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## The Nine Squared Enigma That is Sudoku

For millennia, people have been drawn to things that vexed their minds. The riddles, the word and number puzzles – if they involved intense thinking, they were loved. The 1970s saw the widespread love (perhaps for some love-hate) relationship with a single block containing smaller rotating square blocks of different colors called the “Rubik Cube”. This year, the head-scratching, hair-tearing and downright addictive game of choice is a Japanese creation called Sudoku.

Like the vast majority of large puzzles, Sudoku appears seemingly benign, a simple grid of nine squares, with each square containing nine small squares (eighty-one small squares in total). The nine large squares (“mothers”) are generally considered to belong to one of the puzzle’s three grids called regions. Each of the eighty-one small squares contains, or will contain when completed, a digit between the digits one and nine.

Even the rules of this game – which first appeared in everyday life in Japan in 1986 – seem relatively simple. To “win” at Sudoku you must fill in every region, column and row of the grid, no spaces can remain. Yet the difficulty begins to factor in when you take into account the rule that says each of these areas can only contain the number (one through nine) once. Some squares already contain numbers, these are called “givens”, it is the player’s job to fill in the empty spaces, while respecting the rule of “one occurrence” for each number in each of the three directions of the puzzle.

Interestingly, the numbers are really only used for convenience, as they have no mathematical bearing on the game itself*. They don’t need to add up to a sum or occur in any particular set of patterns. Instead of numbers, the puzzle can contain shapes, colors, symbols, whatever, as long as the same rule (that each appears only once in each area of the puzzle) can be applied. Maybe the appeal of Sudoku is that it looks so easy, what’s hard to fill in a few boxes, right? Still, one try at this game, and all but the most seasoned logistics pros will find themselves in a little over their heads. This does not mean that the game cannot be completed, quite the contrary, and after a while Sudoku “pros” are able to complete a puzzle in a few minutes. But it takes work, a lot of work, study and devotion to this unique Japanese square.

The world has certainly jumped on the Sudoku bandwagon, its popularity-generating websites (which often feature many free puzzles of varying degrees of difficulty) and regular Sudoku puzzles in many magazines and newspapers, even computer software. Sudoku! With a crossword-like appearance and chess-like strategic maneuvers, it’s no wonder Sudoku originated in Japan and became an international obsession.

**In reality, Sudoku is based on a mathematical principle known as “complexity theory”, which classifies Sudoku as an “NP-complete (non-deterministic polynomial time) puzzle (or problem).” The “NP” means that a puzzle/problem with this classification is the hardest problem of its kind to solve. It is a very complex mathematical form that does not yet have a definitive arithmetic solution for each Sudoku grid.*

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