The last day of a century cannot be Tuesday, Thursday, or Saturday.

Explanation:

1. A century (100 years) consists of exactly 36,524 days (including 24 leap years).

2. 36,524 days is exactly 5217 weeks and 1 extra day (since 36,524 ÷ 7 = 5217 remainder 1).

3. This means that if a century starts on a particular day, it will always end on the next day’s weekday (since there is 1 extra day).

Now, let’s check:

For 1600, the last day was Sunday → 1700 ended on Monday

For 1700, the last day was Monday → 1800 ended on Wednesday

For 1800, the last day was Wednesday → 1900 ended on Friday

For 1900, the last day was Friday → 2000 ended on Sunday

For 2000, the last day was Sunday → 2100 will end on Monday

Thus, the last day of a century can only be Monday, Wednesday, Friday, or Sunday, meaning it can never be Tuesday, Thursday, or Saturday.