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