The algorithm I mentioned in the OP is here: https://en.wikipedia.org/wiki/Doomsday_rule
I practiced the algorithm by replacing my doomscrolling time on a trainer app (https://whattheday.com/) over the last 3 weeks. I went from taking 2-20 minutes to usually get the wrong result to about 95% accuracy in 10 seconds.
This training app to teach you to play piano by ear and to sight read also got posted today: https://news.ycombinator.com/item?id=46556210