Problem Statement

A perfect shuffle (or faro/weave shuffle) means splitting a deck of cards into equal halves, and perfectly interleaving them - so that you end up with the first card from the left half, followed by the first card from the right half, and so on:

When you repeatedly perform perfect shuffles on an even-sized deck of unique cards, it will at some point arrive back at its original order. How many shuffles this takes, depends solely on the number of cards in the deck - for example for a deck of eight cards it takes three shuffles:

The TaskTest Cases

Let's start with the solution:

let perfectShuffle xs =
  let h = (List.length xs) / 2
  xs
  |> List.mapi (fun i x->(if i<h then i * 2 else ((i-h) * 2) + 1), x)
  |> List.sortBy fst
  |> List.map snd

let orderCount n =
  let xs = [1..n]
  let rec spin count ys =
    if xs=ys then count
    else ys |> perfectShuffle |> spin (count + 1)
  xs |> perfectShuffle |> spin 1

[ 8; 24; 52; 100; 1020; 1024; 10000 ] |> List.iter (fun n->n |> orderCount |> printfn "%d %d" n)