Originally Posted by

**namelessguy** Since you don't know how many numbers are chosen, you can't just pick a specific number. But Laurent showed you that you can choose all equal numbers, which are is possible by the hypothesis, then compute the sum of their squares. You should follow Laurent's hint.

Square each number, each of them is $\displaystyle \frac{10}{n}$, so its square is $\displaystyle (\frac{10}{n})^2$.

Then add up all of these square $\displaystyle n$ times. See what you get, and check if it is possible that the sum you just computed is less than one-millionth.