# There Are 71 Perfect Squares Less Than 5050

Discrete Mathematics Level 5

Let $$a_1, a_2, \ldots, a_{100}$$ be a permutation of the numbers $$1,2,3, \ldots ,100$$.

Let $$S_i=a_1+a_2+\cdots +a_i$$.

What is the maximum number of perfect squares among the numbers $$S_1,S_2, \ldots ,S_{100}$$?

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