Day of the Week Calculator

Give a date and this returns the weekday, with the working shown either as Zeller's congruence or as the doomsday rule stepping out from the century anchor. It handles the Julian calendar, the Gregorian one, and the switch between them, including the ten days October 1582 skipped and the eleven Britain and its colonies skipped in 1752. A second action finds the nth or the last weekday of a month, and a third lists the weekday a date falls on across a run of years. Every answer is worked a second time from the Julian day number and both are printed, so a slip in one method cannot pass unnoticed.