# Latin dating introduction dating advice from men to women

The applet below offers you two problems: one simple and one less simple.

In the simple one, you are requested to arrange numbers in a square matrix so as to have every number just once in every row and every column. Mc Worter who wrote his Masters Thesis on (orthogonal) latin squares kindly offered his assistance in preparing pages on this entertaining topic. The great mathematician Leonhard Euler introduced latin squares in 1783 as a "nouveau espece de carres magiques", a new kind of magic squares. It was shown in 1960 by Bose, Shrikhande, and Parker that, except for this one case, the conjecture was false.

The latin square A of order 4 below is constructed by cyclically permuting the symbols in the first row for subsequent rows.

1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 The latin square B arises as the multiplication table for the nonzero integers modulo 5: 1 2 3 4 2 4 1 3 3 1 4 2 4 3 2 1 Computers do modulo 2 arithmetic on strings of zeros and ones.

It is a matter of taste how the dating service chooses to order the people and code the days, so the other three latin squares above could display exactly the same information.

Let's say two latin squares are iff one can be transformed into the other by a combination of permuting rows, columns, and symbols.

In one sense all of these latin squares of order 3 are all the same.

The original latin square could be a table of information and the other tables just personal taste on how to display the information and code the data.

Isomorphic comes from greek; iso meaning same and morph meaning form.

Consider the three latin squares constructed below.

The second problem imposes one additional condition: the arrangement must be symmetric with respect to the main diagonal (the one from the North-West to the South-East corner.) There are two ways to manipulate rows of the matrix: originating with L. He also defined what he meant by orthogonal latin squares, which led to a famous conjecture of his that went unsolved for over 100 years. You can get a bunch more latin squares (but only one more of the 2 by 2) by permuting rows, columns, and/or symbols in any combination.