In the same calendar year, which two months definitely share the same calendar (same weekdays on the same dates)?

Introduction / Context:
Two months have “the same calendar” if every date in one month falls on the same weekday as the corresponding date in the other month (e.g., the 1st is the same weekday in both, the 2nd is the same weekday in both, etc.).

Given Data / Assumptions:

• We consider a single year (either leap or non-leap).
• We seek a pair that always matches within that same year.

Concept / Approach:
Shifts between month start weekdays equal (days in month) mod 7. The total shift from March to November sums to 21 days (mod 7 = 0) regardless of leap status because February has already passed and does not affect the March→November spacing.

Step-by-Step Solution:
Month length shifts (Mar→Nov): Mar(31)=+3, Apr(30)=+2, May(31)=+3, Jun(30)=+2, Jul(31)=+3, Aug(31)=+3, Sep(30)=+2, Oct(31)=+3.Total shift = 3+2+3+2+3+3+2+3 = 21 ≡ 0 (mod 7).Therefore, March and November always start on the same weekday and share the same date–weekday pattern.

Verification / Alternative check:
Test with sample years (leap and non-leap) and observe that March 1 and November 1 align on the same weekday.

Why Other Options Are Wrong:
January–August and January–October depend on whether the year is leap or not (February changes the offset), so they are not guaranteed every year.

Common Pitfalls:
Assuming “pairs” like Jan–Oct always match without considering February's 28/29 days.

Final Answer:
March and November