The calendar for the year 1897 will be repeated in which one of the following years?

Introduction / Context:
This question asks when the calendar of a given year (1897) will repeat. Knowing when calendars repeat is useful in mental calendar problems and relies on understanding the roles of leap years and weekday shifts between years.

Given Data / Assumptions:

• Reference year: 1897.
• We need a future year whose calendar (dates vs. weekdays) is identical to 1897.
• Candidate years: 1908, 1901, 1903, 1926, 1915.
• We use Gregorian leap year rules.

Concept / Approach:
Two conditions must be satisfied for calendars to match exactly:

• Both years must be of the same type: either both leap years or both non-leap years.
• The weekday of 1 January must be the same in both years.

For non-leap years, the calendar typically repeats after a sequence of shifts totaling a multiple of 7 days, often after 6, 11 or 28 years depending on intervening leap years.

Step-by-Step Solution:
Step 1: Determine the type of 1897. It is not divisible by 4, so 1897 is a non-leap year.Step 2: Any matching year must also be a non-leap year. Check options: 1901, 1903, 1915 and 1926 are non-leap; 1908 is divisible by 4 and is a leap year, so it can be ruled out.Step 3: For a non-leap year, each following non-leap year shifts the starting weekday by +1, while each leap year shifts it by +2. We look for a year where the total shift from 1897 is a multiple of 7 days, bringing the weekday pattern back to the original.Step 4: Instead of doing detailed year-by-year counting in an exam, you can remember or derive that the calendar of 1897 repeats in 1926, which is 29 years later, after a combined pattern of leap and non-leap years produces a total shift that is a multiple of 7.Step 5: 1926 is also a non-leap year, satisfying the same-year-type condition.Step 6: Therefore, 1926 is the first option in the list that has the same calendar as 1897.

Verification / Alternative check:
For deeper verification, one can consult or mentally reconstruct a calendar: 1 January 1897 and 1 January 1926 both fall on the same weekday, and both years are non-leap. Checking some key dates (for example, the weekdays of a few fixed dates such as 1 March or 31 August) confirms that all months line up in exactly the same way.

Why Other Options Are Wrong:
1908 is a leap year, so it cannot match a non-leap year calendar. 1901 and 1903 are too close to 1897 and do not satisfy the required accumulated weekday shift. 1915 also does not align correctly in weekday pattern with 1897. Only 1926 satisfies both the non-leap condition and the full weekday alignment.

Common Pitfalls:

• Assuming calendars repeat every 11 years or 28 years without checking leap-year positions.
• Ignoring the leap vs. non-leap distinction and matching only the starting weekday.
• Trying to perform detailed counting of days under exam pressure without a systematic method.

Final Answer:
The calendar for 1897 will be repeated in the year 1926.