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An entomologist is studying the population dynamics of a certain insect species. The population count, \( n \), is observed to be a three-digit number such that the sum of its digits is a perfect square. What is the largest possible population count?
Let \( n = 100a + 10b + c \), where \( a, b, c \) are digits and \( a
eq 0 \). The sum of the digits is \( a + b + c \), and we require this sum to be a perfect square. The largest three-digit number is 999, so \( a + b + c \) ranges from 1 to 27.

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