For purposes of calendar repetition, which is the next year after 2003 that has exactly the same calendar (same weekdays on the same dates) as the year 2003?

Introduction / Context:
Some aptitude questions ask about when a calendar year repeats exactly, meaning every date falls on the same weekday as in the original year. Two years have the same calendar if they are both leap years or both common years and if the total weekday shift between them is a multiple of 7 days.

Given Data / Assumptions:

Base year: 2003.
We are asked for the next year after 2003 that has the same calendar.
Options: 2024, 2014, 2009, 2020.
Leap-year rule (Gregorian):
- Years divisible by 4 are leap years, except centuries not divisible by 400.
2000 is a leap year; 1900 was not; 2004, 2008, 2012, 2016, 2020 are leap years.

Concept / Approach:
Each common (non-leap) year shifts the starting weekday of the following year by 1 day; a leap year shifts it by 2 days. To find when the calendar repeats, we calculate the cumulative shift in days from 1 January 2003 to 1 January of the candidate years. If the total shift is a multiple of 7 and the candidate year is also a common year, the calendars match exactly.

Step-by-Step Solution:
Step 1: Note that 2003 is not divisible by 4, so it is a common year. Step 2: Check year 2009. Leap years between 2003 and 2009: 2004, 2008 (2 leap years). Total years from 2003 to 2009: 6. Common years = 6 - 2 = 4. Shift = 4 * 1 + 2 * 2 = 4 + 4 = 8 → 8 mod 7 = 1, so calendar does not match. Step 3: Check year 2014. Leap years from 2003 to 2014: 2004, 2008, 2012 (3 leap years). Total years = 11. Common years = 11 - 3 = 8. Shift = 8 * 1 + 3 * 2 = 8 + 6 = 14 → 14 mod 7 = 0. 2014 is not divisible by 4, so it is also a common year. Therefore, 2014 has the same calendar as 2003.

Verification / Alternative check:
We can quickly see that 2020 and 2024 are leap years (both divisible by 4), while 2003 is not. Leap and non-leap years can never share an identical calendar. 2009 is closer but we already found the shift is 1 weekday, not 0, so it fails. Only 2014 gives a total shift of exactly 14 days, which is two complete weeks, keeping every date on the same weekday.

Why Other Options Are Wrong:
2009 has a one-day shift in the starting weekday compared to 2003, so their calendars differ.
2020 and 2024 are leap years; they will have 29 days in February whereas 2003 had 28, making the calendars incompatible.

Common Pitfalls:
Candidates often apply a simple “6 or 11 years later” rule without counting leap years carefully. Another mistake is ignoring leap-year status and assuming all patterns are purely 7-year cycles. You must always combine leap-year counting with the weekday shift calculation.

Final Answer:
The next year after 2003 with the same calendar is 2014.