Problem 19: How many Sundays fell on the first of the month during the twentieth century?

Relieved .NET DateTime was sufficient for this.

let problem19a = 
    let mutable cur = new System.DateTime(1901, 1, 1);
    let last = new System.DateTime(2000, 12, 31);
    let mutable count = 0
    while(cur <= last) do
        if cur.Day = 1 && cur.DayOfWeek = System.DayOfWeek.Sunday then
            count <- count + 1
            
        cur <- cur.AddDays(1.0)
            
    count

And here’s a functional version.

let problem19b =
    let last = System.DateTime(2000, 12, 31)
    let rec sundays cur count = 
        if cur > last then count
        elif cur.Day = 1 && cur.DayOfWeek = System.DayOfWeek.Sunday then sundays (cur.AddDays(1.0)) (count+1)
        else sundays (cur.AddDays(1.0)) count
    sundays (System.DateTime(1901, 1, 1)) 0