I've been told there's a straightforward way to determine which day of the week a date falls on, by first using Gauss's algorithm, to find the day of the week of 1st of January. Then this can be combined with modulo 7 arithmetic on an ordinal day to calculate the day of the week for a particular date.
For example, Gauss's algorithm can tell us that, this year, the 1st of January fell on a Sunday, the 7th day of the week. Today is the 22nd of October, with an ordinal day of 295. How can this information be used to calculate that today is a Sunday?