What day of the week was/will it be?

In an effort to get the board to move on from election talk (no, nobody hacked my accoont :-) ) here is a math question.

There is an episode of "LA Law" where Becker represents a math genius who is losing a wife who treats him like dirt. She fooled around on him and at the deposition admits it and asks him "March 18, 1983 we did it in Albany! What day of the week was it?! I know you know!"

Later Becker introduces him to a real hottie who loves smart guys. The hottie is amazed he can calcualte the day of the week to any year instantly to which he says, "that is a parlor game." Or for those of you in Rio Linda, it is such a simple trick it is almost beneath a real math guy to do the trick.

But, how do you calculate it? Is there a shortcut trick, or do you have to be an idiot savant to do it that fast?

It's actually really easy.

There are 365 days in the normal year; 364 is divisible by 7, so each normal year, January 1st is one day later in the week than last year. Leap year advances it two days. So you take the present year, count back to the last leap year, and then count 5 for every four years back from that, until you get to the closest leap year to your target date, then count singly from there. So from 2010, count back two to 2008, and count back 5 for every four years back from that, until 1948, the closest leap year, then count two more. Divide the sum by 7, and take the remainder; this is the number of days "back" from this year's New Year's Day that the New Year's Day for the year in question fell on. So, if we want to know what day of the week New Year's Day in 1946 was, we go back to 2008 (2), then subtract 2008-1948 (60 x 5/4, or 75), then go from 1947-1946 (2). So we have a total of 79 "jumps". Divide by 7, and take the remainder. The remainder is 2, so since this New Year's Day was Friday, New Year's Day in 1946 was Wednesday.

Now all you have to do is figure out how many days between New Year's Day and the target date ("thirty days hath September..."), divide by 7, take the remainder, and jump that many days of the week forward.

This would take me about fifteen seconds, but I'm sure there are plenty of people out there who could do it in more like fifteen microseconds.

I used to have the formula memorized, and could do it in my head in about 30 seconds. However, I forgot it. Usually you try to impress people by telling them the day of the week they were born. However, most don't know themselves, so they're not impressed when you come up with an answer they don't know is correct. Here is a page on it.