I Know What Day Of The Week You Were Born
Recently I came across the television series Eureka, in which a small town in Oregon is inhabited by freakishly intelligent engineers and other people you don’t want to meet at a party. In the very first episode, a man encounters a young boy who asks what day he was born. When the man provides the date, the boy thinks for a second and says, “You’re a Tuesday. I was born on a Tuesday too.”
The second I heard that I knew I wanted to be able to calculate dates too (apparently I’m not much fun at parties either). I dove into it, and found several methods of calculation. One of the methods needed only memorizing a few numbers and being able to divide by 7.
Here’s how it goes:
Day of the Week = Day + Month + Year + (Year/4) + Century mod 7
We’ll use the date this post is published as an example (April 28, 2013).
The day is counted as a modulo number. This means you start over counting when you reach a certain figure. An everyday example of a modulo number is a clock. If the current time is 2:59, the next minute is displayed as 3:00 instead of 2:60. The numbers representing the minutes start over every time they get to 60. The same thing happens to hours after they reach 12.
To get the correct number to use for the day in the equation above, count today’s date as a modulo 7 number. Instead of the 28th, today appears as a 7 (you count to 7 then start over. By the time you get to the 28th, this is the fourth time you’ve reached 7 in counting).
Day of the Week = 7 + Month + Year + (Year/4) + Century mod 7
The hardest part of this is remembering a dozen numbers that will represent the various months of the year. In order, they are as follow: 0,3,3,6,1,4,0,2,5,0,3,5. In leap years, January appears as -1 and February as 2. April is the fourth month in this table, so it would appear as 6 in our equation.
Day of the Week = 7 + 6 + Year + (Year/4) + Century mod 7
The year is really easy. Just insert the last two digits of the year in question into the equation. 2013 Becomes 13 in this process. Don’t worry about any remainders left over from the division problem in the middle of the equation, as they will not change the answer. Just concentrate on the whole number it produces.
Day of the Week = 7 + 6 + 13 + (13/4) + Century mod 7
Day of the Week = 7 + 6 + 13 + 3 + Century mod 7
The century brings another set of memorized numbers to the equation. The current century is represented by the number 6. The previous century (1900s) is represented by 0. Each previous century is represented by adding 2 to the next century’s number (1800s are 2, 1700s are 4, and 1600s are 6). These four digits (0-2-4-6) repeat every four centuries.
Day of the Week = 7 + 6 + 13 + 3 + 6 mod 7
Add all of these figures up to get a total
Day of the Week = 35 mod 7
Remember the modulo numbers from when we calculated the day of the month? You’re using modulo 7 again, so divide your total by 7.
Doing this for today’s date gives a remainder of 0. Dates evenly divisible by 7 are Sundays. Any remainders left over correspond with the number of days beyond Sunday (1 = Monday, 2= Tuesday, etc).
So What’s The Point?
Admittedly, being able to quickly name a day of the week from mental calculations is not something you would imagine has a lot of practical applications.
I find its an interesting way to hint to someone that math is not a problem for you without saying it flat out. If a date comes up in a conversation (job interview? bar bet?) you can quickly say, “Oh, that was a Tuesday.” Someone who is not interested or who doesn’t understand that there is a method to naming dates will move on in conversation. Someone who recognizes that you just became a human calculator will be impressed and may follow up with additional questions (what day was I born?). The point is, if the other person doesn’t know there is a simple method behind this, you just became the greatest mathematician they’ve ever seen. If you’re lucky, they will be paying for a trip to send you to Las Vegas to play cards.
- Director: David, can you put together a costume for an actor in the Christmas play in an hour?
- Me: What guidelines do I have to work with?
- Director: The character is a complete nerd, but somewhat cool.
- Me: Challenge accepted.