orthogonal Latin squares

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orthogonal Latin squares

[ȯr¦thäg·ən·əl ¦lat·ən ′skwerz]
(mathematics)
Two Latin squares which, when superposed, have the property that the cells contain each of the possible pairs of symbols exactly once.
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However, there are some papers which would be well within the grasp of enquiring and mathematically literate high school students, such as those exploring Euler's famous formula (E = F + V - 2), the Konigsberg Bridge problem and Graeco-Latin Squares.
At the end of this paper is an application to Graeco-latin squares and balanced factorial groups in the design of experiments.
One application of the Gray codes generated in this paper is in producing Graeco-latin squares (any square of ordered pairs in which each entry of the alphabet appears exactly once as a left-hand entry in every row and every column and similarly for right hand entries) and balanced factorial groups in the design of experiments.