(*
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?
*)

(* coins except for 1p *)
let coins = [200;100;50;20;10;5;2];;

let partitions =
  let rec partitions cs s =
    if s=0 then 1 else
    match cs with
    [] -> 1 (* pay the rest in pennies *)
    | h::t ->
      if (h>s)
      then partitions t s
      else ( partitions cs (s-h) ) + (partitions t s)
  in
    partitions coins 200
;;

Printf.printf "%d\n" partitions;;