Year-end weekday – If Friday is the first day of a non-leap year, what day of the week is the last day of that same year?

Introduction / Context:This problem asks for the weekday of the year's last date, given the weekday of the first date in a non-leap year. The key fact is that a non-leap year has 365 days, and weekdays advance by one day per 1-day increment, cycling modulo 7.

Given Data / Assumptions:

• Non-leap year length = 365 days.
• Day 1 (Jan 1) = Friday.
• Day n has weekday shift of (n − 1) mod 7 from Day 1.

Concept / Approach:The last day is day 365. Its shift relative to day 1 is 365 − 1 = 364 days. Because 364 is a multiple of 7 (52 × 7), the weekday does not change compared to day 1.

Step-by-Step Solution:

Verification / Alternative check:Another way: In a non-leap year, the first day of the next year is one weekday ahead (since 365 ≡ 1 mod 7). Therefore, the last day of the current year is the same as the first day. With Jan 1 = Friday, Dec 31 = Friday.

Why Other Options Are Wrong:

• Sunday/Monday/Tuesday: These reflect offsets of +2, +3, +4 from Friday, which do not apply to a non-leap year's last day.
• None of these: The correct weekday (Friday) is listed.

Common Pitfalls:Confusing leap vs non-leap logic. In a leap year (366 days), the last day would be Saturday if the first day were Friday (because 365 mod 7 = 1). Here, with 365 days, there is no shift.

Final Answer:Friday