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YOUR CHALLENGE: Insert

a number from 1 to 9 in
each cell without repeating
any of those digits in the same
row, column or subgrid (3×3 box).
The solutions to the moderately
difficult Sudoku in the center and to
others in this article appear at www.sciam.
com, along with additional puzzles.

80 S C IE N T IF IC A ME R IC A N

COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC.

The Science behind

SUDOKU
Solving a Sudoku puzzle requires no math,
not even arithmetic. Even so, the game poses
a number of intriguing mathematical problems
BY JEAN-PAUL DELAHAYE

O

ne might expect a game of logic to appeal to very few

people—

mathematicians, maybe, computer geeks, compulsive
gamblers. Yet in a very short time, Sudoku has become
extraordinarily popular, bringing to mind

the Rubik’s cube craze of the early 1980s.
Unlike the three-dimensional Rubik’s cube, a Sudoku puzzle is a fl at, square grid. Typically it contains 81 cells (nine
rows and nine columns) and is divided into nine smaller
squares conta