For which of the following years does the calendar of the year 1939 repeat exactly, that is, dates and days of the week match for all twelve months?

Introduction / Context:
This question asks you to determine another year whose calendar is identical to that of 1939. Two years share the same calendar if the pattern of weekdays for all dates matches exactly, month by month. This is an advanced calendar concept that combines understanding of leap years, ordinary years, and the way weekdays shift from year to year.

Given Data / Assumptions:

• The reference year is 1939.
• Candidate years are 1943, 1964, 1950, and 1956.
• We use Gregorian leap year rules.
• We need to find which candidate year has the same calendar structure as 1939.

Concept / Approach:
Two years have the same calendar when they are both either leap years or ordinary years and when the weekday of 1 January is the same for both years. Over time, calendar patterns repeat after certain cycles, influenced by the number of leap years between two years. To solve this in an exam setting, we focus on whether candidate years have the same leap year status and the correct total day shift modulo 7 relative to 1939.

Step-by-Step Solution:
Step 1: Determine whether 1939 is a leap year. It is not divisible by 4, so 1939 is an ordinary year with 365 days. Step 2: Any year that shares the calendar with 1939 must also be an ordinary year, not a leap year. Step 3: Examine the options. Among 1943, 1964, 1950, and 1956, the leap year status and starting weekdays must be checked. Step 4: Using known calendar tables or systematic counting of years and leap years, 1950 turns out to match the same weekday alignment as 1939 for all months. Step 5: The other options either differ in leap year status or their 1 January weekday does not align, so their calendars do not match 1939.

Verification / Alternative check:
You can verify this by noting that 1939 and 1950 are both ordinary years and that the total number of leap years between them leads to a net shift in weekdays that is a multiple of 7 days. When the total shift in days between 1 January 1939 and 1 January 1950 produces an integer multiple of 7, the weekdays for all dates realign. If you compare month by month calendars for 1939 and 1950 in a calendar table, you find that each date falls on the same weekday, confirming that they share identical calendars.

Why Other Options Are Wrong:
1943 does not have the same starting weekday and thus its calendar pattern is shifted. 1964 is a leap year, whereas 1939 is not, so their February months do not match and thus the entire calendar cannot be identical. Similarly, 1956 is also a leap year, which again breaks the alignment of dates and weekdays. Therefore, these years cannot share the exact same calendar as 1939.

Common Pitfalls:
Candidates sometimes assume that years separated by 7, 14, or 21 years always have the same calendar, without checking leap year effects. That is not always true, because the extra day in leap years can disrupt the pattern. Another mistake is ignoring century rules or misapplying the leap year test. When dealing with calendar repetition questions, always check both year type and the total day shift modulo 7, or lean on reliable calendar equivalence tables when available.

Final Answer:
Hence, the year with the same calendar as 1939 is 1950.