At least three commuters are bent over what appears to be a crossword puzzle, their pens scribbling at a pace that strikes me as more furious than its rules of engagement warrant. In fact, they are so engaged, that even the bus driver’s abrupt and arbitrary decisions to include and exclude stops from the route do not sway them from their task. A fourth commuter, sitting across the aisle and apparently stymied by an intractable problem, notices that I am peering over his shoulder to see what has him so enraptured. “Sudoku,” he explains. “My wife’s banned them from the house. So I get in as many as I can on the ride home. This one’s a bugger.”
If like me, you are not a puzzle fan and unacquainted with anyone who is, the Sudoku craze may have passed you by. Here, then, is a typical example: a standard puzzle grid of 81 cells, arranged in nine rows and nine columns, and divided into nine 3×3 blocks. Some cells have numbers called givens. Your goal is to complete the rest of the grid with numbers 1 to 9 such that these numbers appear only once in each row, each column and each block. A well-formed Sudoku has only one solution (click on the puzzle for its unique solution).
There seems to be two strategies to finding said solution: logic and guessing. Logic is the preferred strategy, and implies that you only assign a number to a cell when you can prove that no other number can occupy this cell. It involves ruling out all impossible candidates for each cell in conflict with other cells, or alternatively, identifying all possible candidates based on compatibility with other cells. That selected candidate, in turn, uncovers at least one other determinable cell value. However, these two methods take you only as far as the simplest puzzles. More complex puzzles require advanced methods that involve pairs (triples and quads) with two (three or four) possible values, and aim to reduce the number of potential candidates so that, sooner or later, a unique candidate or unique hidden candidate will emerge. Some analytic methods with descriptive names such as “swordfish” and “x-wing” involve scanning for patterns across the entire grid, not just its parts, and can be chained or to solve very challenging puzzles. Sudoku may have simple rules, but also sophisticated analytics.
The second strategy, guessing, embraces trial and error. You speculate with a number, explore the consequences, and backtrack as needed if it doesn’t work out. It turns out that guessing is a viable option for solving Sudoku by computer, which can make short work of identifying the solution, but is deeply unsatisfying for humans who take pleasure in the problem-solving process. A quick computer download could easily help my aisle-mate find his way out of the quagmire of cross-referenced columns, rows and blocks. “I’ve been working on this particular puzzle all week,” he says. “When I finally get it, it will be real sweet, though.”
Sweet, indeed. Sudoku can be as engaging, addictive, and flow-embracing as the flashiest, real-time, shoot-em-up game available.
