Doomsday Game - What Day of the Week is it?

About

Lifted straight from Wikipedia: The Doomsday rule is an algorithm of determination of the day of the week for a given date. The idea of this game is to improve you mental arithmetic skills by calculating the day of the week from the date given.

Help

Where to start?

I'd suggest the Wikipedia article. This explains the background, history, and provides a few ways to calculate it.
Doomsday rule - https://en.wikipedia.org/wiki/Doomsday_rule

Anchor Years

List of anchor years for centries the date may come from:
Century Anchor day
1800–1899 Friday
1900–1999 Wednesday
2000–2099 Tuesday
2100–2199 Sunday