Calendar questions are solved with odd days: the number of days left over after complete weeks.
1Odd days
Ordinary year = 365 days = 1 odd day; leap year = 366 days = 2 odd days
100 years = 5 odd days, 200 years = 3, 300 years = 1, 400 years = 0
Odd days → weekday: 0 Sunday, 1 Monday, 2 Tuesday, 3 Wednesday, 4 Thursday, 5 Friday, 6 Saturday
2Leap years
Divisible by 4 but not by 100, or divisible by 400 (2000 was a leap year; 1900 was not)
3Months
Odd days: Jan 3, Feb 0 (1 in a leap year), Mar 3, Apr 2, May 3, Jun 2, Jul 3, Aug 3, Sep 2, Oct 3, Nov 2, Dec 3