Very difficult to me,
It is a question about leap years:
"In the western calendar, a year having 365 days is called a common year, while a year having 366 days (with an extra day, February 29) is called a leap year. People always say that when a year is a multiple of 4 , it should be a leap year. However, it is not totally correct because there is an extra rule about leap year:
'The extra day will not be added for years which are multiples of 100, unless the year is a multiple of 400.'
For example, years 1800, 1900 and 2100 are not leap years while year 2000 is a leap year.
From the above rules, can you estimate the average number of days for each year from year 1001 to 2000."
The answer is 365.243. But I don't get it!
Can any buddy help?? Thanks
Basic Approach. There are $1000$ years between $1001$ and $2000$ inclusive. Under the old Julian calendar, where every fourth year was a leap year, that would mean $1000/4 = 250$ leap years. Now, how many of those years are not in fact leap years under the newer Gregorian calendar, the rules of which are described above in your question? There are several of them, beginning $1100, 1300, 1400, \ldots$
Count them up, subtract the count from $250$ to get the actual number $n$ of leap years between $1001$ and $2000$. You then have $n$ years of $366$ days each, and $1000-n$ years of $365$ days each. Compute the average in the usual way:
$$ \text{Average} = \frac{(1000-n)(365)+(n)(366)}{1000} $$