Zeller$$s congruence $($source:Click$\_$here$\_$for$\_$more$)$ is an algorithm devised by Christian Zeller to calculate

the day of the week for any calendar date. For today$$s Gregorian calendar, Zeller$$s congruence is

G $=($q $+($m $+1)13$

$5+$ U $+$ U

$4+$ V

$42$ V $)$ mod $7(1)$

where G is the day of the week $(0$ means Saturday, $1$ means Sunday, $2$ means Monday, $...),$ q is the day of

the month $(1<=$ q $<=31),$ m is the month $(1<=$ m $<=12),$ and y is the year of the calendar date $(1582<=$ y $<=2099).$

Further, the above equation distinguishes V as the century $($that is$,$ V $=$ y

$100),$ and U as the year of

the century $($that is$,$ U $=$ y mod $100).$

Finally, there is an exception in Zeller$$s congruence for the months of January and February which need to

be counted as month $13$ and $14,$ respectively, of the previous year. Thus, if m $=1$ or m $=2,$ then we need to

add $12$ months to the value of m$,$ and subtract $1$ year from y before we feed the values into the above equation.