the last day of the century cannot be

The last day of a century cannot be Tuesday, Thursday, or Saturday. This is because in 100 years (a century), the total number of odd days is 5. The last day of each century cycles through Friday, Wednesday, Monday, and Sunday, respectively, for the 1st, 2nd, 3rd, and 4th centuries, and then the pattern repeats. Therefore, the last day of a century cannot fall on Tuesday, Thursday, or Saturday.