Is there a mathematical equation to determine how many leap years there are between two different years?

Question

For example, say you want to determine how many leap years are between the years 1941 and 1961.

I have tried to find a mathematical way to come up with an answer to this equation, but I have been unable to find a site that tells of this.

Answer 1

all leap years are divisible by 4.
lemme think...ok so round the lower year up to the closest # number divisible by 4, and round the higher # down.
so 1944 and 1964.
1964-1944=20, 20/4=5, and there's your answer. Find the difference and divide by 4 (you are finding the number of years that could possibly contain a leap year and as every 4 years is a leap year, you divide by 4, you just have to start and end on leap years).
oops round both either up or down.


One more thing:if one of the years IS a leap year, you have to round up for the other one. So you inlude everything (you need the higher up endpoint).


Don't listen to the other guys: you have to round. For example, what if you were asked to find the leap years between 1960 and 1970. The difference is 10. Not evenly divisibly by 4. There are 3 leap years in that time span and you would know that if you rounded 1970 to 1972 and divided the diff (12) by 3..

1960,64,&68 are the leap years.

Answer 2

Well let's see there are 97 leap years every 400 years. We've just finished a century where there was a leap year at the turn of the century. After 1900 which was not a leap year until 2100 which is also not a leap year every fourth year will be a leap year. So, for between 1900 to 2100, just subtract year one from year two and divide by 4. The whole number will give you the number of leap years. e.g. 1961 - 1941 = 20 and 20 / 4 = 5 i.e. there are 5 leap years between 1941 and 1961 [ 1944; 1948; 1952; 1956; 1960]. Just subtract 1 from your answer if they include the years without a leap year i.e. 1700; 1800; 1900 (in recent times) and 2100; 2200; 2300.(for the future).

Answer 3

Jedi is correct above that you can round each of the years up to the next leap year (so if either one is already a leap year it will not change) and then subtract to find the length of the span in years. When you have the span, divide that by 4 to find the number of leap years.

Before you are finished, you need to check for a few exceptions to the leap year rules, such as years that are divisible by 100 and not by 400 (so years like 1800 and 1900 were NOT leap years, but 2000 was!)

This is done because it takes the Earth 365.24 days to go around the sun, so that is 1460.96. Since we add Feb 29th to the calendar every 4 years, it is 1461 days, which averages to 365.25 days per year. To make up for this very slight difference, they do not have leap years in the 100th year 3 out of 4 times. In other words, year 100, 200 and 300 are not, but 400 is, and then repeat the pattern.

Since 1961-1941 is a 20 year span, there should be 5 leap years. There was 1944, 1948, 1952, 1956, and 1960. Any years where the last two digits are a multiple of 4. There are no exceptions to worry about in that span.

Answer 4

jeap yrs occur every 4 yrs
& its divisible by 4
between 1941 &1961,
its 20yrs so 20/4=5 leap yrs between 1941 &1961

Answer 5

leap yrs occur every 4 yrs,and are divisible by 4.(i.e 2000,2004,2008... are leap yrs.)

if U consider period 1941 to 1961 that's 20 yrs so there should be 5 (20/4) leap yrs in between

Answer 6

leap yrs occur every 4 yrs,and are divisible by 4.(i.e 2000,2004,2008... are leap yrs.)

if U consider period 1941 to 1961 that's 20 yrs so there should be 5 (20/4) leap yrs in between.

Answer 7

This is an easy one. If the world gets too hot, we've proven that we can survive it because the "Cradles of Civilization" were in hot, dry areas. If the world gets cold, then we've already proven that we can withstand ice ages, and that's without any "high" technology. If the world gets overpopulated, it will, out of necessity, balance itself out. I don't think we need to worry about surviving the next 100 years. The real question is how to we keep the next 100 years from becoming the next Dark Age.

Answer 8

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Answer 9

no because a leap year comes every four years

Answer 10

y1 is the smaller year y2 is the bigger

=pos((y2-(y2/4-int(y2/4))*4)
-(y1+4-(y1/4-int(y1/4))*4)/4)
+1
I named two functions, I don't know what are their real names
the first is int() function which gets the integer part of a number .. i.e int(2.3)=2
the second is pos() .. pos(x) = x if x >=0 and =-1 if x<0