Here’s a cool trick to find a day for any date !!

How to figure out the day of the week of anyone’s birthday. This is actually a very practical skill. It’s not every day that someone will ask you to square a three-digit number, but hardly a day goes by without somebody mentioning a date to you in the past or future. With just a little bit of practice, you can quickly and easily determine the day of the week of practically any date in history.

Let’s get started !

For finding a day for any date we need three things:

  1. Date ( already given )
  2. Month Code ( to be calculated )
  3. Year Code ( to be calculated )

First, we assign a code number to every day of the week. They
are easy to remember:

Code No. to Every Day of the week
Code No. to Every Day of the week
Month Codes

Next, we need a code for every month of the year. These month
codes are applicable for every year, with two exceptions. In a leap year
(like 2000 or 2004 or 2008 or . . .) the month code for January is
5, and the month code for February is 1. To make the month
codes easier to remember, we provide a table of mnemonics below.

Table for code for every month
Table for code for every month

*In a leap year, the code for January is 5 and the code for February is 1.

Year Code

Every year is also assigned a code number.

Code for every year
Code for every year

Now let’s calculate the day of the week for any date in 2006. After that, we will describe 2007, then 2008, and so on, for the rest of your life

Thus, for example, May 2, 2007, has

Month Code + Date + Year Code = 0 + 2 + 1 = 3

so the day is Wednesday. Let’s try another

For September 10, 2006 we have

Month Code + Date + Year Code = 4 + 10 + 0 = 14

Now since the week repeats every seven days, we can subtract any multiple of 7 from our answer (7, 14, 21, 28, 35, . . .) and this will not change the day of the week. So the answer is 14 – 14 = 0. That’s Sunday!

Now I know what you’re thinking “No way! I can’t memorize that bullshit f$*@king long year table !”. What if I tell you that you dosen’t have to memorize that long year table.

We can mentally calculate the year code for any date between 2000 and 2099. For the year code of 2000 + x, we simply take the number x/4 (ignoring any remainder) and add that to x. The year code is then reduce by subtracting any multiple of 7.

For example for the year, 2062, we see that 62/4 = 13. Thus year code for 2062 is 13 + 62 = 75. And since we can subtract any multiple of 7, we use the simpler year code of 75 – 70 = 5.

Now that’s EASY!! All you have to memorize the 12 column month table.(that’s why mnemonics are given).

Some Exceptions!!

For calculating year codes of years in 1900’s you have to add 1.

For instance , if we calculate year code 1952 , 52/4 = 13 (ignore that the remainder if any) . 13 + 52 + 1 = 66. And now we can subtract 66 by multiple of 7, 66 – 63 = 3.

For dates in the 2100s, we add 5 to the year code (or, equivalently, subtract 2 from the year code). For example, since 2009 has a year code of 4, then 2109 has a year code of 4 + 5 = 9, which, after subtracting 7 is the same as a year code of 2.

Reference : Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

For more math tricks stay tuned to MathCompt!