In order to find leap years, why must the year be indivisible by 100 and divisible by 400?
I understand why it must be divisible by 4. Please explain the algorithm.
Answer
The length of a year is (more or less) 365.242196 days. So we have to subtract, more or less, a quarter of a day to make it fit :
365.242196 - 0.25 = 364.992196 (by adding 1 day in 4 years) : but oops, now it's too small!! lets add a hundreth of a day (by not adding that day once in a hundred year :-))
364.992196 + 0,01 = 365.002196 (oops, a bit too big, let's add that day anyway one time in about 400 years)
365.002196 - 1/400 = 364.999696
Almost there now, just play with leapseconds now and then, and you're set.
(Note : the reason no more corrections are applied after this step is because a year also CHANGES IN LENGTH!!, that's why leapseconds are the most flexible solution, see for examlple here)
That's why i guess