The calendar for the year 1939 is to be matched with another year so that all dates fall on the same days of the week. The options below give four different years. For which one of these years is the calendar exactly the same as that of 1939?

Introduction / Context:
Same calendar year questions appear frequently in aptitude exams. Two years have the same calendar when the days of the week align for all dates, which means that 1 January falls on the same weekday and the leap year pattern is also the same. This problem asks which of the given years shares the same calendar as 1939.

Given Data / Assumptions:
- Reference year = 1939. - Candidate years = 1943, 1964, 1950, 1956. - We use the Gregorian calendar rules. - A non leap year has 365 days, a leap year has 366 days. - Every normal year shifts the starting weekday of the next year by 1 day, and every leap year shifts it by 2 days.

Concept / Approach:
To have the same calendar as 1939, the target year must satisfy two conditions. First, both years must be either leap years or non leap years. Second, the total shift in weekdays from 1939 to the candidate year must be a multiple of 7 days so that 1 January falls on the same weekday again. We check each candidate by counting leap years and normal years in between and computing the total day shift modulo 7.

Step-by-Step Solution:
Step 1: Determine whether 1939 is a leap year. It is not divisible by 4, so 1939 is a non leap year. Step 2: Check each candidate year type: - 1943: non leap year. - 1964: leap year because 1964 is divisible by 4 and not a century year. - 1950: non leap year. - 1956: leap year. Step 3: Only non leap years can match 1939, so 1943 and 1950 remain possible; 1964 and 1956 are eliminated. Step 4: Find number of years between 1939 and 1950: 11 years. Step 5: Count leap years between 1939 and 1949 inclusive of endpoints only where applicable: 1940, 1944, 1948 are leap years, so there are 3 leap years and 8 normal years. Step 6: Total day shift from 1 January 1939 to 1 January 1950 = 8 normal years * 1 day + 3 leap years * 2 days = 8 + 6 = 14 days. Step 7: Since 14 mod 7 = 0, the weekday of 1 January repeats in 1950. Step 8: Similar checks show that the total shift from 1939 to 1943 is not a multiple of 7, so 1943 calendar does not match.

Verification / Alternative check:
You can cross check by writing down the day change year by year. Starting from 1939, go to 1940 with a shift of 1, then to 1941 with an extra 2 (since 1940 is leap), and so on until 1950. Adding all shifts gives 14, a perfect multiple of 7. Hence 1950 must start on the same weekday as 1939 and both are non leap years, so month day layouts are identical.

Why Other Options Are Wrong:
- 1964 and 1956 are leap years, so their February pattern is different from 1939 and cannot give the same calendar. - 1943 is a non leap year, but the cumulative day shift from 1939 to 1943 is not divisible by 7, so 1 January does not fall on the same weekday. - Any extra year not meeting both conditions will change the weekday layout of many dates.

Common Pitfalls:
Many learners only compare leap year or non leap year status and forget about the weekday of 1 January. Others do not count leap years correctly in the interval. Also, some assume that the pattern repeats every 28 years without considering century corrections. For exam questions, following the day shift method between the given years is usually safest.

Final Answer:
The year that has exactly the same calendar as 1939 is 1950.