The calendar used in the year 1856 repeats exactly which one of the following earlier years?

Introduction / Context:
This question asks which earlier year has exactly the same calendar as 1856. In other words, we must identify a previous year in which all dates fall on the same weekdays as in 1856. Such questions help you practise identifying calendar repetitions and applying leap-year rules.

Given Data / Assumptions:

• Reference year: 1856.
• Candidate years: 1828, 1850, 1830, 1852, 1840.
• We need the year whose calendar repeats in 1856.
• Leap-year rules for the Gregorian calendar apply: year divisible by 4 is a leap year, unless it is a century year not divisible by 400.

Concept / Approach:
Two years share the same calendar if:

• They are both leap years or both ordinary years.
• The weekday of 1st January is identical in both years.
• The cumulative odd days between them are a multiple of 7.

First, we check whether 1856 is a leap year. As 1856 is divisible by 4 and not a century year, it is a leap year. Therefore, the matching earlier year must also be a leap year with the same weekday pattern.

Step-by-Step Solution:
Step 1: Determine whether 1856 is a leap year. Since 1856 mod 4 = 0 and it is not a century year, it is a leap year. Step 2: Among the options, identify leap years: 1828, 1830 (not divisible by 4), 1850, 1852, and 1840. Of these, 1828, 1840, and 1852 are leap years. Step 3: Now we must determine which leap year has the same 1st January weekday as 1856, meaning the total odd days between the two years is a multiple of 7. Step 4: Detailed calendar analysis or standard references show that the calendar of 1828 repeats exactly in 1856, giving identical weekdays for all dates. Step 5: The other leap years (1840 and 1852) do not meet the exact odd-day alignment condition when checked, so their calendars do not match 1856 month by month.

Verification / Alternative check:
A precise verification can be made by comparing the weekday of 1st January and the layout of each month in 1828 and 1856 using a perpetual calendar or trusted date-calculation tools. When this is done, both years are found to have identical calendars, confirming that 1828 is the correct matching year. Similar checks for 1840 or 1852 show mismatches in weekday alignment for various dates.

Why Other Options Are Wrong:
1850: This year is not a leap year, so it cannot share the same leap-year calendar pattern as 1856.

1830: Also an ordinary year, not divisible by 4, so its calendar differs from that of the leap year 1856.

1852: Although a leap year, the total odd days between 1852 and 1856 do not sum to a multiple of 7, leading to mismatched weekdays.

1840: Another leap year, but the alignment of weekdays and month starts is different from 1856 when checked.

Common Pitfalls:
One common error is to think that any leap year separated by a fixed interval (for example, 28 years) will always share the same calendar; however, the presence of century years and the exact number of leap years in between can break this pattern. Another mistake is to ignore the leap-year status and only look at numeric similarity in years. Always check both the leap-year property and the accumulated odd days when determining calendar repetition.

Final Answer:
The calendar used in the year 1856 repeats the calendar of 1828.