Calendar

This is a method used by professionals according to World Mental Calculation. Yes, the method is also from there.

So we have our date.

We have 4 parts we can split it into.
The century,
the year,
the month, and
the day.

For the century,
mod 4 = 0: +2
mod 4 = 1: +0
mod 4 = 2: +5
mod 4 = 3: +3.

For the year,
+ floor(5*year/4) mod 7.

For the month (yes you will have to memorize all this),
Jan: +4
Feb: +0
Mar: +0
Apr: +3
May: +5
Jun: +1
Jul: +3
Aug: +6
Sep: +2
Oct: +4
Nov: +0
Dec: +2.

For the day,
+ day mod 7.

And finally,
- 1 if the year is leap and the month is Jan/Feb.

Do all that, and then
0 = Sun
1 = Mon
2 = Tue
3 = Wed
4 = Thu
5 = Fri
6 = Sat

If you want to go further, you can:
- adjust the century values and then cancel it off with new year values,
- memorize the value for every year,
- memorize the values for all the 366 days of the year.

And that's it!

Example solve: 1644-08-29
16 mod 4 = 0 so +2
44*.8 = 55 mod 7 = +6
Aug = +6
29 mod 7 = +1
-1: no

-> In the end we get that this day was a Monday.