The last day of a century cannot be

The last day of a century can never be Tuesday.

Odd days at a century's end follow a fixed cycle: 100 years give 5, 200 give 3, 300 give 1, 400 give 0.

These remainders 5, 3, 1, 0 correspond to Friday, Wednesday, Monday and Sunday.

So 31 December of any century is only Friday, Wednesday, Monday or Sunday.

Tuesday never appears in this set.