prob31.fs

(*
    Problem 31 - Coin sums
    ----------------------
    In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:
        1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).   
    It is possible to make £2 in the following way:
        1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p
    How many different ways can £2 be made using any number of coins?
*)

let targetAmount = 200

let coins = [ 200; 100; 50; 20; 10; 5; 2; 1 ]

let rec coinCombs coin target =
    if target < 0 then 0
    elif target = 0 then 1
    else 
        coins
        |> List.filter (fun c -> c <= coin && (target-c) >= 0)
        |> List.map (fun c -> coinCombs c (target-c))
        |> List.sum
        
coins
|> List.map (fun coin -> coinCombs coin (targetAmount-coin))
|> List.sum