10. Among the first 1000 positive integers, the number of positive integers that can be expressed as $[2 x]+[4 x]+[6 x]+[8 x]$ is $\qquad$ .
10. 600 Let $f(x)=[2 x]+[4 x]+[6 x]+[8 x]$.

When $x$ varies in $(0,1]$, the value of $f(x)$ changes at 12 jump points: $\frac{1}{8}, \frac{1}{6}, \frac{1}{4}, \frac{1}{3}, \frac{3}{8}, \frac{1}{2}, \frac{5}{8}, \frac{2}{3}, \frac{3}{4}$, $\frac{5}{6}, \frac{7}{8}, 1$, so $f(x)$ takes 12 different positive integer values in $1 \sim 20$. On the other hand, $f(x+n)=$ $f(x)+20 n$ holds for any positive integer $n$. Dividing $1 \sim 1000$ into 50 segments, with 20 in each segment, in each segment, $f(x)$ can take 12 values, so in total it can take $50 \times 12=600$ values, that is, 600 of the first 1000 positive integers can be expressed in the form $[2 x]+[4 x]+[6 x]+[8 x]$.