The last day of a century cannot be

∴ 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.