Explanation:
To understand why the last day of a century cannot be Tuesday, we need to understand the concept of leap years and century years.

- A leap year is a year that is divisible by 4, except for century years that are not divisible by 400. For example, 2000 was a leap year because it is divisible by 4 and 400, but 1900 was not a leap year because it is divisible by 4 but not by 100.

- Century years are years that end in 00. For example, 1900, 2000, and 2100 are all century years.

Now let's consider the last day of a century. The last day of a century is always a year that ends in 00. For example, the last day of the 20th century was December 31, 2000. To determine which day of the week this was, we need to know the day of the week for January 1, 2000, which was a Saturday. We can then count the number of days between January 1, 2000, and December 31, 2000, which is 365 - 1 (because 2000 was a leap year) = 364 days. Since 364 is divisible by 7, we know that December 31, 2000, was also a Saturday.

Now let's consider why the last day of a century cannot be Tuesday. If the last day of a century were a Tuesday, then January 1 of the following year (which is the first day of the next century) would be a Wednesday. This means that the year in question (the last year of the previous century) would be a leap year. However, a century year is only a leap year if it is divisible by 400, and the year in question is not divisible by 400. Therefore, the last day of a century cannot be Tuesday.

In summary, the last day of a century cannot be Tuesday because it would require the previous year to be a leap year, which is not possible for a century year that is not divisible by 400.