Every so often, I see a savant on television that is able to name the day of the week for any date. For example, the host will ask what day March 1, 1999 fell on, and the genuis will answer “Monday”. While I’m sure this takes a great amount of brainpower, I’m almost as sure that there must be a pattern that helps. In the same way that any multiple up to 9 is composed of numerals that can be added to equal 9, I figure there has to be some trick to at least help name the day. Surely, the dates aren’t complete random - most patterns repeat themselves every so often, right? My challenge to the masses is to reveal to me the pattern that these people use. I stand to make mucho banko at the bar pending this revelation and subsequent memorization :).
There might be a shortcut to this, but I doubt that the savants you have seen could explain how they do it. Also I have seen a guy like this who could also tell you the weather on that day.
A couple of months ago I saw a woman on a talk show while I was at the gym (I think it was probably on Oprah) who had a rare memory disorder where she remembered virtually everything that happened to her. She could do these feats of memory usually associated with savants, but she was otherwise intellectually normal (most savants, IIRC, have some form of autism). So there is probably something in brain development that creates or exaggerates this ability without the need for algorithms.
What exactly do you need to know to do this, though? Like, if they were given a run down of some other calendar (the Hebrew calendar, for example), could they do it with that?
Follow Mhendo’s link to the “Doomsday” algorithm. Despite the lengthy explanation on that page, it is easy to use.
The deficiency of the Doomsday approach is the OP asked how to determine the day of the week for any year. The Doomsday approach only works if you know what day of the week Feb 28/9 is.
The method I learned for all years in the 1900s, which I can do in my head but it takes a bit of time, is as follows:
All arithmetic is modular 7. I will use today as an example.
Use the last two digits of the year (since I learned this in the 1900s you need to use 100+ the last two digits for this century. 109 = 4 mod 7
divide the same number by 4 (discarding any remainder) and add: 109\4= 27 = 6 mod 7. 4 + 6 = 3 mod 7
add the day of the month: 3 + 1 = 4
Now you must remember this table:
Jan 1 Feb 4 Mar 4
Apr 0 May 2 Jun 5
Jul 0 Aug 3 Sep 6
Oct 1 Nov 4 Dec 6
(note that the first three lines 144 025 036 are perfect squares)
4+0=4 So April 1 2009 is the fourth day of the week or Wednesday.
The one correction you have to also remember is that in leap years January and February are one day earlier than given by the method
The lady from Taxi, Marilu Henner can do that. I saw her on a talk show and she could name the day of a week from any date you gave her, so you don’t have to be a savant to do that
Perhaps I may offer a little clarification.
Anyone can learn to calculate ‘the day for any date’ in their head. There are various formulae, all slightly different and with their own fans, and they are featured in books on recreational mathematics, memory training and ‘mentalism’ (the kind of magic associated with powers of the mind). You don’t need to be a savant. It’s just about learning to apply an algorithm in your head, plus a little memory work.
Savants who can do this can do it faster than ‘normal’ people who have just learned to do the mental arithmetic, and, as CWG points out, are probably unable to explicate exactly how they do it. Daniel Tammet is a rare creature, a savant who can articulate what’s going on in his mind, but even when he does his best to describe his mental processes it’s hard for the rest of us to understand what he means.
The guy who can describe what the weather was like… clearly this is a prodigious memory feat, rather than one of calculation.
No, Doomsday is in two parts - determine Doomsday (last day of February) for any year, then determine day of week for any date in that year.
I have on several occasions had a room full of folks astounded at my ability to name the day of the week within 1-2 seconds of being given any date, any year. For the record I am not a savant, I think I’m decent at mental arithmetic but I’m no lightning calculator, and I was never even on Taxi.
Here’s the secret:
Lie.
Very few people have any idea what day of the week it was on any date in the past. Announce you can do it, wait for someone to throw out a date, put a look of fierce concentration on your face, glance up at the ceiling for a second, and then say “Thursday”. Repeat until people think you’re a genius. Nobody ever checks (although with calendars on cell phones anyone can now).
Hint - if someone gives you the 13th of any month say “Friday”; either they don’t know (in which case it makes no difference) or something special happened on a Friday the 13th (birthday, cat died, etc).
It’s a great con. If you give your answers with confidence people think you’re right.
There’s an autistic fellow at my night job who can do this. The first time I met him, he asked “What’s your birthday?” I told him the truth, “August 19th.” He got a little agitated and demanded “What year?!” I told him 1970. He then said “Wednesday’s child. Wednesday’s child is full of woe.” Whatever the day of the week, he always makes sure to add the “[Whatever day]'s child is…” bit from the poem.
And by the way, he wasn’t lying. August 19, 1970 was, in fact, a Wednesday.
I also saw a guy do this on Dateline NBC or a similar show. They put a mathmetician up against a savant. The savant could name the day in 1-2 seconds; the mathmetician got out his calculator and gave the answer in about 30 seconds.
Another approach is Zeller’s Congruence.
I was once in a math class where the teacher mentioned pi in some context, and started rattling off digits… Except that I had actually memorized more digits than he had, and I caught him bluffing after around ten places.
Except for the sixteen-year-old kid I saw at a high school talent show last year.
His gimmick was to ask what date a random audience member was born on. Most people know what day they were born on, so your scam would leave you somewhat red-faced.
I have no idea what day of the week my birthday was so I’d have been an easy mark 
Like I said, I’ve pulled this one many times at parties and other gatherings. People swallowed it hook, line and sinker.
Thank you for the link to the doomsday method. I always figured there was a completely deterministic way to calculate the day of the week, but I didn’t realize it was that easy.
The only thing I would add to their explanation:
To calculate the doomsday for a particular century, divide the century number by 4 and check the remainder. If it is 2, Friday; 3, Wednesday; 0, Tuesday; 1, Sunday.
(By century number I mean the date divided by 100; for 1900 the century number is 19.)
In my opinion, this is easier than trying to add or subtract increments of 400 years.