compelling. Addicts of both forms of self-torture have much in common.
3×3 Latin squares
A square array containing exactly one symbol in each row and each column is
called a Latin square. The number of symbols equals the size of the square and is
called its ‘order’. Can we fill out a blank 3×3 grid so that each row and column
contains exactly one of the symbols a, b and c? If we can, this would be a Latin
square of order 3.
In introducing the concept of a Latin square, Leonhard Euler called it a ‘new
kind of magic square’. Unlike magic squares, however, Latin squares are not
concerned with arithmetic and the symbols do not have to be numbers. The
reason for the name is simply that the symbols used to form them are taken
from the Latin alphabet, while Euler used Greek with other squares.
A 3×3 Latin square can be easily written down.
If we think of a, b and c as the days of the week Monday, Wednesday and
Friday, the square could be used to schedule meetings between two teams of
people. Team One is made up of Larry, Mary and Nancy and Team Two of Ross,
Sophie and Tom.