In calendar calculations, the calendar of the year 1897 will repeat exactly (same weekdays on the same dates) in which of the following future years?

Introduction / Context:
A common type of calendar aptitude question asks in which later year an earlier year’s calendar will repeat exactly. Two years have the same calendar if both are either leap years or non-leap years and if the weekday pattern for all dates matches. Here, we must find which year shares the same calendar as 1897.

Given Data / Assumptions:

Year in question: 1897 (a common, non-leap year).
Candidate years: 1901, 1903, 1908, 1926.
A year repeats a calendar if:
- It has the same leap/non-leap status, and
- The total day shift from 1 January 1897 to 1 January of that year is a multiple of 7.
We use the Gregorian leap-year rule (multiples of 4, excluding centuries not divisible by 400).

Concept / Approach:
Each ordinary year shifts the starting weekday of the next year by 1 day; each leap year shifts it by 2 days. The total shift in weekdays between 1897 and a later year Y is:
Shift = (number of common years) * 1 + (number of leap years) * 2 (mod 7). If this shift is 0 (mod 7) and both years are non-leap, the calendars match.

Step-by-Step Solution:
Step 1: Note that 1897 is not divisible by 4, so it is a non-leap year. Step 2: Count leap years between 1897 and 1926. Leap years in this interval (excluding 1900 as it is not a leap year) are: 1904, 1908, 1912, 1916, 1920, 1924. Number of leap years = 6. Step 3: Count total years from 1897 up to 1926. Total years = 1926 - 1897 = 29. Step 4: Compute the total weekday shift. Common years = 29 - 6 = 23. Shift = 23 * 1 + 6 * 2 = 23 + 12 = 35 days. Since 35 mod 7 = 0, the weekday cycle returns to the same starting day. Step 5: Confirm year type. 1926 is not divisible by 4, so it is also a non-leap year, matching 1897.

Verification / Alternative check:
You can also rule out the other options quickly. For 1901 and 1903, fewer years have passed, and the cumulative shift is not a multiple of 7. For 1908, the shift still does not come back to 0 mod 7. Only by 1926 does the total shift equal exactly 35 days, which is 5 full weeks, ensuring the same pattern of weekdays.

Why Other Options Are Wrong:
1901 and 1903 are non-leap years but do not produce a total shift that is a multiple of 7 days, so their 1 January weekdays differ from that of 1897.
1908 is a leap year, while 1897 is not, so their calendars can never be identical even if the weekday shift matched.

Common Pitfalls:
Learners often assume the calendar repeats every 11 or 28 years without checking for leap-year adjustments. Another common error is incorrectly counting 1900 as a leap year; it is not, because it is divisible by 100 but not by 400. Always apply the Gregorian rule carefully.

Final Answer:
The year with the same calendar as 1897 is 1926.