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civil Maths

Maths Shortcut Tricks (Calculate the Day of the week of any Given Date)

How to Calculate the Day of the week of any given date in no time. It’s a calendar calculation technique that I learned from a book. By Practicing it allows you to take a date, like 15 August 1947, and mentally calculate which day of the week it fell on.

 

Note: “Mod” means to divide the number and keep only the remainder. For Example, if the Total of all codes is 58 mod 7, then divide 58/7 and keep only the reminder i.e. 2

The Year Code
To calculate the Year Code, use this formula:

YY is the last two digits of the year. For the year 1947, it’s 47.
First, divide YY by 4 and discard the remainder: 47 div 4 = 11.
Then add 11 back into the YY number, which is 47 in this case, resulting in 58.
The next step is: 58 mod 7. We’ve divided 58/7 and left with a remainder of 2. That is the Year Code for 1947.
Hold that in memory while you calculate the items below.

The Month Code
This is easy — just memorize the number 033614625035:

Memorize it as (033)(614)(525)(035)

The Century Code
Just remember the number 4206420:
(420)6(420)


Leap Year Code

Note : The other thing to take into account is whether you are dealing with a leap year. If the date is from January or February of a leap year, you have to subtract one from your total before the final step and for other months except Jan and Feb.

If you can divide a Gregorian year by 4, it’s a leap year, unless it’s divisible by 100. But it is a leap year if it’s divisible by 400.
1992 is a leap year because you can divide it by four.
1900 is not a leap year because you can divide it by 100.
2000 is a leap year because you can divide it by 400. Calculating the Day

Back to the original formula:
(Year Code + Month Code + Century Code + Date Number – Leap Year Code) mod 7
For 15 August 1947, here are the results:
Year Code: 2
Month Code: 2
Century Code: 0
Date Number: 15 (the 15th of the month)
Leap Year Code: 0
So:

(2 + 2 + 15) mod 7 = 19 mod 7 = 5

Match the resulting number in the list below, and you’ll have the day of the week:

0 = Sunday
1 = Monday
2 = Tuesday
3 = Wednesday
4 = Thursday
5 = Friday
6 = Saturday

15 August 1947 was on a Friday.

Leap Year Example :

Lets calculate the Day for 18 July 1996
Year Code : 1 (96/4=24+96=120, 120 Mod 7 = 1)
Month Code : 6
Century Code: 0
Date Number : 18
Leap Year Code : 0 (No minus because it doesn’t fall in Jan and Feb)
So:
(1 + 6 + 18) mod 7 = 25 mod 7 = 4

18 July 1996 was on a Thursday

Another Leap Year Example :

1 January 2000: Start with ’00, leaving a Year Code of zero.
January has a Month Code of zero.
The Day Number is 1.
The Century Code for dates in the 2000s is 6.
2000 is a leap year since it can be divided by 400, and the date is in a January or February, so subtract 1 from the total in the final step.
Answer: 0 + 0 + 1 + 6 – 1 = 6.

1 January 2000 was a Saturday

Another Example
07 November 2017
Year Code : (17/4=leaving reminder we get 4) (4+17 Mod 7 = 0) because reminder is zero
Month Code : 3 (November)
Century Code : 6 (year falls in 2000 century)
Leap Year : 0 (No 2017 is not a leap year)
So.
(3 + 6 = 9 Mod 7 = 2)

The day is Tuesday!