What day of the week will 22 apr 2222 be?
Answers
Given date:- 22nd April 2222.
Consider the year 2222. We are going to expand this year as the following.
2222 = 2000 + 200 + 21 + 1.
2222 is expanded in such a way that the 2000 added in it is a multiple of 400, which is because of the concept that consecutive 400 years have totally no odd days! And 200 is added, which is for the reason explained below. 1 should be split from 2222 in the expansion.
[Odd days are those which remain in a year not as a week.]
Now, consider a consecutive 100 years which starts from a non-leap year which is immediately after a leap year, mentions about 1st, 5th, 9th, 13th years and so on. (Simply we say to consider a century!)
This 100 years actually contain 76 ordinary years and 24 leap years, due to some scientific reasons. (I just don't know why!)
We know an ordinary year has 1 odd day and a leap year has 2 odd days. Hence the no. of odd days in 100 years will be (24 · 2 + 76 · 1) = 48 + 76 = 100 + 24 = 124, this in turn gives 5. (The remainder on dividing 124 by 7, the no. of days in a week.)
[No need to add odd days of 24 leap years and 76 ordinary years for finding no. of odd days of 100 years. Just add the no. of leap years 24 in the 100 years to this 100. We also get 124.]
So,
100 years ≡ 5 odd days
200 years = 100 years + 100 years ≡ 5 odd days + 5 odd days = 10 odd days ⇒ 3 odd days (3 is the remainder of 10/7)
300 years = 100 years + 100 years + 100 years ≡ 5 odd days + 5 odd days + 5 odd days = 15 odd days ⇒ 1 odd day (1 is the remainder of 15/7)
But since 400 years contain one more odd day, the total no. of odd days will be (5 · 4 + 1) = 20 + 1 = 21 ⇒ 0.
Hence, this may be remembered.
100 years ≡ 5 odd days
200 years ≡ 3 odd days
300 years ≡ 1 odd day
400 years ≡ 0 odd days
This is why 200 is added in the expansion of 2222. Hence 3 odd days must be added if 200 is added in the expansion.
Now consider 21 added in the expansion.
21 years contain 5 leap years, so the total no. of odd days in 21 years is 21 + 5 = 26 ⇒ 5 (Remainder of 26/7)
Now, 3(no. of odd days in 200 years) + 5(no. of odd days in 21 years) = 8 ⇒ 1.
This 1 is the no. of odd days in 2221 years!
Now, the following below should each be added to this 1.
January 2222 contains 3 odd days → 1 + 3 = 4
Since 2222 is not a leap year, February 2222 contains no odd days → 4 + 0 = 4
March 2222 contains 3 odd days → 4 + 3 = 7 ⇒ 0
Okay, now we get 0 successfully!
We have to find which day 22nd April 2222 will be. For this, add first 22 days of April 2222 to this 0.
0 + 22 = 22 ⇒ 1
Now, find out the 1st day of a week, counting from Monday.
Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
1st day is Monday here.