Dispatch: On Sudoku, Engagement and Flow

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 3x3 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.