Latin square

Displaying a 7 × 7 Latin square, this stained-glass window at Gonville and Caius College, Cambridge, honored Ronald Fisher, whose Design of Experiments discussed Latin squares. The Sir Ronald Fisher window was removed in 2020 because of Fisher's connection with eugenics. 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 3 × 3 Latin square is

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. Euler began the general theory of Latin squares.