Problem Statement

A Latin square of size n is an arrangement of n symbols in an n-by-n square in such a way that each row and column has each symbol appearing exactly once. For the purposes of this task, a random Latin square of size n is a Latin square constructed or generated by a probabilistic procedure such that the probability of any particular Latin square of size n being produced is non-zero. Strict uniformity in the random generation is a hard problem and not a requirement of the task.

Let's start with the solution:

// Generate 2 Random Latin Squares of order 5. Nigel Galloway: July 136th., 2019
let N=let N=System.Random() in (fun n->N.Next(n))
let rc()=let β=lN2p [|0;N 4;N 3;N 2|] [|0..4|] in Seq.item (N 56) (normLS 5) |> List.map(lN2p [|N 5;N 4;N 3;N 2|]) |> List.permute(fun n->β.[n]) |> List.iter(printfn "%A")
rc(); printfn ""; rc()