Consider the following historic capitals of Indian kingdoms: (1) Pataliputra, (2) Kannauj, (3) Rajahmundry, (4) Karur.
A scholar assigns a numeric rank to each capital based on its geographic latitude from North to South (Rank 1 being the northernmost, Rank 4 being the southernmost).
The scholar then defines a historical time window starting from Year and ending at Year .
According to the strict Gregorian calendar rules, how many leap years fall within this inclusive time window from Year to Year ?
22
Step-by-Step Solution
Key idea: This is a language_to_math synthesis question requiring you to translate geographic rankings into a mathematical calendar boundary problem.
Step 1: Determine the North-to-South geographic ranks of the capitals.
- Kannauj (Uttar Pradesh) N Rank 1
- Pataliputra (Bihar) N Rank 2
- Rajahmundry (Andhra Pradesh) N Rank 3
- Karur (Tamil Nadu) N Rank 4
Step 2: Calculate Year and Year .
Step 3: Count the leap years in the inclusive range [1824, 1912] using Gregorian rules.
- 1824 to 1896: These are standard years divisible by 4. Count = leap years.
- 1900: This is a century year. Since is not divisible by , it is NOT a leap year. Count = .
- 1904 to 1912: Standard leap years. Count = (1904, 1908, 1912).
Step 4: Sum the counts. Total = .
Answer: 22