said. And, unlike crosswords, which require the ability to recollect words, Sudoku doesn’t require memory or even math skills. “It’s absorbing. Your worries disappear,” Gupta said.

—Kimberly K. Barlow