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2008 AIME I Question 7

AIME · 2008 AIME I

Question 7

Let $S_i$ be the set of all integers $n$ such that $100i \le n \lt 100(i + 1).$ For example, $S_4$ is the set $\{400, 401, 402, \ldots, 499\}.$ How many of the sets $S_0,$ $S_1,$ $S_2,$ $\ldots,$ $S_{999}$ do not contain a perfect square?