Two lines of a Latin square

Task number: 3901

In how many ways can the first two lines of a Latin square of the order \( n \) be filled in correctly?

  • Solution

    The first two lines can be seen as a notation of the permutation. Because two identical symbols must not appear in the same column, this permutation is without fixed points.

    However, the first line of each such permutation can be selected in \(n!\) ways.

  • Answer

    These two lines can be filled in \(n!\cdot s(n)\) ways, where \(s(n)\) is the function from the cloakroom problem.

Difficulty level: Easy task (using definitions and simple reasoning)
Reasoning task
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