The last day of a century year (e.g., 1800, 1900, 2000) cannot be which weekdays?

Introduction / Context:
Century years (multiples of 100) have special day-of-week behavior due to the number of “odd days” accumulated over 100 years in the Gregorian calendar.

Given Data / Assumptions:

• Options list: I. Tuesday, II. Thursday, III. Saturday, IV. Sunday.
• We refer to the last day (December 31) of a century year.

Concept / Approach:
In the Gregorian calendar, the last day of a century year can only fall on Monday, Wednesday, Friday, or Sunday. Therefore, it cannot be Tuesday, Thursday, or Saturday.

Step-by-Step Solution:
Known results from odd-day analysis across centuries show the last day of century years excludes Tue/Thu/Sat.Thus the set of impossible weekdays = I, II, III.

Verification / Alternative check:
Check examples: 1900-12-31 was Monday; 2000-12-31 was Sunday. These align with the allowed set, not with Tue/Thu/Sat.

Why Other Options Are Wrong:
Any set including IV (Sunday) is incorrect because Sunday is possible (e.g., year 2000).

Common Pitfalls:
Confusing “first day” vs “last day,” and mixing Julian/Gregorian rules.

Final Answer:
I, II and III