(*
You are given the following information, but you may prefer to do some research for yourself.

    * 1 Jan 1900 was a Monday.
    * Thirty days has September,
      April, June and November.
      All the rest have thirty-one,
      Saving February alone,
      Which has twenty-eight, rain or shine.
      And on leap years, twenty-nine.
    * A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
*)

let sundays =
  (* year, month, day, weekday (0..6) *)
  let rec sundays y m d w s =
    Printf.printf "%d.%d.%d %d (%d)\n" y m d w s;
    if (y=2001) then s else

    if (m=13) then sundays (y+1) 1 1 w s else
    if (m=2 && d=30) then sundays y 3 1 w s else
    if (m=2 && d=29 && ((y mod 100=0)||(y mod 400!=0)) && (y mod 4!=0)) then sundays y 3 1 w s else
    if (d=31 && (m=9||m=4||m=6||m=11)) then sundays y (m+1) 1 w s else
    if (d=32) then sundays y (m+1) 1 w s else

    sundays y m (d+1) ((w+1)mod 7) (if (w=6 && d=1 && y>1900) then (s+1) else s)
  in
    sundays 1900 1 1 0 0
;;