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Let n!, the factorial of a positive inte...

Let n!, the factorial of a positive integer n, be defined as the product of the integers 1,2, …n. In other words, n! `=1 xx 2xx……xxn`. What is the number of zeros at the end of the integer `10^(2)! + 11^(2)! + 12^(2)! + --- + 99^(2)!`?

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