Day of the Date - Funny Math Shortcut

Finding Number 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 from the number.
Step5 :Finally, multiply the resultant value with 2.

Example:

Calculate century 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 number i.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,

Find The Year Offset:
Year Offset = ( Last two digit of year + (Last two digit of year / 4) ) mod 7
Note : If the given year is leap year and month is Jan/Feb, then the Year Offset = ( ( Last two digit of year + (Last two digit of year / 4) ) mod 7 ) - 1

Find the Month Offset:
Consider there are 4 weeks in a month, which means 4 x 7 = 28 days. 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:

Numbers for the weekdays are,

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, then Year 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: 5^th sep 2016
Step2: Take the century offset from the first table, 2000 is 6.
Step3: Calculate the year offset for 86 is ((16 + 16/4) mod 7) = 6
Step4: Take the month offset from the second table, June is 5.
Step5: Calculate the day offset, that is 5 mod 7 = 5
Step6: Now add all the 4 numbers: 6 + 6 + 5 + 5 = 22.
Step7: Divide 22 by 7 = 1 remainder 1.
The reminder tells you the day.
Answer: Monday