A latin square is an n × n array filled with the integers 1 to n, each occurring once in each row and column.

You can make it as random as you want as long as it's a Latin Square

Is the output meant to be a random square of size nxn? This is actually a complex mathematical problem, and then add to that the computational problem of finding a algorithm efficient enough so that it won't time out at high values of n; the ranking of this problem as 7kyu feels way too low. Unless we're just meant to submit a non-random square. If that's the case please clarify.