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Is there a positive integer n such that among 200th digits

Source: Tuymaada 2009, Senior League, First Day, Problem 4

July 19, 2009
algebra unsolvedalgebra

Problem Statement

Is there a positive integer n n such that among 200th digits after decimal point in the decimal representations of n \sqrt{n}, \sqrt{n\plus{}1}, \sqrt{n\plus{}2}, …, \ldots, \sqrt{n\plus{}999} every digit occurs 100 times? Proposed by A. Golovanov
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