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A Latin square is an n × n matrix of n distinct symbols, where each row and column contains exactly one of each symbol. The number of size-n Latin squares is a rapidly growing function, although not terribly impressive from a googologist's point of view: \begin{eqnarray*} L(1) &=& 1 \\ L(2) &=& 2 \\ L(3) &=& 12 \\ L(4) &=& 576 \\ L(5) &=& 161280 \\ L(6) &=& 812851200 \\ L(7) &=& 61479419904000 \end{eqnarray*} No simple formula is yet known for the function \(L(n)\). It is upper-bounded by the function \(n \mapsto (n!)^n\), since each of the \(n\) rows has an arrangement of \(n\) distinct symbols.

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  • Latin square
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  • A Latin square is an n × n matrix of n distinct symbols, where each row and column contains exactly one of each symbol. The number of size-n Latin squares is a rapidly growing function, although not terribly impressive from a googologist's point of view: \begin{eqnarray*} L(1) &=& 1 \\ L(2) &=& 2 \\ L(3) &=& 12 \\ L(4) &=& 576 \\ L(5) &=& 161280 \\ L(6) &=& 812851200 \\ L(7) &=& 61479419904000 \end{eqnarray*} No simple formula is yet known for the function \(L(n)\). It is upper-bounded by the function \(n \mapsto (n!)^n\), since each of the \(n\) rows has an arrangement of \(n\) distinct symbols.
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  • A Latin square is an n × n matrix of n distinct symbols, where each row and column contains exactly one of each symbol. The number of size-n Latin squares is a rapidly growing function, although not terribly impressive from a googologist's point of view: \begin{eqnarray*} L(1) &=& 1 \\ L(2) &=& 2 \\ L(3) &=& 12 \\ L(4) &=& 576 \\ L(5) &=& 161280 \\ L(6) &=& 812851200 \\ L(7) &=& 61479419904000 \end{eqnarray*} No simple formula is yet known for the function \(L(n)\). It is upper-bounded by the function \(n \mapsto (n!)^n\), since each of the \(n\) rows has an arrangement of \(n\) distinct symbols.
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