The last day of a century cannot be

100 years contain 5 odd days.
∴ Last day of 1^st century is Friday.
200 years contain (5 x 2) ≡ 3 odd days.
∴ Last day of 2^nd century is Wednesday.
300 years contain (5 x 3) = 15 ≡ 1 odd day.
∴ Last day of 3^rd century is Monday.
400 years contain 0 odd day.
∴ Last day of 4^th century is Sunday.
This cycle is repeated.
∴ Last day of a century cannot be Tuesday or Thursday or Saturday.