In the nineteenth century, the calendar for the year 1856 was reused from an earlier year. Which of the following earlier years has exactly the same calendar as 1856?

Introduction / Context:
Historical calendar questions sometimes ask which earlier year shares the same calendar as a given year. Here we are told that the calendar used again in 1856 matched some previous year. We must decide which of the listed earlier years has exactly the same layout of days and dates as 1856.

Given Data / Assumptions:
- Reference year for reuse = 1856. - Candidate earlier years = 1828, 1850, 1830, 1852. - We work under the Gregorian calendar rules. - Leap year rule: divisible by 4, except century years must also be divisible by 400.

Concept / Approach:
To share the same calendar, two years must both be leap years or both be normal years and they must start on the same weekday. 1856 is a leap year, so only earlier leap years can be candidates. After identifying which candidates are leap years, we consider the cumulative shift in weekdays between each candidate and 1856. When that shift is a multiple of 7 days, the starting weekdays match, and the calendars align exactly.

Step-by-Step Solution:
Step 1: Confirm that 1856 is a leap year. Since it is divisible by 4 and not a century year, 1856 is indeed a leap year. Step 2: Check leap year status of candidate years: - 1828 is divisible by 4 and not a century year, so it is a leap year. - 1850 is not divisible by 4, so it is a normal year. - 1830 is not divisible by 4, so it is a normal year. - 1852 is divisible by 4 and not a century year, so it is a leap year. Step 3: Only 1828 and 1852 are leap years. 1850 and 1830 are eliminated immediately. Step 4: To match calendar, the starting weekday must be the same. Consider the shift from 1828 up to 1856. This interval contains an integer number of years over which weekday shifts from leap and normal years combine. Step 5: The accumulated weekday shift from 1828 to 1856 is a multiple of 7 days, which means both years start on the same weekday. Step 6: By contrast, when we compute the shifts from 1852 to 1856, we do not end up with a multiple of 7 days, so their calendars differ. Step 7: Therefore 1828 is the earlier year whose calendar was reused in 1856.

Verification / Alternative check:
You can confirm this using a standard day of week calculation for 1 January 1828 and 1 January 1856. Both dates fall on the same weekday, and both years are leap years, so February has 29 days in each case and all months line up perfectly. Checking a few months side by side confirms that every date corresponds to the same weekday.

Why Other Options Are Wrong:
- 1850 and 1830 are not leap years, so their February length and subsequent month layouts differ from 1856. - 1852, while a leap year, does not have its 1 January on the same weekday as 1856, so the calendars are not identical. - Any difference in starting weekday or leap year status prevents full calendar reuse.

Common Pitfalls:
Learners may only look for the nearest leap year such as 1852 without checking the weekday alignment. Others may misapply leap year rules or forget that century corrections can alter long term repetition cycles. For safe results, always verify both leap status and starting weekday before concluding that two years share a calendar.

Final Answer:
The calendar used again in 1856 was the calendar of 1828.