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.