Mathematics shortcuts : Finding day

Day of the Date

Finding Numbers of Months

Century offset calculation (Gregorian Calendar):
Step1 :Take the first two digit of the given year.
Step2 :Calculate the next highest multiple of 4 for the first two digit number.
Step3 :Subtract 1 from the number.
Step4 :Then, subtract the first two digit of the given year
Step5 :Finally, multiply the resultant value with 2.

Example:

Calculate centruy offset for 1900s century.
Let us take the first two digit 19.
The next highest multiple of 4 for the first two digit number 19 is 20.
Subtract 1 from the number. i.e. 20-1
Subtract the first two digit of the given numberi.e ((20-1)-19)
Finally, multiply the resultant value with 2..
1900s = ((20-1)-19)*2 = 0.
Below given Gregorian Century Offsets table shows the other century and offset values,

Century	Offset
300, 700, 1100, 1500,1900, etc.	0
400, 800, 1200, 1600, 2000, etc.	6
100, 500, 900, 1300, 1700, etc.	4
200, 600, 1000, 1400, 1800, etc.	2

Find the Month Offset:
Consider there are 4 weeks in a month, which means 4x7=28days. January has 31 days. The days remaining are 31-28=3. The reminder helps you in calculating the numbers for each month.
Initially, Take Jan as 0
February = ( Number of days in Jan + Remaining days in Jan ) / 7) = (31+0)/7 = 3
March = ( Number of days in Feb + Remaining days in Feb ) / 7) = (28+3)/7 = 3
April = ( Number of days in Mar + Remaining days in Mar ) / 7) = (31+3)/7 = 6
Continue the same process till December... The numbers for the months are,

Month Offsets table:

Month	Offset
January	0
February	3
March	3
April	6
May	1
June	4
July	6
August	2
September	5
October	0
November	3
December	5

Numbers for the weekdays are,

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

You are about to remember this table before proceeding with the trick.
Now let us play the trick

Remember the formula Century offset + Year offset + Month offset + Day Offset 
Where,

Day Offset = Given day mod 7 
Year Offset = ( Last two digit of year + (Last two digit of year / 4) ) mod 7 
if the given year is leap year and month is Jan/Feb, thenYear Offset = ( ( Last two digit of year + (Last two digit of year / 4) ) mod 7 ) - 1
Step1: Ask for any specific date and challenge them you could tell the weekday of the date mentioned without any calculation. Example: 23^rd June 1986
Step2: Take the century offset from the first table, 1900 is 0.
Step3: Calculate the year offset for 86 is ((86 + 86/4) mod 7) = 2 
Step4: Take the month offset from the second table, June is 4.
Step5: Calculate the day offset, that is 23 mod 7 = 2
Step6: Now add all the 4 numbers: 0 + 2 + 4 + 2 = 8.
Step7: Divide 8 by 7 = 1 remainder 1.
The reminder tells you the day. 
Answer: Monday