Answer
Saturday
Work Step by Step
The formula for the day of the week in $N$ days is $DayN = ((DayT)+N)\ mod\ 7$, where $DayN$ is the day of the week in $N$ days, $DayT$ is the day of the week today, and the days Sunday through Saturday are numbered $0$ through $6$, respectively.
If January 1, 2000 is a leap year, then there are 13 leap days (in the years 2000, 2004, 2008, etc.) between that day and January 1, 2050, for a total of $365(50)+13=18263$ days.
Therefore, if $DayT=6$ and $N=18262$, we have $DayN = (6+18263)\ mod\ 7=18269\ mod\ 7=6$, because $18269=7(2609)+6$. See example 4.4.3 for an explanation of the formula $DayN = ((DayT)+N)\ mod\ 7$.
