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 = 3
February : 28 mod 7 = 0 or 29 mod 7 = 1
March : 31 mod 7 = 3
April : 30 mod 7 = 2
May : 31 mod 7 = 3
June : 30 mod 7 = 2
July : 31 mod 7 = 3
August : 31 mod 7 = 3
September : 30 mod 7 = 2
October : 31 mod 7 = 3
November : 30 mod 7 = 2
December : 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 : 0 or 7
Monday : 1
Tuesday : 2
Wednesday : 3
Thursday : 4
Friday : 5
Saturday : 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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