According to the leap-year rules of the Gregorian calendar, which one of the following years is not a leap year?

Introduction:
Leap-year questions test your knowledge of the Gregorian calendar rules. Some years that are divisible by 4 are leap years, but for century years (like 1900 or 2000), there is an additional rule involving divisibility by 400. Here, we must identify which of the given years is not a leap year.

Given Data / Assumptions:
Years given: 2000, 2008, 2009, 2012, 2016. We assume the standard Gregorian leap-year rules.

Concept / Approach:
In the Gregorian calendar: 1. A year is a leap year if it is divisible by 4. 2. However, if the year is a century year (ends with 00), it is not a leap year unless it is also divisible by 400. So, for each year, we check divisibility by 4, and for century years, also check divisibility by 400, to decide whether it is a leap year or not.

Step-by-Step Solution:
Check 2000: 2000 is divisible by 100, and also divisible by 400 (2000 ÷ 400 = 5). Therefore, 2000 is a leap year. Check 2008: 2008 ÷ 4 = 502 with no remainder, and it is not a century year. So, 2008 is a leap year. Check 2009: 2009 ÷ 4 leaves a remainder; it is not divisible by 4. Therefore, 2009 is not a leap year. Check 2012: 2012 ÷ 4 = 503 exactly, and it is not a century year. Hence, 2012 is a leap year. Check 2016: 2016 ÷ 4 = 504 exactly, and again not a century year. So, 2016 is also a leap year.

Verification / Alternative check:
We can recall that the sequence of leap years around this period includes 2000, 2004, 2008, 2012, 2016, and so on, with 2009 clearly appearing between two leap years (2008 and 2012) and hence not being a leap year.

Why Other Options Are Wrong:
2000: Special century year that is divisible by 400, so it is a leap year. 2008, 2012, 2016: All are simple multiples of 4 and are known leap years.

Common Pitfalls:
Some candidates misremember that century years are never leap years, forgetting the exception for those divisible by 400 (like 2000). Others mix up nearby years and may incorrectly pick 2008 or 2012. Always apply both rules carefully.

Final Answer:
The year that is not a leap year is 2009.