I met somebody that could do this, and I have no idea how he does it. Give him any day from any month and year, and he knows what day it was. How is this done? Can anybody tell me? Thank you!
One way to do it would be to memorize the formula I posted in this thread:
http://boards.straightdope.com/sdmb/showthread.php?threadid=8734
First of all, welcome, Hockeyguru. I hope you have a lot of fun here, and learn a lot. To answer your question, in some cases, no one really knows. I’m thinking of those people that are called idiot savants. You can find out a lot of info at this website.
The brain is a very strange thing. Some of these people have very minimal education, or capacity for it, yet excel in things that others would consider minute. Days of the week, math, etc. Rain Man was a pretty good example, if you saw the movie. Dustin Hoffman actually based his character Raymond off of Kim Peek.
Years ago, I read a pretty straightforward formula for this in a book of mathematical puzzles and such, by a guy named “Royal Vale Heath.”
As I recall, it wasn’t simple, but it wasn’t so complicated that you couldn’t memorize it and apply it in your head if you were so inclined.
I saw Ed Begley Jr. perform this feat on Letterman. I was underwhelmed.
My guess is… it’s a trick!!! 
I can do this trick - it takes me about six seconds to figure it for any date from 1900 to 2020. Usually I can reduce the six seconds by asking for the year, month, and day separately to let me calculate while I talk, so I usually have to think for about two seconds after talking to tell someone the weekday.
It’s an algorithm I came up with myself - I take the difference of the year to one of the nearby cardinal years, which I’ve memorized, then add for leap years, then add a number for the month (I’ve memorized a number for each month), then add that to the day number, then take the remainder when divided by seven.
It’s something that I’ve had to practice, plus I’m pretty quick with numbers in general. I tell people that I’m an idiot savant, or tell them that I remember that date. The trick is often underappreciated - people say something like “Oh, there’s just a formula for it.” It’s insulting - like telling a magician that his work is “just a trick.”
There are various standard formulas for doing this which anyone can learn and use if they really want to. You can find them in books on memory demonstrations or mentalism (mind-reading magic). Or you can search the web for sites devoted to recreational mathematics, or mental feats, or memory demonstrations, or relevant terms like ‘day for any date’.
This guy’s website will do the trick for you (see the Instant day for any date’ box) and contains many other cool and totally free stunts as well.
I had a roommate in college who could do this. Someone would discuss some historical date and he would smirk: “Wednesday” with complete confidence. He explained there was a formula. I personally think he was making it up.
It’s not too hard. Here’s the way I learned to do it (for 20th century dates). Apologies if this is in one of the links provided - I didn’t see it with a quick scan.
We’ll use November 22, 1963 as an example.
- Take last two digits of year = 63
- Divide last two digits of year by four and discard remainder = 15
- Add these numbers ==> 63 + 15 = 78
- Add day of month (22) ==> 78 + 22 =100
- Add ‘correction factor’ for that month
[sub][sup]- Jan 1
- Feb 4
- Mar 4
- Apr 0
- May 2
- June 5
- July 0
- Aug 3
- Sept 6
- Oct 1
- Nov 4
- Dec 6[/sup][/sub]
So for November add 4 ==> 100 + 4 = 104
Divide this number by 7. What is remainder? Answer 6
Now,
Sun = 1
Mon = 2
Tues = 3
Wed = 4
Thur = 5
Fri = 6
Sat = 7 (or 0)
November 22, 1963 was a Friday.
[sub][sup]For Jan and Feb of leap years, the correction factors change by 1[/sup][/sub]