Math, asked by kareem47, 11 months ago

the first day of the century cannot be​

Answers

Answered by solardroids
30

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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

There the remaining days will not be the first day of the century

Answered by AadilAhluwalia
1

The first day of the century cannot be Wednesday, Friday & Sunday.

A leap year has 2 extra days while a normal year has only one.

A century supposedly has 25 leap years.

It is important to keep in mind that unless it is also divisible by 400, a year that is divisible by 100 is not a leap year. For instance, the year 200 is not a leap year since it is divisible by 100 but not by 400. However, 800 is a leap year since it may be divided by 400. Some centuries have 24 leap years as a result of this.

In the first century,

             the number of odd days= 5 odd days(Because of the remainder after dividing 76×1+24×2 by 7 =5).

           ∴ the last day of this century will be the 5th day of the week i.e. Friday.

In the second century,

              the number of odd days=2×5 ( twice the extra days in one century)= 10 odd days.

           ∴ the last day of this century will be Wednesday.

In the third century,

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

However, the fourth century includes no additional days because 400 is a leap year while 100, 200, and 300 were not, giving 20 + 1 additional days. This equates to three weeks that are made up entirely of the days in a week. Sunday is the last day of the century. This cycle continues starting in the fifth century.

A century's final days can fall on a Friday, Wednesday, Monday, or Sunday.

Naturally, in accordance with the list of last days above, the first days of the next century will be Saturday, Thursday, Tuesday, and Monday.

The first day of the century cannot be Wednesday, Friday & Sunday.

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