Brain Teasers
How Many Days in a Year?
How many days are there in a 400 year period (Gregorian cycle)?
Hint
Leap Frog!Answer
146,097 days146,000 days and 97 leap days
It doesn't matter what year it started on because a Gregorian cycle contains the same pattern of days and years.
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This is my second teaser that has come out. The other is Hotstuff under Trick teasers for those who want to see it.
I agree with the answer.
The trick, however, is not explained - knowing how many leap years to count.
Three years out of four, approximately, have 365 days. For the most part, every year divisible by four is a leap year - 366 days - the "exception". The "exception to the exception" comes every century - years ending in 00 - which have only 365 days (not a leap year). Finally, the "exception to the exception to the exception" comes in every year divisible by 400(!), which is indeed given the extra day - 366 days.
So in every 400 year cycle, there are: (400/4)-4+1 = 97 leap years. So you can simply multiply 400x365, then add 97. Equivalently, multiply 400x365.25, and then subtract 3.
Many people don't realize that the year 2000 was actually the "exception to the exception to the exception", giving it 366 days following these rules! Of course 2008 is also a leap year, but of the more boring variety.
The trick, however, is not explained - knowing how many leap years to count.
Three years out of four, approximately, have 365 days. For the most part, every year divisible by four is a leap year - 366 days - the "exception". The "exception to the exception" comes every century - years ending in 00 - which have only 365 days (not a leap year). Finally, the "exception to the exception to the exception" comes in every year divisible by 400(!), which is indeed given the extra day - 366 days.
So in every 400 year cycle, there are: (400/4)-4+1 = 97 leap years. So you can simply multiply 400x365, then add 97. Equivalently, multiply 400x365.25, and then subtract 3.
Many people don't realize that the year 2000 was actually the "exception to the exception to the exception", giving it 366 days following these rules! Of course 2008 is also a leap year, but of the more boring variety.
I am now a little bit smarter . *not sarcasm* never thought about it like that
I am now a little bit smarter . *not sarcasm* never thought about it like that
Sorry didn't mean to post twice.
oh............
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