*Hello Learners!*

People have always wondered whether one can manually find the day of the week of any particular date in the past or future. Well, the answer is “Yes” and today I am going to teach you how to find it.

This technique will not need you to be genius in mathematics. It is a simple trick and I am sure, you will get it with some practice.

The first date that comes to everybody’s mind is their birthdate. Mine is **6th of August, 1988**. We will like to know Which day of the week was this date? Let’s find out.

The concept revolves around a number, called *Index number*. Index number will help us determine which day of the week is the given date. We need to calculate this *Index number* step by step. There is an interesting fact about it. You can always reduce it to below 7. You just need to divide the number by 7 and the remainder will be your new *Index number*. You will learn it through the example.

##### Step I: Calculate Index number of century.

The first step is to calculate the *Index number* for the century of the given date. For each block of **4** centuries or **400** years, *Index number* is “**0**“. Thus for **400**, **800, 1200, 1600** and **2000** – *Index number* is “**0**“. We will like to see which block lies just before our date. It’s **1600** here. Now, we are left with **19-16** =** 3** centuries. For each century, value is **5**. Therefore, for **3** centuries, value will be

3 * 5 = 15

*15 mod 7* = **1* **(15, when divided by 7 leaves **1** as remainder)

We have found the Index number for Century. Let’s move forward to years.

##### Step II: Calculate Index number of year.

We have found Index number for** 19 centuries** or **1900** years. Now, we are left with **1988 – 1900** =** 88** years. However, only **87** of these years are complete. So, we will find only *Index number* for only complete years, i.e., **87**.

You may be well versed with the concept of leap year. In **87** years, there will be **87/4** =** 21.75**(~**21**) leap years and **87-21** = **66** Ordinary years. For each leap year, value is “**2**” and for each ordinary year, value is “**1**“. So, we can find *Index number* for years like this:

21 * 2 + 66 * 1 = 42 + 66 = 108

*108 mod 7* = **3***

##### Step III: Calculate Index number of months:

The next step is to calculate *Index number* for months. This one is simple. You can find *Index number* of any month by dividing number of days in that month by **7** and note the remainder. e.g., January has **31** days, thus *31 mod 7* = **3**. If February has **28** days, Index number will be* 28 mod 7* = **0** and for leap year, index number will be *29 mod 7* = **1**. To know whether the given year is a leap year, divide it by **4**. If it divides exactly, it is a leap year. For our example, **1988** is a leap year as it is a multiple of **4**.

**Index number for months:**

January :

31 mod 7=3February :

28 mod 7= 0 or29 mod 7=1March :

31 mod 7=3April :

30 mod 7=2May :

31 mod 7=3June :

30 mod 7=2July :

31 mod 7=3August :

31 mod 7=3September :

30 mod 7=2October :

31 mod 7=3November :

30 mod 7=2December :

31 mod 7=3

In our example, **6th August** , we have complete months of January, February(of leap year), March, April, May, June and July. So, we will add *Index numbers* for the respective months like this:

3 + 1 + 3 +2 +3 +2 + 3 = 17

17 mod 7 = **3***

##### Step IV: Calculate Index number of day of month:

*Index number* of day will be the day itself. i.e., 6 mod 7 = **6***.

##### Step V: Add All Index numbers:

The final step is to add all the *Index numbers*. In our case,

Index number of centuries: **1*** + Index number of years: **3***** **+ Index number of months: **3* + **Index number of days: **6* = 13**

*13 mod 7* = **6**

Compare this number with the day of the week starting with Monday. Here’s the key:

Sunday :

0or7Monday :

1Tuesday :

2Wednesday :

3Thursday :

4Friday :

5Saturday :

6

Clearly, I was born on Saturday (6). Its your time to check your birthday. In case of query, feel free to leave a comment.

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