Some of the oldest combinatorial objects, whose studies apparently goes back to ancient times, are the Latin squares. To obtain a Latin square, one has to fill the cells of an (n x n)- square array with the numbers 1,...,n so that every number appears exactly once in every row and in every column. Say someone started filling the cells with the numbers {1,...,n}. At some point she stops and asks us to fill in the remaining cells so that we get a Latin square. When is this possible? To find out, come to the talk.
