A student writes:

  i just did a little research on the subject and it turns 
  out the "official" rules or whatever you wanna call them 
  are: every four years except for those ending 00 unless its 
  divisible by 400. so there's an exception to the rule and 
  an exception to the exception. so there you go. 

  <<and then he had a comment on what he thought of all of the above.>>
  <<name withheld...>

Actually, the rule was set out in order to have the number of days in a year
 coincide with the amount of time it takes the earth to make one full revolution
 around the sun.  That is, it would be kind of nice to have January 1 show up
 every year with the earth in the same place.  Otherwise, some Januarys would
 be the hottest month of the year, some Julys and Augusts would have snow in 
the mid-West, etc.

So, they started with 365 days = one year.  The problem is the earth is too 
slow.  It can't do the whole revolution in 365 days. 

So, every four years they added a day to allow the earth to catch up to where
 it should be.  And that works pretty well.  Except a day every four years is
 too much.  So, the result is the earth gets into the next year before January
 1 arrives.

So, every hundred years, they said: Don't add the extra day.  But that 
overcompensated too much in the other direction.

So, every four hundred years, we don't NOT add the extra day....

This is an example not unlike a common technique in solving problems 
where we creep up on the answer in both directions.  The fancy word for 
this is we *converge* on the answer.  In the normal use of convergence, we
 successively choose values for the "answer" (the nth is too big, the (n+1)th
 is too small, the (n+2)th is too big) using smaller and smaller increments until
 we find an answer (i.e., converge) on one that is sufficiently close that we are
 happy.  Here, we know the answer, how long it actually takes the earth to complete
 its annual path.  The answer is 365.24.....  Now, we want to come up with a formula
 that produces that answer.  Ergo: 365 days, + a day every four years, - a day every
 hundred years, + a day every four hundred years, until we are satisfied.

Anyway, hope you enjoyed it.

Yale Patt