The calendar for the year 2003 will be repeated in which one of the following years?

Introduction / Context:
This question is another example of calendar repetition. You are asked to find the next year after 2003 that has an identical calendar, meaning all dates fall on the same weekdays. This requires you to consider both leap-year patterns and weekday shifts over a span of years.

Given Data / Assumptions:

• Reference year: 2003.
• We must find a later year with exactly the same calendar.
• Options include: 2024, 2014, 2009, 2020, 2010.
• We use Gregorian leap year rules.

Concept / Approach:
Two conditions must be satisfied for two years to share the same calendar:

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

A non-leap year typically repeats its calendar after 6 or 11 years, depending on how leap years are positioned in between, and fully stabilises in a 28-year cycle.

Step-by-Step Solution:
Step 1: Identify the type of 2003. It is not divisible by 4, so it is a non-leap year.Step 2: A matching year must also be a non-leap year.Step 3: The next candidate years in the list are 2009, 2010, 2014, 2020 and 2024. Among these, 2009 and 2010 are non-leap; 2014 is also non-leap; 2020 and 2024 are leap years (divisible by 4).Step 4: We also need the same starting weekday. For non-leap years, after a non-leap year the weekday of 1 January shifts by +1, and after a leap year it shifts by +2.Step 5: If you track the weekday shifts or consult a year–calendar table, you find that 1 January 2014 falls on the same weekday as 1 January 2003 and that both years are non-leap years.Step 6: Therefore, 2014 is the first year after 2003 that has an identical calendar to 2003.

Verification / Alternative check:
A more concrete verification can be done by counting shifts: from 2003 to 2014 you have a specific combination of leap and non-leap years that results in a net shift that is a multiple of 7 days, restoring the weekday alignment. Checking key dates (for example, whether 1 March or 1 October fall on the same weekdays in both years) confirms that the calendars indeed match.

Why Other Options Are Wrong:
2024 and 2020 are leap years and cannot share a calendar with the non-leap year 2003. 2009 and 2010 are non-leap years but do not align in weekday pattern with 2003. Only 2014 satisfies both the non-leap condition and the correct weekday alignment.

Common Pitfalls:

• Assuming that any year that is a multiple of 7 years ahead must have the same calendar, which ignores leap-year effects.
• Matching only leap vs. non-leap status and forgetting about the starting weekday.
• Trying to perform year-by-year counting of days without a systematic or tabular approach.

Final Answer:
The calendar for 2003 is repeated in the year 2014.