thumb|Construction of Ramanujan's birthday magic square from a 4×4 Latin square with distinct diagonals and day (D), month (M), century (C) and year (Y) values, and Ramanujan's birthday example The problem of determining if a partially filled square can be completed to form a Latin square is NP-complete.
thumb|construction of ramanujan's birthday magic square from a 4×4 latin square with distinct diagonals and day (d) month (m) century (c) and year (y) values and ramanujan's birthday example the problem of determining if a partially filled square can be completed to form a latin square is np-complete