In the Gregorian calendar, the last day of a century (such as 31st December 1900, 2000, etc.) can fall only on certain weekdays. Which of the following days of the week can never be the last day of a century?

Introduction / Context:
This question is about deeper properties of the Gregorian calendar. It asks which weekday cannot occur as the last day of a century. Centuries correspond to years like 100, 200, 300, 400, 500, … and so on, and their last days follow a repeating pattern because of how leap years are distributed.

Given Data / Assumptions:
• We work with the Gregorian calendar rules.• Century years are multiples of 100.• A year is a leap year if it is divisible by 4 but not by 100, unless it is divisible by 400.• We consider the weekday of the last day of such century years.

Concept / Approach:
Using odd-days analysis, every 400 years the calendar pattern repeats. In a span of 400 years, only certain weekdays occur as the last day of century years (100, 200, 300, 400). By calculating the odd days contributed by each block of 100 years, we can determine which weekdays are possible and which are not.

It can be shown that the last days of centuries can only be Sunday, Friday, Wednesday, or Monday. Therefore, weekdays like Tuesday, Thursday, and Saturday can never be the last day of a century year.

High-Level Calculation Idea:
• Each 100-year block contributes 5 odd days.• Starting from a known reference, the weekdays of century ends cycle through a limited set.• This cycle excludes Tuesday, Thursday, and Saturday from ever appearing as last days of centuries.

Why the Correct Option Fits:
Among the options given (Monday, Wednesday, Tuesday, Friday), only Tuesday is in the set of impossible days (Tuesday, Thursday, Saturday). Monday, Wednesday, and Friday are all possible last days of certain centuries.

Common Pitfalls:
Many candidates try to guess based on intuition or think that any day is possible. Others mis-handle leap-year rules for century years, especially the special case of years divisible by 400. Knowing or deriving the standard result that the last day of a century cannot be Tuesday, Thursday, or Saturday is the key.

Final Answer:
The last day of a century can never be a Tuesday.