# Inspired by Pi Han Goh

Algebra Level 3

Note that $$\sqrt{79} - 8 \approx 0.888$$ and $$\sqrt{320} - 17\approx 0.888$$ in the sense that the first 3 decimal places of these two numbers are equal.

Now we see that $$\lfloor 1000 (\sqrt{79} - 8) \rfloor =\lfloor 1000 (\sqrt{320} - 17) \rfloor = 888$$.

Suppose $$\lfloor 1000 (\sqrt{x} - y) \rfloor =888$$ where $$x, y$$ are positive integers and $$x>320$$. What is the minimum value of $$x+y$$?

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