019 - Counting Sundays

Problem 19 / Challenge #19: Counting Sundays

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)?

ProjectEuler+ Problem Statement

The Project Euler problem is equivalent to the ProjectEuler+ challenge with $T = 1$, $Y_{1} = 1901$, $M_{1} = 1$, $D_{1} = 1$, $Y_{2} = 2000$, $M_{2} = 12$, and $D_{2} = 31$.