first slot we receive signals from both frequency 1 and frequency 2; while the third slot has signals from frequencies 1, 2 and 3. Because of the noise, we can no longer tell if the first two slots were 1,1 or 1,2 or 2,1 or 2,2. But the 1,2 case is the only one that yields a sequence matching a letter in the above table, the letter A. Similarly, we may imagine a burst of static over all frequencies in the third slot: Again, we are able to infer from the table of encodings that it must have been the letter A being transmitted. The number of errors this code can spot is one less than the number of time slots. It has also been proven that if the number of frequencies is a prime or a power of a prime, the orthogonal Latin squares produce error detecting codes that are as efficient as possible. Mathematical puzzles The problem of determining if a partially filled square can be completed to form a Latin square is NP-complete. The popular Sudoku puzzles are a special case of Latin squares; any solution to a Sudoku puzzle is a Latin square. Sudoku imposes the additional restriction that nine particular 3×3 adjacent subsquares must also contain the digits 1–9 (in the standard version). See also Mathematics of Sudoku. The more recent KenKen and Strimko puzzles are also examples of Latin squares. Board games Latin squares have been used as the basis for several board games, notably the popular abstract strategy game Kamisado. Agronomic research Latin squares are used in the design of agronomic research experiments to minimise experimental errors. Heraldry The Latin square also figures in the arms of the Statistical Society of Canada, being specifically mentioned in its blazon. Also, it appears in the logo of the International Biometric Society. Generalizations A Latin rectangle is a generalization of a Latin square in which there are n columns and n possible values, but the number of rows may be smaller than n. Each value still appears at most once in each row and column. A Graeco-Latin square is a pair of two Latin squares such that, when one is laid on top of the other, each ordered pair of symbols appears exactly once. A Latin hypercube is a generalization of a Latin square from two dimensions to multiple dimensions. See also Block design Combinatorial design