# What day of the week was 20th June, 1837 A.D.?

Chetan Mandayam Nayakar
312 Points
11 years ago

Dear Sathyaram,

Today is Sunday,October 16,2011. So 2/10/2011 was Sunday. So 25/9/2011 was a Sunday. So 4/9/2011 was a sunday. 28/8/2011 was sunday. so 7/8/2011 was sunday. so 31/7/2011 and 3/7/2011 were sundays. so 26 june 2011 was sunday. so 20 June 2011 was Monday. from now on I will refer to February 29th of a leap year as leap day.

Consider dates dd/mm/yyyy and dd/mm/(yyyy-1). If there is no leap day between the two dates, and if dd/mm/yyyy was, say Monday, then dd/mm/(yyyy-1) was Sunday. This principle holds for any day of the week.

But, if there was a leap day during the two dates, dd/mm/(yyyy-1) would be Saturday. This principle also holds for any day of the week.

Between today and 20th june 1837 AD all years (EXCEPT 1900) yyyy,such that yyyy is divisible by four were leap years.

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All the best Sathyaram !!!

Regards,

CHETAN MANDAYAM NAYAKAR

Sathya
35 Points
11 years ago

290 Points
11 years ago

Hi Sathyaram,

This is a logical question, where you should know the concept that,

A year divisible by 100 will be a leap year, only if it is also divisible by 400.

So consider the day of 20th June 1837 as Day X.

Between 20th June 1837 and 20th June 2011, we have 174 years.

At first, one will quickly say it has 174/4 = 43.50.

So 43 Leap years and 131 Non-Leap years.

But remember 1900 is not a leap year. So the correct way is 42 leap years and 132 Non-Leap years.

Now a Non-Leap year has 365 Days---- which is 52 weeks + 1 day.

And a Leasp year has 366 Days---- which is 52 weeks + 2 days.

So if 20th June 1837 was Day X, 20th June 2011 will be day X+(1*132)+(2*42) = X+216.

Note that every 7 Days the same day will occur again. So X+216 is X+7*30+6.

So same as (X+6)th day.

If you see, 20June 2011 is Monday. which is X+6.

So X should be Tuesday, and that was 20th June 1837.

Hope that helps.

Best Regards,