Faster version

supernova.fsx

open System
open System.Collections.Generic
open System.IO

let words = File.ReadAllLines(@".\brit-a-z.txt")
            |> Array.filter (fun x -> x.IndexOf('\'') < 0)

let nines = words
            |> Array.filter (fun x -> x.StartsWith("a"))
            |> Array.filter (fun x -> x.Length = 9)
printfn "%d candidate words" nines.Length

let fives = words
            |> Array.filter (fun x -> x.Length = 5)
printfn "%d candidate sub-words" fives.Length

let bag (x : String) = x |> Seq.cast<Char>

let takeChar (c : Char) (l : List<Char>) =
  if l.Remove(c) then Some l
  else None

let takeChars (l : Char seq) (c : Char seq) =
  Seq.fold (fun l' c' -> Option.bind (takeChar c') l') (Some (List<Char>(l))) c

let solutions (t9 : Char seq) =
  let l5 = fives
           |> Array.map (fun x -> (x, bag x))
           |> Array.filter (fun x -> Option.isSome (takeChars t9 (snd x)))
  let matches = l5 
                |> Seq.map  (fun x -> l5
                                      |> Array.filter (fun y -> ((fst x).Chars 2) = ((fst y).Chars 0))
                                      |> Array.filter (fun y -> let all = Seq.skip 1 (Seq.concat [| snd y ; snd x |])
                                                                Option.isSome (takeChars t9 all))
                                      |> Array.map (fun y -> (fst x, fst y)))
                                      |> Seq.concat
  matches |> Seq.toList

let suitable  (t9 : string) =
  match solutions (bag t9) with
  | x :: [] -> Some (t9, x)
  | _ -> None
  
  
printfn "%A" (suitable "supernova")
let sw1 = System.Diagnostics.Stopwatch.StartNew()


let total = nines 
            |> Seq.choose suitable 
            |> Seq.map (fun x -> printfn "%A" x
                                 x)
            |> Seq.length
printfn "%A" total

sw1.Stop()
printfn "%A" (sw1.Elapsed)

;;
//9
//00:00:03.0791484
//161
//00:00:38.0018055