Counting Sundays

Problem Statement

You are given the following information:

• 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)?

Approach

Method 1: Manual calculation

• Start from 1 Jan 1900 (Monday)
• Iterate through each month from Jan 1901 to Dec 2000
• Track what day of the week it is
• Count when the first of the month is a Sunday

Method 2: Using Java’s date libraries

• Use Calendar or LocalDate classes
• Iterate through each month in the range
• Check if the first day is a Sunday
• Count the occurrences

Key considerations:

• Correctly handle leap years (divisible by 4, except centuries unless divisible by 400)
• Account for varying month lengths
• Start counting from 1901, not 1900

The manual calculation approach helps understand the problem better, while the library approach is more concise and less error-prone.