Calendar – Offset across years: Given that January 16, 1997 was a Thursday, what day of the week was January 4, 2000?

Introduction / Context:
We have one fixed weekday (Jan 16, 1997 = Thursday) and must find the weekday for a later date (Jan 4, 2000). We step through whole years and partial months counting leap days to compute the weekday shift.

Given Data / Assumptions:

• Jan 16, 1997 = Thursday.
• Find weekday for Jan 4, 2000.
• 1997 and 1999 are common years; 1998 is common; 2000 is a leap year.

Concept / Approach:
Weekday progression advances by +1 per common year and +2 per leap year when comparing same dates. We also adjust for partial-month offsets where needed.

Step-by-Step Solution:
1) From Jan 16, 1997 (Thu) to Jan 16, 1998: +1 weekday (common year) → Friday.2) Jan 16, 1998 to Jan 16, 1999: +1 → Saturday.3) Jan 16, 1999 to Jan 16, 2000: +1 (1999 is common) → Sunday. 2000 is leap but Feb 29, 2000 lies after January, so no Jan-shift from leap day yet.4) Now move back from Jan 16, 2000 (Sunday) to Jan 4, 2000: 12 days earlier → Sunday − 12 ≡ Tuesday.

Verification / Alternative check:
Direct calculation via a congruence (or a calendar reference) confirms Jan 4, 2000 is Tuesday.

Why Other Options Are Wrong:
Thursday, Wednesday, Friday → do not match the computed weekday shift.

Common Pitfalls:
Miscounting leap-day effects in early months of a leap year (Feb 29 comes after January).

Final Answer:
Tuesday