A few years ago, if you had noticed someone filling in a
crossword puzzle with numbers instead of letters, you might
well have looked askance. Today you would know that the
puzzle is not a crossword but a Sudoku. The craze has
circled the globe. It's in the newspaper, the bookstore, the
supermarket checkout line; Web sites offer puzzles on
demand; you can even play it on your cell phone.
Just in case this column might fall into the
hands of the last person in North America who hasn't seen a
Sudoku, an example is given on the opposite page. The
standard puzzle grid has 81 cells, organized into nine rows
and nine columns and also marked off into nine
three-by-three blocks. Some of the cells are already filled in
with numbers called
givens
. The aim is to complete the
grid in such a way that every row, every column and every
block has exactly one instance of each number from 1 to 9. A
well-formed puzzle has one and only one solution.
The instructions that accompany Sudoku often reassure the
number-shy solver that "No mathematics is
required." What this really means is that no
arithmetic
is required. You don't have to add up
columns of figures; you don't even have to count. As a matter
of fact, the symbols in the grid need not be numbers at all;
letters or colors or fruits would do as well. In this sense
it's true that solving the puzzle is not a test of skill in
arithmetic. On the other hand, if we look into Sudoku a
little more deeply, we may well find some mathematical ideas
lurking in the background.