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vikash sangwan

· started a discussion

· 1 Months ago

solution (Question: 186313.0 )

how?

Question:
The first day (like 1 January, 2000) of any century leap year can begin with –
Options:
A) Friday
B) Saturday
C) Sunday
D) Monday
Solution:

Solution: (B) Saturday                   


Let's commence at an outright basic level.

The number of days in a normal year=365. Now, 365= 52 weeks + 1 day.

The number of days in a leap year = 366. Now, 366= 52 weeks + 2 days.

This outlines that a normal year has 1 extra day while a leap year has a couple of them.

For now, let's shove this fact aside.

The second basic concept we ought to clear is the number of leap years in any century. Ostensibly, a century has 25 leap years. But life is more complex than that. 

It is pertinent to keep in mind that if any year is divisible by 100, it is NOT a leap year UNLESS it is ALSO divisible by 400. As an example, 200 is not a leap year cause it is divisible by 100 without being divisible by 400. But 800 is a leap year because it is divisible by 400. Owing to this fact, some centuries have 24 leap years. 

Let's now hit the main point.

In the 1st century, 

number of odd days= 5 odd days(Because the remainder after dividing 76*1+24*2 by 7 is 5). This implies that the last day of this century will be the 5th day of the week i.e. Friday. 

In the 2nd century,

number of odd days=2*5 (twice of the extra days in one century)= 10 odd days. This implies the last day of this century will be Wednesday.

In the 3rd century,

number of odd days=15 days. The last day of this century will be Monday.

But the 4th century has no extra days since 400 is a leap year while 100. 200. and 300 weren't. and this gives 20+1 extra days. this amounts to 3 weeks with no days protruding out of a perfect week. The last day of this century is Sunday From 5th century onwards, this cycle repeats. 

The last days of a century can be Friday, Wednesday, Monday and Sunday. 

Naturally, the first days of the following centuries will be Saturday, Thursday, Tuesday and Monday respective to the above list of last days.

It is clearer than crystal that Monday is the only day which can be the first and last of any century. 

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