The last day of a century cannot be:

100 years contain 5 odd days. So, last day of 1st century is 'Friday'

200 years contain (5×2)=10 odd days =3 odd days. So, last day of 2nd century is 'Wednesday'.

300 years contain (5×3)=15 odd days =1 odd day. So, last day of 3rd century is 'Monday'.

400 years contain 6 odd days. So, last day of 4th century is 'Saturday'

Since the order is continually kept in successive cycles, we see that the last day of a century cannot be Tuesday, Thursday or Saturday.