The calendar for the year 2024 will be exactly repeated in which one of the following future years?

Introduction / Context:
This problem tests knowledge of how and when calendars repeat. A year's calendar is determined by two key features: whether it is a leap year or a non-leap year, and on which day of the week 1 January falls. The question asks when the entire calendar of 2024 will be reused, a common type of reasoning in calendar aptitude questions.

Given Data / Assumptions:

• We are considering the year 2024.
• We want a future year whose calendar is identical to that of 2024.
• A calendar is identical if dates and days of the week line up exactly for all 12 months.
• We assume the standard Gregorian calendar rules.

Concept / Approach:
A calendar repeats when:

• The year type (leap or non-leap) is the same.
• The year starts on the same day of the week (same weekday for 1 January).

Under the Gregorian system, leap years generally repeat their calendars every 28 years, except around century years not divisible by 400. Since 2024 is a leap year and not near such an exception, its calendar will typically repeat after 28 years.

Step-by-Step Solution:
Step 1: Check whether 2024 is a leap year. Since 2024 is divisible by 4 and not a century year, it is a leap year.Step 2: For an ordinary leap year, the calendar usually repeats after 28 years (a 28-year cycle where leap year positions and weekday shifts realign).Step 3: Add 28 years to 2024: 2024 + 28 = 2052.Step 4: Year 2052 is also divisible by 4 and not a century year, so it is a leap year, matching the leap status of 2024.Step 5: Because the 28-year cycle has completed, 1 January 2052 falls on the same day of the week as 1 January 2024, giving the same calendar.

Verification / Alternative check:
Between 2024 and 2052, weekday shifts caused by 24 non-leap years (+24 days) and 4 leap years (+8 days) total 32 days. Since 32 mod 7 = 4, we need a whole number of 7-day cycles to return to the same weekday alignment while keeping leap-year positions fixed. The known 28-year rule for such leap years ensures that 2052 is the first repeat year, which aligns with standard calendar tables.

Why Other Options Are Wrong:
2030 and 2036 are too close; they do not complete the full leap-year alignment cycle. 2048, while 24 years ahead, does not reset the day-of-week pattern for all months. 2060 is beyond the first repeat and would not be the immediate next matching calendar.

Common Pitfalls:

• Assuming calendars repeat every 4 years for leap years, which is not always true.
• Ignoring the requirement that both the year type and the weekday of 1 January must match.
• Not being aware of the 28-year calendar cycle for ordinary leap years.

Final Answer:
The calendar for the year 2024 will be repeated in the year 2052.