How many odd days are there in 1600 years ? I calculated it but I guess the result is wrong? I had to calculate the number of odd days in 1600 years. I have read the answer to be equal to 0. But I don't get it to equal to 0.
This is the way I am calculating the number of odd days in  1600 years :
1600 years = 24 x 16 = 384 leap years   (100 years = 24 leap years)
(because 100 years have 24 leap years)
1 leap year = 2 odd days (52 weeks + 2 odd days)
384 leap years = 384 x 2 = 768 odd days --(A)
1600 years = 1600 - 384 = 1216 ordinary years
1 ordinary year = 1 odd day (52 weeks + 1 odd day)
1216 ordinary years = 1216 x 1 = 1216 odd days--(B)

Total number of odd days = (A) + (B) = 768 + 1216 = 1984 odd days in 1600 years

and 1984 is not divisible by 7 !

Am I making a mistake ? If yes,what is it ?
 A: Remember that a year divisible by $400$ is a leap year.  Although $2100$ will not be a leap year. $2400$ will be.
So in $400$ years there are precisely $97$ leap years.  
And yes, the calendar repeats every $400$ years, so the number of days in $1600$ years is divisible by $7$. For $400$ years, to the $(400)(364)$ days,  just add $400+100-3$ (ordinary advance by $1$ day, plus 100 for the leap years sort of, minus $3$ for the multiples of $100$ that are not multiples of $400$).  Then multiply by $4$. So for $1600$ we get $4(500-3)$ "additional" days. Your $1984$ was essentially computed correctly, except that we need $4$ additional days for the $4$ multiples of $400$.
A: While your definition of "odd days" is unclear to me, what I get is that if the number of days is a multiple of $7$, the number of odd days is $0$. In the following I'll therefore show that the number of days indeed is a multiple of $7$.
The rule for leap years is:


*

*If the year is divisible by $400$, it is a leap year.

*Otherwise, if it is divisible by $100$, it is not a leap year.

*Otherwise, if it is divisible by $4$, it is a leap year.

*Otherwise, it is not a leap year.


This means, the leap year rule has a $400$ year period. Therefore if we want to know how many days there are in $1600$ years, we can calculate the days in $400$ years, and multiply by $4$.
Now the number of days in $400$ years is $400\cdot 365 + \text{number of leap years}$. Now to calculate the number of leap years in $400$ years, we go through the above list in reverse order:


*

*Years divisible by $4$ are generally leap years, there are $400/4=100$ of them.

*However this way we have also counted the years divisible by $100$ (because they are all divisible by $4$). There are $400/100=4$ of them, which we therefore subtract, so we get $100-4=96$.

*However now we have also removed the years divisible by $400$, of which there's one in $400$ years. Therefore we have to add that one back, so we end up with $97$ leap years in $400$ years.


Therefore $400$ years have altogether $146\,097$ days. Now it is not hard to check that this number indeed is a multiple of $7$. Therefore there are no odd days in $400$ years, and thus also not in $1600$.
A: In $400$ years there would be $100$ leap years, but $3$ of them are suppressed. An ordinary year has one "odd day", and a leap year has an extra "odd day". Therefore there are $497$ odd days in $400$ years, which is divisible by $7$. A fortiori there remains no "odd day" in $1600$ years.
A: Every 4th century is a leap year and no other century is a leap year. Therefore there will be 96 + 1=97 leap year and 303 ordinary years. So the equation becomes 303*1 +97*2 =497 odd days or 0 odd days.
A: @Sahil u r making a mistake in finding no. of leap years in 1600 years.. here is my solution..
as every 100 yrs has 24 leap years. so
• first 300 yrs-24*3 leap yrs
• 4th 100 yrs-24+1 leap yrs because 400th year is also a leap yr as it is divisible by 400
• next 300 yrs-24*3 leap yrs
• 8th 100 yrs-25 leap yr
• next 300 yrs-24*3 leap yrs
• 12th 100 yr-25 leap yrs
• next 300 yrs-24*3 leap yrs
• 16th 100 yrs-25 leap yrs
so now total no. of leap yrs in first 1600 yrs becomes=24*3*4+25*4=388
so no. of non leap yrs=1600-388=1212
so total no. of odd days in 1600 yrs=388*2+1212=1988
which is divisible by 7.
So there're 0 odd days in 1600 yrs.
A: It is easy. Just remembr the answer. :)
Just joking. 
Here is my simple solution:
As each 4th century's a leap year & no other century is a leap year,  there will be 96 + 1=97 leap year and 303 ordinary years. So we get  303x1 + 97x2 =497 odd days or 0 odd days.
Hope it helped.
Afterall, better late than never, huh?
A: If the number is divisible by $400$ then zero odd days.
In $1200$ or $1600$ years, you will find $0$ odd days.
In $100$ years, you will get $5$ odd days.
