Project Euler – Problem 19 Solution


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)?


open System

let ans =
    |> List.collect (fun y -> [1..12] |> (fun m -> new DateTime(y, m, 1)))
    |> List.filter (fun d -> d.DayOfWeek = DayOfWeek.Sunday)
    |> List.length

The solution here is simple, for the int list [1901..2000] generates the Cartesian product with the int list [1..12] to get a DateTime object representing the first day in each month from 1901 to 2000, e.g.


From this point, all that’s left is to filter the list of DateTime values to find the ones which represent a Sunday and count them.

1 thought on “Project Euler – Problem 19 Solution”

  1. open System
    let p19 = [for y in 1901..2000 do
    for m in 1..12 do yield new DateTime(y,m,1)]
    |> List.filter (fun d -> d.DayOfWeek = DayOfWeek.Sunday)
    |> List.length

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