# The minimum value, may be without Calculus

Algebra Level 5

$\begin{cases}a+2b+3c &=&1\\a^2+b^2+c^2 &=&29 \end{cases}$

Suppose $$a,b$$ and $$c$$ are real numbers fulfilling the above equations. Find the minimum value of $$\lfloor 1000c\rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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