Zeller's rule to calculate the day

Zeller's rule is used to calculate the day on which any date falls for any year. The rule is as follows

f = k + [(13*m - 1)/5] + d + [d/4] + [c/4] - 2*c

where,

k = day of month
m = month number, taking Mar=1, ..., Dec=10, Jan=11, Feb=12
d = last two digits of year, using the previous year for Jan and Feb
c = first two digits of year

Rules:

1.In Zeller's rule the year begins in March and ends in February. Hence, the month number from March is 1, April is 2, May is 3 and so on up to January, which is 11, and February is 12.

2.January and February are counted as the 11th and 12th months of the previous year. Hence, if you are calculating the day of any date on January 2026, the notation will be (month=11 and year= 2025) instead of (month=1 and Year=2026).

3.While calculating, we drop off every number after the decimal point.

4.Once we have found the answer we divide it by 7 and take the remainder. Remainder 0 corresponds to Sunday; Remainder 1 corresponds to Monday ; Remainder 2 corresponds to Tuesday and so on....

Example 1:

Find the day on 26th June 1983

f = k + [(13*m - 1)/5] + d + [d/4] + [c/4] - 2*c

Here k=26, m=4, d=83, c =19

f= 26+(13*4-1/5)+83+83/4+19/4-2*19
= 105

105 divided by 7 leaves a remainder 0. Hence the day is a Sunday!

Example 2:

Find the day on 25/03/2009
F = 25 + [{(13 x1)- 1}/5] + 09 + 09/4 + 20/4 - (2 x 20)
= 25 + 12/5 + 09 + 09/4 + 20/4 - 2x20
=25+2+09+2+5-40
[ We will just consider the integral value and ignore the value after decimal]
= 43 - 40 =3

Replace the number with the day using the information given below.

1 = Monday
2 = Tuesday
3 = Wednesday
4 = Thursday
5 = Friday
6 = Saturday
7 = Sunday
So it's Wednesday on 25th march, 2009.

Example 3:

Find the day on 15/08/1947

F =15 + [{(13 x6)- 1}/5] + 47 + 47/4 + 19/4 - (2 x 19)

          =15+15+47+11+4-38

          =92-38

          =54/7

Remainder  =5

So it's Friday on 15th august, 1947

Posted in: APTITUDE