If January 5, 1965 was a Tuesday, in which year will January 5 again fall on a Tuesday?

Introduction / Context:
Weekdays shift by +1 day after a common year and by +2 after a leap year (for dates not before 29 February). We seek the next year when January 5 returns to Tuesday.

Given Data / Assumptions:

• Jan 5, 1965 = Tuesday.
• Leap years between 1965 and 1974: 1968, 1972.

Concept / Approach:
Accumulate weekday shifts year by year: +1 for common years, +2 for leap years, until net shift is a multiple of 7.

Step-by-Step Solution:
1965→1966: +1 (common) → total +1.1966→1967: +1 → total +2.1967→1968: +1 → total +3.1968→1969: +2 (leap) → total +5.1969→1970: +1 → total +6.1970→1971: +1 → total +7 ≡ 0 mod 7.Thus Jan 5, 1971 is Tuesday.

Verification / Alternative check:
Counting weekdays with a known calendar or modular arithmetic yields the same result.

Why Other Options Are Wrong:
1970 is +6 days (Monday), 1973 and 1974 land on other weekdays given intervening leap shifts.

Common Pitfalls:
Forgetting that leap years add +2 when the target date is after February 28; stopping at +6 instead of reaching +7.

Final Answer:
January 5, 1971