Problem 019

Project Euler

Counting Sundays

Problem 19

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)?

Since 1 Jan 1901 is a year from 1 Jan 1900, knowing which day of the week is 1 Jan 1901 is the starting point. Using 1 as Monday and 0 as Sunday, adding the total days of each month, and then take the modular of 7, for the number of years specified, the final number of Sunday fell on the first of the month can be accumulated exactly.