Century starts — Which weekdays can a century year (…00) NOT start on?

Difficulty: Medium

Correct Answer: None of these

Explanation:


Introduction / Context:
Not all weekdays are possible for 1 January of a century year. Under Gregorian rules, century starts occur only on a subset of weekdays.


Given Data / Assumptions:

  • Consider years …, 1700, 1800, 1900, 2000, 2100, …
  • We examine which weekdays are attainable on 1 January of those years.


Concept / Approach:
Empirical (and theoretical) analysis shows that century years start only on Monday, Wednesday, Friday, or Saturday.


Step-by-Step Solution:

1) Known examples: 1900 began on Monday; 2000 on Saturday; 2100 on Friday; 1800 on Wednesday.2) Therefore, the possible set is {Monday, Wednesday, Friday, Saturday}.3) The complements (Tuesday, Thursday, Sunday) are not possible.


Verification / Alternative check:
Apply 100-year weekday shifts (+5, +6) and cycle through samples to see the attainable set.


Why Other Options Are Wrong:

  • Options A–C include weekdays that actually can occur (e.g., Wednesday, Friday, Saturday). Hence none of those groupings are correct.


Common Pitfalls:

  • Mistyping “Sunday” as “Sunady.”
  • Assuming any weekday is possible.


Final Answer:
None of these

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