QA – Basics of Calendars

Welcome to this simple and interesting lesson on Calendars!

Let’s begin with a simple problem.

Suppose 12th June 2013 is a Wednesday. So, 12th July 2013 would fall on which day of the week?

This question can be solved in just 3 steps!

Step 1: Calculate the number of days between the two dates.

June is a 30 day month – so we would have 30 days between the two dates.

Step 2: Divide the number of days by 7 and note down the remainder.

30 / 7 gives 2 as remainder.

Step 3: Consider the reference day as zero and add the remainder to it.

Wednesday = 0

Thursday = 1

Friday = 2

Thus, July 12 would be Friday.

Do note that each day repeats itself after 7 days. In questions on calendars, the extra days are called “odd days”. So we have 2 odd days in the previous question. Hence, we added the number of odd days to the given day (Wednesday + 2 = Friday) to get the required day.

Leap year: A leap year is a year in which February has 29 days. An ordinary year has 365 days while a leap year has 366 days.

There are two rules to determine if a year is a leap year or not:

  • Leap years come every 4 years. So, if the given year is divisible by 4, then it will be a leap year. For example, years such as 2004, 2008, 2012, and 2016 are leap years.
  • For years that are divisible by 100, if the year is also divisible by 400, then (and only then) that year would be a leap year. So, 1200, 1600, 2000 are leap years whereas 1900 would not be a leap year.

Interesting results:

An ordinary year would have 365 days = (52 weeks + 1 day) = 1 odd day. So, if January 1 is a Sunday of an ordinary year, then 1st January for the next year would be a Monday.

A leap year has 366 days = (52 weeks + 2 days) = 2 odd days. So, if January 1 is a Sunday of a leap year then 1st January for the next year would be a Tuesday.

A century has 100 years = (76 ordinary years + 24 leap years)

= (76 * 1 + 24 * 2) odd days = 124 days

124 days = (17 weeks + 5 days) = 5 odd days.

Similarly, 200 years = (5 * 2) = 10 = 1 week + 3 days = 3 odd days.

Likewise, 300 years = (5 * 3) = 15 = 1 odd day

And finally, 400 years = (5 * 4 + 1 leap day) = 21 = 0 odd days

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