How Math Can Tell You the Day of the Week for Any Date in History

With a dash of math, know the day of the week for any date on the calendar.

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.

PRODUCTION CREDITS

Videography & Production
Ari Daniel

Original Footage
© WGBH Educational Foundation 2016

MEDIA CREDITS

Music
APM

Additional Imagery
Flickr/Dustin Liebenow

Special Thanks
Brunswick Junior High School
Peter Stevens' Class

[karthikdasaraju]

Yes there is a pattern for the code of years i.e

for every leap century (800, 1200, 1600, 2000) the code will be zero
for every other than leap century i.e for 300-1, 200-2, 100-3
Now if the year is in 1800's then 1600(code 0)+200(code 2)
Now if the year is in 1900's then 1600(code 0)+300(code 1)
Now if the year is in 2000's as the year is a leap century code will be zero
After this coming to 2 digits-for example if it is 2026 first, last two digits(-1) should be divided by 4 to find leap years and ordinary years so 25/4=6 (leave the remainder) so there are 6 leap years and 19 ordinary ones(25-6). Now multiply the leap number with 2 and ordinary with 1 and add them. at last get the remainder when the the sum is divided with 7.

Example: 1951
1600(o)+300(1)
50/4=12 leap and 38 other
12 times 2+ 38 times 1=64 when 64/7 remainder will be 1

SO THE YEAR CODE IS 1600(0)+300(1)+50(1)=2

[josefwintzentlibot]

Today in AGT a Malaysian pulled impressively the Calendar Trick. The Calendar Trick is to tell accurately the day of the week any random date presented to. It is actually memory game with a little arithmetic. Just subtract 1900 to the year; add the date; add the number of leap days from 1900 till that date; then add 0 if it falls in a January or October, 1 if May, 2 if August, 3 if February, March or November, 4 if June, 5 if September or December, or 6 if April or July; and finally continuously subtract 7 unto it till the answer is less than 7. When the final answer is 0 it falls on a Sunday, 1 on Monday, 2 on Tuesday, and so on. One has to do it mentally and without any use of any device even if just pen and paper to be impressive

[acarvey]

Great video! Lots of other resources I went to were REALLY CONFUSING! I'll now be using this method in a school programming project to produce a dynamic calendar, thanks so much!

[ynnekthennek]

i hate how they don't want to give up the trick. they make it more complicated than it has to be. forget their month code and use the one i'll give you. you can master it this way in under an hour. its pretty easy once you get the hang of it. you have to add 4 numbers and divide by 7. add the year, + 25% of the year(or year divided by 4), + month code(033-614-625-035), + day of month

example: March 3rd, 1948 or 3/3/48 =
year =48__ the year divided by four = 12__ the month code=march = 3, day of the month = 3
so 48+12+3+3=66 divided by 7 = 9 remainder 3 and 3 is Wednesday
that works perfect for leap years, as long as the date is after feb 29

also, we used march 3rd, but you must subtract 1 if the date is before feb 29th on a leap year. it takes a little getting used to but its really easy once you get the hang of it. remember, leap years start in 2000, just like in 1900, for this century. just get good at the 1900's and you'll understand how the 2000's work a lot easier. you can get really fast in just a week if you work at it an hour a day. in the 200's you have to subtract 1 or 2 days from your final answer depending whether it is a leap year or not.

all years divisible by 4 are leap years(1900, 1904, 1908, 12, 16, 20, . . .40, . . . 80, . . .88, 92, 96, 2000, 2004, 2008, 12, 16, 20)

another example:
jan 30, 1948
1/30/48; that was a leap year. you must subtract a day because it was before the 29th of february.
walkthrough: 1/30/48 __ 48 + 12 + 0 + 30 = 90 = 84 w/remainder of 6 = Saturday minus one equals Friday. you must subtract one since the leap day wasnt added yet, because it is before feb 29, which would make it Friday, not Saturday. [for the remainders in years not divisible by 4, just drop the remainder]

for the 2000's, you do the same thing, but now you always subtract a day from your final answer unless it is a leap year, then you subtract 2 days from your final answer
so, after feb 29th 2000, you subtract 1 day from the final, but on or before the 29th of feb. you subtract 2 days from your final answer. i hope i explained it clearly. any questions, let me know.

[drtroyturner]

A few people missed it, were asking so: The 21 came from adding the Month code which was 622 503 514 624 for months January through December plus persons chosen day plus year code of 4 for 2015 gives us a total of 21 because November is 2 plus 15 (girls birthday) plus 4 is 21. Divide by 7 but concentrate on the remainder. Remainder zero is zero day Sunday.

[coreymcdonald]

Year codes: 2000 is 0. you can either add 1 for every year, and add 2 for leap years. or you can take the last 2 digits of the year, divide it by 4, then add that answer back to the original number... 2015 for example. 15/4=3.75. Ignore the .75 and add 3+15 to get 18. subtract the largest multiple of 7, without going over. 18-14=4. 2015 has a year code of 4.

[drtroyturner]

I give my volunteers the choice of 1950, 1975, 2000 and 2025. It seems perfectly fair considering you have alternating odd and even numbers spaced out equally and it makes horse sense that for the sake of time (not really), we need to narrow down what calendars that the volunteer will Google and isolate. No one need know that I just cut out much of my confusion by having year codes of zero, three, zero and three.

[Swirl_J]

0:39
Me: [calls brother]
Him: Yeah
Me:found your twin

[drtroyturner]

The easiest way I know is 1) memorize month values. check
2. plus day . a gimme 3) plus year value. Difficult but I know 1904 is a 6 value and 11 years later is also 6 as is 6 years after that and these serve as landmarks for other years. You can also add a couple of family members birth years and years of graduation as check points. 4) obviously divide by 7 and the remainder determines the day of the week. Tell your audience that you can guess within 3 days until you get very good at it. Then 2, Then spot on.

[DanTheStripe]

I did this 3 years ago and forgot how to do it since. I'm re-learning it, and the system used here is the same one I used 3 years ago.

[GENIUSAA]

Just watched this guy's TedX talk

[drtroyturner]

ps. 1955, 1966, 1977 and 1988 are all 6 values. 99 is a 5 whereas 2000 leap year moves ahead one and is a zero (same as 7).

[georgiapanagopoulou]

i found a better way -

every year with leap saturday is a key year.
count days from a doomsday + years from a key year + leap years since a key year
then mod 7
if
sunday=1
monday=2
tuesday=3
wednesday=4
thursday=5
friday=6
Saturday = 0 or 7
its real

[jesserianbayani]

how to get the codes for the remaining years?

[meghaarya]

What are the 'code' numbers for any other year? Is there a pattern to it or memorizing?

[drtroyturner]

Took some doing but I found out how to find year codes from scratch. 2015. Zero in on the last 2 numbers only. 15. Divide by 4 ignore the remainder = 3. Add the result to the original # so 15 +3 =18, Divide by 7 but this time you are only concerned with the remainder as that is your year code. So 18/7 means year code for 2015 is 4. Let's do 2018. 18/4 is 4 which is added to 18 so 22, Divide by 7 and the remainder is code so 1 is the code for 2018. 1 more. 2020. 20/4=5, 25/7, 4 is the code for 2020. What day is January 6, 2020. Today. But seriously, 6 (for January) plus 6 day plus 4 year code is 16/7 is remainder Tuesday.

[drtroyturner]

Honestly, there is this method, there is Doomsday method (I'm leaning towards as possible easiest) and there is Spam School which is easy, but not sure how they arrive at their year codes. I will need to chose 1 and stick with it so my mnemonics don't become intertwined and jumbled. This method is a little scary because you are expected to divide by 4 then add that number to original 2 digit year, then you still have to divide by 7 and your answer is the remainder. That's a little more involved than other methods I'm almost certain.

[krishnamurthythondebavi]

How to calculate years codes for 16th, 17th, 18th, 19th & 20th centuries years.

[PuneethSaiBhaskar]

what could be the codes for other years ?

[GFApryl]

What is the method to determine the year code? I can do THIS year, but what of other years, like when a person was born?