Many years ago I see similar algorithm in detailed paper calendar.
Calendar Math
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It is the lowest common algorithm. There are several of these and simplest with a programmable calculator.
Jan 14, 2015
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#5
I am used to make this calculations myself and I do not use this method but another one I myself developed.
It is a good thing to do in a social meeting ("Do you know which day of the week you were born?") but I have to admit it is a little more restrict than this one presented by Louisa.
Abrazos.
What day of the week will May 12, 2034 be?
What day of the week was May 12, 1298?
The following algorithm will tell you.
(Note: all divisions, except where noted otherwise, are integer divisions, in which remainders are discarded.)
First figure out the values for \(a\), \(y\), and \(m\) -- variables to be plugged into a formula.
\(a = \frac{14 - month}{12}\) (month = # of month, 1 for Jan, 2 for Feb, etc)
\(y = year - a\) (year = the 4 digit year)
\(m = month + 12a - 2\)
Next, plug the values of y and m into the following formula to calculate the day:
\[ d = (day + y + \frac{y}{4}-\frac{y}{100}+\frac{y}{400}+ \frac{31m}{12}) \:mod \:7 \]
(Note: mod 7 means "modulo division." That is, take the remainder instead of the quotient as your answer. For example, 20 mod 3 = 2, because the remainder is 2.)
The answer you get for \(d\) will correspond to a day of the week as such:
0 = Sunday1 = Monday
2 = Tuesday
3 = Wednesday
4 = Thursday
5 = Friday
6 = Saturday
Example: What day of the week will April 5, 2020 fall on?
First figure out \(a\), \(y\), and \(m\):
\(a = \frac{14-4}{12} = 0\)
(remember, it's integer division so remainders are discarded. 4 represents the month of April since it's the fourth month of the year.)\(y = 2020 - 0 = 2020\)
\(m = 4 + 12(0) - 2 = 2\)
Now plug \(y\) and \(m\) into the \(d\) formula to calculate the day:
\[ d = (5 + 2020 + \frac{2020}{4} - \frac{2020}{100} + \frac{2020}{400} + \frac{31(2)}{12}) \: mod \: 7\] \[ d = (5 + 2020 + 505 - 20 + 5 + 5) \: mod \: 7 \] \[ d = 2520 \: mod \: 7 \] \[ d = 0\]Note: 2520/7 = 360 with a remainder of 0.
Recall from above that 0 = Sunday. So April 5, 2020 will be a Sunday.