Amazing Calendar Trick
 By Ari Daniel
 Posted 02.04.16
 NOVA
Arthur Benjamin blends his loves of math and magic into a rare performance genre he calls mathemagic. One of his acts involves telling people the day of the week for any date, past or future, on the calendar. Here, he breaks the magician’s rule and explains how he does the trick.
Transcript
Benjamin: Well, good afternoon, ladies and gentlemen. My name is Art Benjamin, and I am a mathemagician. What that means is I combine my loves of math and magic to do something I call mathemagics.
Does anyone here happen to know the day of the week that they were born on? Alright, starting with you, what year were you born?
Student: 2004.
Benjamin: 2004. And what month?
Student: May.
Benjamin: May. May what?
Student: 25^{th}.
Benjamin: 25^{th}. Was that a Tuesday?
Student: Yes.
Benjamin: Yes, good, somebody else. What year?
Student: 2004.
Benjamin: 2004. And what month?
Student: August.
Benjamin: August what?
Student: 17^{th}.
Benjamin: Was that a Tuesday? Do we have any faculty or staff who know the day of the week…ok, we’ve got one right here. What year, if I may?
Teacher: 1970.
Benjamin: 1970. And what month?
Teacher: July.
Benjamin: July what?
Teacher: 28^{th}.
Benjamin: 28^{th}! Was that a Tuesday? What is it with Tuesdays in this state?
The short answer is I’m taking information from the year, the month, the date—I’m getting a number that comes from each of those. I add those three numbers together, and the total tells me the day of the week.
So, every year gets a code number and the code number for 2015 happens to be 4.
Next, we need a code for every day of the week. And the code numbers for Monday through Sunday are 1, 2, 3, 4, 5, 6, and Sunday is 7 or 0. And that’s real easy to remember because Monday is ONEday, Tuesday is literally TWOSday, Wednesday, if you put the W on your fingers, that gives you the 3…
Ok, finally, we need a code for every month of the year, and the codes from January to December go like this—it’s not as easy as you’d think. It’s: 6, 2, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4. And to make it worse, if it’s a leap year, the codes for January and February are 5 and 1.
Ok, yeah, I know.
Benjamin: Ok, now we have everything we need to be able to figure out the day of the week. So, somebody give me their birthday.
Student: November 15^{th}.
Benjamin: November 15^{th}, 2015. Ok, so what was the code for November? Two. For the 15^{th}, we add 15. And for 2015, we always add…
Student: Four.
Benjamin: Four. So now I add 2+15+4, and that gives me 21. Now, every 7 days, the week repeats, so we can subtract any multiple of 7 and that won’t change the day of the week. So I’ll subtract 21 here ’cause that’s the biggest multiple of 7. And 21–21 is zero, and NONEday is…
Students: Sunday.
Benjamin: Sunday. So your birthday will be on a Sunday. Thank you very much!
Pi, pi, mathematical pi.
Twice 11 over 7 is a might fine try.
A good ol’ fraction you may hope to supply.
But the decimal expansion won’t die.
Decimal expansion won’t die.
Pi, pi, mathematical pi.
3.141592653589…
A good ol’ fraction you may hope to define.
But the decimal expansion won’t die.
Thank you!
Additional Information:
The calendar is a mathematical object with regular patterns, such as leap years happening every four years. This results in your birthday increasing by one or two days as you go from one year to the next in a very predictable pattern. Using easy mnemonics, and by adding three numbers together  derived from the month, date, and year  the total yields the day of the week. This is a practical application of something called modular arithmetic  in this case, we're adding and subtracting mod 7 because there are 7 days in a week.
See more here.
Credits
PRODUCTION CREDITS
 Videography & Production
 Ari Daniel
 Original Footage
 © WGBH Educational Foundation 2015
MEDIA CREDITS
 Music
 APM
 Additional Imagery
 Flickr/Dustin Liebenow
 Special Thanks
 Brunswick Junior High School
Peter Stevens' Class
POSTER IMAGE
 (main image: numbers)
 © WGBH Educational Foundation 2016
Related Links

Zombies and Calculus
The zombie apocalypse is here, and calculus explains why we can't quite finish them off.

Zombies and Calculus, Part 2
You're being chased by zombies, and understanding tangent vectors may save your life.

Knotty Thrills
Three physicists untie a 150yearold tangle of a puzzle.

Do We Live in a Multiverse?
Could parallel universes exist? If so, what would they look like and how would they form?