单选题
Solving Sudoku Puzzles
The principle behind Sudoku puzzles is fairly straightforward. A typical Sudoku grid is made up of nine rows and nine columns containing 81 individual cells. This basic fiat square grid is further divided into nine smaller 3X3 squares called sub-grids. Each sub-grid thus consists of its own nine cells. At the beginning of the puzzle some numbers are already printed in certain cells. A player must completely fill in the empty cells with numbers ranging from the 1 to 9 so that no digit appears in the same row, column or subgrid twice. Any Sudoku puzzle has only one possible solution. In spite of the fact that it is an analytical game involving numbers, it does not require any mathematical skills because no arithmetic operations assist players in completing the grid.
This must be why Sudoku puzzles are all the rage amongst logic games right now. Not since the three-dimensional Rubik cube of the 1980s has a game attracted more players. But, unlike its modern times predecessor, Sudoku dates way back to the Middle Ages, when so-called Latin squares were being filled up with icons or colors instead of numbers. The German mathematician Leonard Euler was the first scientist to draw attention to these number-games and study their rules during the 18th century. The first printed Sudoku puzzle appeared in the May 1979 edition of "the Dell Pencil Puzzles and Word Gaines" under the care of retired architect Howard Garns. But the name Sudoku derives from its 1984 Japanese translation in a magazine, and means something like "single numbers." A Hong Kong retired judge named Wayne Gould came across one such puzzle during a visit to Japan in 1997 and proceeded to write a computer program that would automatically generate Sudoku grids. He managed to publish a stream of such puzzles in two major London newspapers during 2004-2005, and thus a new craze was to be born.
At the moment, no respectable magazine or even weekend flyer can hope to sell if it does not include a Sudoku. The game is more often than not played online too, and there are dedicated websites that cater to any Sudoku aficionado. From novice to diabolical grids, computer programs can pretty much spew out any puzzle as one"s heart desires. For those fans already bored by the traditional grid, there are several compelling alternatives. The Dum-Sum-Oh puzzle replaces numbers with letters or dominoes, and square sub-grids with other types of geometric shapes. In another variant, six triangular sub-grids intertwine to add numerical challenge, or else three game boards overlap for even more complexity. Further complications can be added by requiring players to perform side-by-side mathematical operations, or by making use of the "greater-than-less-than" signs. Thus, a Sudoku can take anywhere from a few minutes to several hours to complete.
But it is not only players who got obsessed with Sudoku. Mathematicians have also started to analyze a host of fascinating issues that Sudoku raises. They have yet to solve the question of how many Sudoku starting grids exist. They are also still scratching their heads about the smallest number of start-up digits in a grid that can still guarantee a single solution, although the answer seems to be 17 after 16 was ruled out. It is very time-consuming to verify this answer since there are over 5 trillion valid Sudoku puzzles out there although their total number had not been identified yet. Even a speedy and proficient computer program would need something close to 173 years to check for all possibilities. One thing is for certain, nonetheless. The maximum number of givens to guarantee a unique solution is 77.
Glossary
grid:
network of evenly spaced horizontal and vertical lines that can be superimposed on a map, chart, etc., especially in order to locate specific points
variant:
an example that differs from a standard
a host of:
a very large number of