I can tell you the day of the week for any date you give me.
This week I memorized the entire history of mankind... No, I’m kidding. But I actually can give you the day of the week on any date you give me.
Here’s how that happened:
It was about two days ago, I was sitting in my room, procrastinating on YouTube when I came across a video by an excellent Youtuber Mike Boyd. Mike makes videos, learning different skills, from wheelies to muscle-ups and in amazingly short periods of time. (If you’re reading this, you’ll probably love his content. Go check him out.)
In the video Mike gives an introduction and some key facts but he quickly passes the torch onto another video by the YouTube channel ‘Numberphile’, so I clicked the link through to their video and there was so much more to see:
For some reason I really wanted to know how to do this. This had my full attention.
This video does an excellent job of explaining the concept but if you want to hear my explanation, with some extra tips that I learned on my own, keep reading:
My Explanation
What I am about to explain to you is something called the ‘Doomsday method’, devised by John Conway in the 1970s.
The way our modern day ‘Gregorian Calendar’ is structured has a peculiar quirk to it: These dates; 4/4, 6/6, 8/8, 10/10 and 12/12 will all land on the same day, often called the ‘doomsday’ for that particular year. For the year 2021 this is a Sunday. There’s also these: 9/5, 5/9, 7/11, 11/7. (To remember this: “I work 9 to 5 at the 7-11.”)
If you’re smart you’ve probably realized that this pattern repeats for every week of the year. So there’s more…
I’ve attached a list of the dates that I remember:
(4/1 and 29/2 are leap year cases)
For all these dates in 2021, the day of the week is Sunday. So, if someone asked me what day Christmas will be, it won’t take me long to say “Saturday.”
Okay… that’s cool and all but…
What about other years?
So we know that the doomsday for 2021 is a Sunday. What will the doomsday for 2022 be? Answer: a Monday. Yep, it’s just the next day along.
2022? A Monday.
2023? A Tuesday.
2024? A Thursday.
Wait a second…
Every year the doomsday moves by one day but every leap year the doomsday leaps an extra day ahead.
***
So, here’s a test for you:
Given that the doomsday for the year 2000 was a Tuesday how do we calculate the doomsday for 2021?
Answer:
Tuesday + 21 days + 21/4 leap days = Tuesday + 26 days, which is Sunday.
Let’s make things easier:
Some Tips
Convert days of the week into numbers.
When calculating how many leap years, remainders cancel to zero because the leap day doesn’t happen until the 4th year.
Multiples of 7 will also cancel to 0. Those 21 days will bring us right back to Tuesday. We can ignore it.
Key Years
Did you know there are only 28 possible calendars before the cycle repeats itself? For this reason an addition in years of 0, 28, 54 and 84 will cancel to 0.
Some other years that Conway found are as follows:
0 will cancel to 0, 12 will cancel to 1 etc.
***
So, once more, given that the doomsday for the year 2000 was a Tuesday how do we calculate the doomsday for 2021?
2 + 1 + 9 + 2 = 14 (0) which is Sunday.
Other centuries?
We know that the doomsday for 2000 was a Tuesday. What’s the doomsday for 2100? A Sunday. Then Friday, then Wednesday, than back to Tuesday.
The pattern for centuries repeats every 4 years: 5, 3, 2, 0, repeat. Look carefully and you’ll notice that every century that is a multiple of 4 (16 hundred, 20 hundred, 24 hundred) will be a Tuesday. You can use these as anchor points.
I bet you could do this now:
What is the day of the week for the 1st of January 1951?
Answer:
3 + 4 + 3 + 0 = 10 (3) (so the doomsday is Wednesday) - I add zero because there are ‘zero leap years’ to add within 3 years.
Nearest doomsday: 3rd of January.
(We need to go back 2 days.)
3 - 2 = 1 which is a Monday.
Common Mistakes.
After testing myself countless times (using the excel doc method that Mike describes in his video) I had many epiphanies that the video didn’t teach me…
The first thing I realized was that this trick only works after the year 1582. This was when the Gregorian calendar replaced the Julian calendar. I spent hours wondering why I was getting those dates wrong, save yourself the time.
Secondly, when calculating the doomsday for a certain year, counting back from a leap-year will also be 2 steps back. That seems obvious but I had to make that mistake to realize.
This one might really surprise you. I had no idea about this. Let me ask you: Will 2100 be a leap year? Answer is no! What!? Apparently, a ‘100 year’ must be divisible by 400 to be a leap year.
Conclusions
Since this article got so long, I will go into how I went about learning this in a few hours in another article. - Following the article, I wrote about the book ‘Make it Stick’ my learning habits have definitely improved and I want to write in more detail about that.
This is definitely not the most useful skill to learn these days when we have smartphones and technology ready to tell us that kind of information. However, at least I’ll definitely be the coolest kid at the next party I go to.
