100 years contain 5 odd days.

$\therefore$ Last day of 1^st century is Friday.

200 years contain 5 x 2 $\equiv$ 3 odd days.

$\therefore$ Last day of 2^nd century is Wednesday.

300 years contain 5 x 3 = 15 $\equiv$ 1 odd day.

$\therefore$ Last day of 3^rd century is Monday.

400 years contain 0 odd day.

$\therefore$ Last day of 4^th century is Sunday.

This cycle is repeated.

$\therefore$ Last day of a century cannot be Tuesday or Thursday or Saturday.