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.
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.
At the end of this paper is an application to Graeco-latin squares and balanced factorial groups in the design of experiments.