Speaking of calculating the day of the week, I remember seeing someone on TV about twenty years ago who could correctly tell you the day of the week for any given date. I doubt they were doing such complex calculations, so they might have had a special method. If I recall correctly, it was a young boy with savant syndrome, so he might have simply memorized an incredible number of patterns...
There was this[0] famous answer on University Challenge, but it's a pretty simple calculation.
[0]: https://www.youtube.com/watch?v=-dh7COSiB7g