How to Figure Out the Day of the Week For Any Date Ever

[PBS Bumper] Thanks to for supporting PBS Digital Studios. [OPEN] December 26, 1937… was a Sunday. It was also the birthday of a mathematician
named John H. Conway. Conway has spent most of his life obsessed
with games, from backgammon to his famous Game of Life… a machine that follows simple
rules, but can evolve incredible complexity. And he can also tell you the day of the week
for any date, past or future, in a couple seconds. Conway is smart, but he hasn’t memorized
1000s of years of calendars. He figured out how to answer this complex
question with a simple set of rules. He invented… an algorithm. And after watching this video–and with a
little bit of practice–you’ll be able to do it too… all with just one hand. Gimme a date! Here’s how it works: First let’s give
every day of the week a number. Here’s an easy way to remember ‘em: NONEday,
ONEday, TWOsday, THREEsday, FOURsday, FIVEday, SIXturday. We’ll use this in a sec. Next, Conway realized in any given year, specific
dates always share the same day of the week. April 4, always the same weekday as October
10. We can make another easy list: For even numbered
months, it’s the same date as the month, unless it’s February, when it’s the last
day of the month. The odd months are a little less obvious,
but just remember “I’m working 9 to 5 at the 7-11” and you’re almost there. All that’s left is Pi Day, and January,
which is the 3rd, unless it’s the 4th in a leap year. And now we’ve got our list: a set of dates
that are the same day, one every month. These are what Conway called Doomsdays. Scary name, but relatively easy to memorize. And since weekdays repeat by 7s, we have a
reference for any day of the year. 2018’s Doomsdays are all Wednesdays. Most years, the weekday for a date moves forward
one day. So in 2019 Doomsdays will be Thursdays. But 2020’s a leap year, and weekdays jump
by two. This is getting confusing. We need to find our Doomsday a different way. Start with the first year of the century. 2000’s Doomsday was Tuesday. Let’s hold that number (2) here, on our
index finger. To find the Doomsday for any other year in
a century was Conway’s stroke of genius. 2057. First, figure out how many times 12 goes into
the year, 4, and hold that number here. Put the remainder, 9, here. Finally, how many times does 4 go into the
remainder? 2. Put it on your pinky. Add these four numbers. If the number’s more than 6, divide 7 into
it as many times as you can, and what’s left over? Seven and Seven and… three. Wednesday’s the Doomsday for that year. For a different century, we just need to change
the index number, or century day. 1900? Wednesday. 1800, Friday. And 2100’s Doomsday will be Sunday. Since our calendar, the Gregorian calendar,
repeats every 400 years, we can figure out any other century, just by remembering these
. Now we have all we need to figure out the
Doomsday for any year, and once we know that, we can figure out any other day that year. Let’s try. EXAMPLES:
What day was the Declaration of Independence signed? Just like 2100, the century code is 0. 76 is 6 twelves, remainder 4, and there’s
1 four in the remainder. 0 + 6 + 4 + 1 is 7 and 4. The Doomsday for 1776 was a Thursday, and
since 7/11 is a Doomsday, so is 7/4. The first moon landing? The century code is 3. ‘69 is 5 twelves, remainder 9, which is
2 fours. July 20 is 2 days after a Doomsday, put it
on your thumb, so 2 + 3 + 5 + 9 + 2 is… 7 and 7 and 7 and 0. It was a NONEday. Kate McKinnon’s birthday’s January 6,
1984. 3, 7, no remainder, and since it’s a leap
year**, 2 days after the Doomsday. If you ever meet her, you can tell her she
was born on a Friday. Congrats, you just performed an algorithm. Algorithms are a set of instructions for solving
a problem step by step. We know them best from computers. But we run algorithms too, all the time. In fact, the word “algorithm” comes from
a Persian mathematician who wrote a book for doing math by hand… the same book that gave
us “algebra”. We’re interested in algorithms getting more
than just the right answer. We also want algorithms to do things efficiently. Lewis Carroll, the author of Alice in Wonderland,
and a mathematician, developed his own algorithm for solving the day of the week. It was printed in Scientific American on June
18, 1887, a Saturday. But Conway’s is quicker. These days, this kind of information is only
a few clicks away, but it shows us how the right algorithms can extract answers from
even complex data, and how, with a little bit of practice, you can be as smart as a
computer. At least for one day. Stay curious. If you’re sitting there thinking “there’s
no way I can do that”, trust me, if you can do arithmetic, you can. I’ve been practicing this method for a few
days, and now I can calculate any date in a handful of seconds. And I’m usually right. If you’d like to practice, we’ve made
this cheatsheet for you… and there’s a non-US version too, because I know we write
dates funny. I hope I’ve sparked your curiosity and showcased
the beauty and fun of mathematics. When I was preparing for this, I couldn’t
simply memorize this formula. I had to critically reason it through to understand
how and why all the various parts fit in, so I could explain it clearly. If you’d like to sharpen your brain and
develop the tools for mathematical thinking, then Brilliant could be the place to go for
that. You don’t just watch stuff, you actively
do stuff. I enjoyed their Joy of Problem Solving course
that presents fun puzzles cut up into easy to digest bits, which can help you think critically
and understand the how and why. It could help you sharpen your thinking up
so much that you’ll be able to cut through any problem put in your way like a… math
Samurai. You can go to brilliant dot org slash be smart
and sign up for free. As a bonus for future human computers, the
first 200 people that click on the link will get 20% off the annual Premium subscription.

100 thoughts on “How to Figure Out the Day of the Week For Any Date Ever

  1. Sure, you could just Google it… but where's the fun in that?!

    I promise, if you can do arithmetic, you can learn this trick. Let me know how impressed your friends are!

  2. If nobody kept the time for about a hundred years for some unknown reason, how would we know what day/month/year it is?

  3. I'm just gonna say now the American way of writing dates makes more sense than the other bullshit. Ascending makes things harder, it's better to go from broad to narrower, leaving yy/mm/DD. However because everyone knows what year it is, the year being at front is unnecessary leaving mm/DD/yy. Just because you aren't used to something doesn't mean it's better. I'm not used to the metric system of measurement, but I can acknowledge it is better than imperial

  4. See…the strange thing here is that Europeans and others can bash Americans for having their dates out of order YET they still use the same generally bassackwards calendar we do. Why is that exactly? To me, it would be easier to have 5 day weeks, 73-week years as those are the only prime factors for 365. To me, if we did that, we'd NEVER have a problem on the week side of things. If we started EVERY YEAR on the same day, we wouldn't have such complicated mind games like this.

  5. I set it my goal to learn this method. I’ve always told myself I’m too stupid for maths but now I want to prove myself wrong. I’m gonna update if I made it

  6. I gave a thumbs down because he did not explain this well at all:
    1) the first example happened to have a 4 as the reminder of 12 and I thought that was what you used for the second reminder, he didn't explain it's always a 4 and this example just happened to be the same number
    2) He didn't explain that the doomsday is not necessarily the exact dates each month, but the day off the week its self so I got confused when he did the example with 7/20/1969 and he said that was "2 days after the doomsday" because I kept thinking it was 9 days after it

  7. NOPE! Nope… nope… nope… nope… nope…

    I didn't live long enough to reach the computer age to go back to doing maths in my head.

  8. Everything works for me except for some leap year January and February's for some reason.

    Ex. January 18 1048
    5 (cc) + 4 (dividing 12s) + 0 (remainder of dividing 12s) + 0 (dividing 4s into remainder) = 9-(7*1)=2
    Therefore doomsday should be Tuesday, January 4th (leap year, 1048 is divisible by 4)
    This would put the 18th as a Tuesday as 4+(7*2=14)=18. This is untrue, however, as the calendar says this date should actually be a Monday. What am I doing wrong?

  9. It would have bern a good tutorial if you hadn’t been in such a hurry, also insread of the finger nonsense it would have been easier for me if the procedure had been written on a board, step by step… but I forget you don’t think that older people might want to understand as well… I’m 75 and I was left in the dust…I hope that makes you happy to know that…

  10. I've been using the other method mentioned for a while now. This is so much faster, I'll definitely be switching to this one now

  11. Dude has that special public school teacher talent for confusing those who want to learn. (I reviewed the video and deciphered the information after an hour, though).

  12. Awesome trick! But how can we do it with years that are less than 12? And what is the deal witg leap years? Is it just me that cant make it work when its a leap year?

  13. I like these things, have had a nerdish interest in this ever since I saw an old formula by Gauss, when I was about 10 years old. 🙂
    There are many ways to do this, and personally I find this doomsday thing a bit awkward to keep in my head, I remember devising a different system but can't for the life of me find it now, and have long since forgotten.
    What I did do at one point, that others have had use for is more of a simple step by step table based version, where one just follows along, without having to memorise anything, can be found at should anyone be interested. 😀

  14. I wrote a day-of-the-week challenger.
    It asks you the weekday of dates, you choose one and it tells you if you're right:

  15. The week starts with Monday, NOT Sunday. Sunday is the end of the week, hence Weekend (Sat and Sun). Monday is when the week starts

  16. I really dont get it, how you know 20 july is 2 days afterdooms day? i read on that link 7/11
    sry for asking

  17. I made it to four minutes in. This was a really stupid waste of time. You guys can definitely do better.

  18. This ( is way easier. Just subtract 1 from the FINAL ANSWER in case of leap year.

  19. Whoa… this is much simpler than calculating the odd days to find the day of the week. Thanks for sharing this method!

  20. I was doing okay or so I thought initial he said the remainder but dosen’ specify where the 48 came from.

  21. I thought this was going to be an easy trick like using your knuckles to find out which months have less than 31 days

  22. …I fan solve a rubix cube in 1minute 13seconds using algorithms, but I got lost in this video… I'm going to go ear some rat poison now.

  23. The only thing i cant get my head around is the leap years and if it was a year like 2003 so how would you work it out if you have the date June 27th 2003?

  24. i keep trying but i cant seem to have it work for new years day. i tried using 1/1 1949(saturday), so century code (3) 12 goes into 49 (4) times the remainder is (1) and 4 goes into 1 (0) times 3+4+1+0=8. 1/1 isn't a doomsday and is 6 days after the last doomsday(december 26th 1948) 8+6=14. 14-7-7=0 or sunday. is there something that needs to be used for new years day to find out what day of the week it is/was

  25. Guys it's simple, just got it, finally!
    If the year is below 12 (exm. 01; 02; 03; 04; 05; 06; 07; 08; 09; 10; 11) you just take it, not divide it by 12, then the magic works 🙂 Enjoy everyone!

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