You learn something new every day.

[captainsblog]

I've listened to NPR's Car Talk, on and off, for well over 20 years. I picked up the fandom around the time I met Eleanor, but got the addiction from our friends Jim and Jean. They were living in Philly at the time, but were from the Our Fair City's environs around Boston made famous on the show, and I bonded with it pretty quick.  I remember many of the high points of their radio show, and the sadness of their effort to turn themselves into a sitcom starring George "Norm!!!!" Wendt that lasted about three weeks.  Little has changed on the air over those years, except for a better Internet presence and an easier-to-remember toll free number (although their original 800 number still works), and the only real variable for me has been how much attention I've paid to the Brothers Magliozzi at any given time of my mid-adult life.

Over the years, I've faded in and out based on work and other schedules, but since I've had the house to myself on Saturday mornings since late last year, I've resumed more-or-less regular listening, especially tuning in for the Puzzler. It's a 20-past and 20-of staple of the 10 a.m. Saturday show (except in summer months when the Puzzler goes on vacation), where they answer the previous week's question in the former slot and pose the new one in the latter; and while I've never won and rarely even entered the contest, it's a good mid-Shabbos test of my brainpower to see if I can puzzle it out.

Last Saturday's was one I didn't get.  Here's the setup from that day's show ("Ray" being, not me, but co-host Ray Magliozzi):

Ray: We used to refer to our Associate Producer David Greene as Rainman due to his peculiar ability to effortlessly figure out a certain date's day of the week. Now he recently displayed this talent when I recently asked him if there was a conflict with the upcoming Fuzzy Dice Conference and our weekly court-ordered community service. He asked the date of the convention. It was April 20th, 2012.
 
"Oh, that’s a Friday," he said, effortlessly. "And your sentences have you committed for the next few dozen Wednesdays so you'll be able to go." And of course he was right.
 
One day a few weeks ago I asked out loud in the office about the date June 5th. And of all people, my brother piped up and said "Oh, that's a Tuesday."
 
"That's right," said David.
 
Well how about Ocober 3rd?
 
"That's a Wednesday," said my brother.
 
Then I asked about Christmas Day 2012.

"Oh, that's a Tuesday."
 
David nodded in agreement.
 
Do we now have two rainmen? Or had Tommy figured something out?

I had no clue. I suspected it had to do with some annual repetition of dates throughout the calendar, and in that vaguest of senses I was right, but here's the answer as revealed today, which, despite being a major math and puzzle geek all my life, I'd never heard of or thought even possible:



RAY: Here’s what was going on. Tommy was using something called anchor dates.  And these dates apply to each and every year.  April 4th, or 4/4 we’ll call it from now on, June 6th or 6/6, 8/8, 10/10, 12/12, are all the same day of the week, each and every year.
 
TOM:  Yeah, I know that!
 
RAY:  So too are 5/9 and 9/5,  May 9th and September 5th.  So too are 7/11 and 11/7, and all the above dates are the same day of the week, as is the last day in February, Leap Year or not.  And they’re all the same day as January 4th, it would otherwise be January 3rd, but this was a leap year, and that’s changes the anchor day from January 3rd to January 4th, OK?
 
TOM:  Yes.
 
RAY:  So Tommy also knew that New Year’s Day was a Sunday.  He was sobered up by then.  And he knew it was a Sunday because Christmas was a Sunday in 2011, so New Year’s Day is a Sunday, so the Anchor Day for 2012, January 4th, has to be a Wednesday!
 
So if that’s a Wednesday 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7 and February 29th, all the same day of the week and they’re all Wednesdays. So when I ask for example, about October 3rd, he knew October 10th was a Wednesday, 10/10.  So 10/3 must also be a Wednesday.  12/12 is a Wednesday in 2012, so it’s 12/26, which is two weeks later.  So 12/25, or Christmas Day, must be a Tuesday.


That's pretty freakin' awesome, considering how entropic we've been about our calendar over the past few millennia. And I usually pay attention to stuff like that; I know I was born on a Monday in 1959, and can therefore compute fairly quickly that my birthday will fall on a Friday this year. (I use Outlook to cheat, but I COULD do it the other way if I had to;) I've had a mnemonic I've used for years when trying to extrapolate a day of the week based on knowing a given year's one: the date moves forward, the day moves back.  But this? Mannagliozzi from heaven:)