Calendar Practice Questions

A century year is a leap year only if divisible by 400. 800, 1200 and 2000 are divisible by 400; 700 is not, so 700 is not a leap year.

Leap years normally come every 4 years, but a century year not divisible by 400 is skipped (e.g. 1900). So 1896 → 1904 is a gap of 8 years, the maximum possible.

Count odd days up to 25 Jan 1975: 1600 years → 0 odd days (every 400 years has 0 odd days); next 300 years → 1 odd day(s) (100 yrs = 5, 200 yrs = 3, 300 yrs = 1); next 74 years (1901–1974): 18 leap + 56 ordinary = 36 + 56 = 92 days → 1 odd day(s); in 1975 (ordinary year): 25 days of Jan → 25 days → 4 odd day(s). Total odd days = 118 → 118 mod 7 = 6. Since 0 = Sunday, 1 = Monday, …, 6 = Saturday, the day is Saturday.

x weeks = 7x days. Adding x days gives 7x + x = 8x days.

100 years have 5 odd days, so the last day of the 1st century is Friday. 200 years → 10 → 3 odd days → Wednesday; 300 years → 15 → 1 odd day → Monday; 400 years → 0 odd days → Sunday. The cycle then repeats, so the last day of a century can only be Friday, Wednesday, Monday or Sunday — never Tuesday, Thursday or Saturday.