needing help/direction on 'perpetual calendar' questions

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defeated_soldier

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The following simple facts should be remembered:

1) An ordinary year contains 365 days; that is, 52 weeks and 1 odd day.

2) A leap year contains 366 days; that is, 52 weeks and 2 odd days.

3) One hundred years (a century) contain 76 ordinary years and 24 leap years:
. . .= (76 × 52) weeks + 76 odd days + (24 × 52) weeks + 48 odd days
. . .= [(76 × 52) + (24 × 52)] weeks + 124 odd days
. . .= [(76 × 52) + (24 × 52) + 17] weeks + 5 odd days

That is, 100 years contain 5 odd days.

Two hundred years contain 10 and thus 3 odd days. Similarly, 300 years contain 1 odd day, and 400 years will have (20 + 1) odd days; that is, 0 odd days. Similarly, the years 800, 1200, 1600, and 2000 each contains no odd days.

4) First January 1 AD was Monday. Therefore, we must count days from Sunday; that is, Sunday for 0 odd days, Monday for 1 odd day, Tuesday for 2 odd days, and so on.

5) February in an ordinary year gives no odd day, but in a leap year gives one odd day.
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QUESTION 1: (Regarding the above...)

I dont understand the phrase "400 years will have (20+1) odd days i.e 0 odd days"

This is confusing. We have seen 100 years contains 5 odd days, so naturally 400 years will contain 5 x 4 = 20 odd days. I don't understand why they are saying "20+1 odd days"? Where is this extra "1" coming from?

I think the extra 1 may be due to 400 years being a leap year. However, as we have already considered leap year in 100 years, there is no meaning to count it again for 400 years being a leap year -- is there? I'm feeling like my logic must be wrong.

QUESTION 2: On what of the week did the 17th of November, 1982 fall?

I started this way:

1982=100 x 19+ 82 =5 odd days x 19 + 82 years
17th november = 11 month + 17 days

I don't know whether I am on the right track, and the calculation is becoming complex. Is this even the right way to go?

Thank you!
 
Leap years skip every 400 years. Leap years normally fall every 4 years. Correct?.

For instance, 1992, was a leap year. 1996 was a leap year. BUT, 2000 was not

because, though normally it would've been, it was a year divisible by 400.

Therefore, 2000 was not a leap year. The last time this happened was in 1600.

The year 2400 will not be a leap year. Though, 2100, 2200, amd 2300 will be.

It may have something to do with that.
 
defeated_soldier said:
I dont understand the phrase "400 years will have (20+1) odd days i.e 0 odd days"
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The algorithm they give is cutting whole (that is, seven-day) weeks out of the count. But it appears to have left out the rule that years divisible by 100 are not leap years, unless they are also divisible by 400. So 1900 was not a leap year, but 2000 was.

I think the extra "1" is coming from something related to this rule, but I'm just guessing....

Eliz.
 
ok, so in that case , i should check whether the year is divisible by 400 or not ALWAYS and apped 1 extra in my calculation .


I have a knowledge/belief( i read somewhere) that , if a year is divisible by 4 and 400 then its called a leap year
 
could you please answer my second question . will that be solved by the first concept or it needs some other concept ?
 
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