# Greatest integer need greater mind

$\large x - \left( \lfloor r_1 x \rfloor + \lfloor r_1 x \rfloor + \lfloor r_1 x \rfloor + \ldots + \lfloor r_nx \rfloor \right)$

Let $$r_1, r_2,r_3, \ldots, r_n$$ be positive rational numbers such that their sum is 1. If $$x$$ is an integer, in terms of $$n$$, find the maximum value of the expression above.

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