Subscription puzzle with perfect square total: If each of n subscribers pays n rupees and the total collection is ₹ 2582449, find the number of subscribers.

Introduction / Context: This is a classic perfect square identification problem wrapped in a money context. If n people each pay n rupees, the total collected equals n^2 rupees. We must find n when n^2 is known.

Given Data / Assumptions:

• Total = ₹ 2,582,449
• Total = n^2 (since each of n subscribers pays n rupees)

Concept / Approach: If n^2 is given, then n is the positive square root of the total. Compute √2,582,449 exactly by estimation and checking near square numbers around 1600^2.

Step-by-Step Solution: 1600^2 = 2,560,000 (slightly low).Check 1607^2 = 2,560,000 + 2*1600*7 + 7^2 = 2,560,000 + 22,400 + 49 = 2,582,449.Therefore, n = 1607.

Verification / Alternative check: A quick calculator or binomial expansion (a + b)^2 confirms 1607^2 = 2,582,449. Hence the count is exact.

Why Other Options Are Wrong: Numbers like 1603, 1503, 1291 are not exact square roots for this total; their squares will not match the given amount.

Common Pitfalls: Mixing up n^2 with n×(n−1), or approximating the square root without a final exact check can lead to off-by-one mistakes.

Final Answer: 1607