What is "latin square"

In combinatorics and in experimental design , a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3x3 Latin square is:

A

B

C

C

A

B

B

C

A

The name "Latin square" was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols, but any set of symbols can be used: in the above example, the alphabetic sequence A, B, C can be replaced by the integer sequence 1, 2, 3.