Q$1$: For a given date $($year$,$ month, day$),$ calculate how many days have passed since Jan. $1$st$,2000.$

$*$ There are $365$ days in a regular year, $366$ days in a leap year.

$*$ Number of days for all $12$ months are $[31,28,31,30,31,30,31,31,30,31,30,31].$

$*$ There are $29$ days in Feb if that year is leap year.

$*$ Assume the given date is later than the starting date.

Q$2$: Given that January $1,2000$ falls on a Saturday, what day of the week is today $(1/31/2024)?($Sunday$,$ or Monday, etc.$)$

Q$3$: What day of week for the given date: $12/31/2050?$