1、The set $\{[x]+[2 x]+[3 x] \mid x \in R\} \mid\{x \mid 1 \leq x \leq 100, x \in Z\}$ has $\qquad$ elements, where $[x]$ represents the greatest integer not exceeding $x$.
1.67

Analysis: When $x \in\left[0, \frac{1}{3}\right)$, $[x]+[2 x]+[3 x]=0$. When $x \in\left[\frac{1}{3}, \frac{1}{2}\right)$, $[x]+[2 x]+[3 x]=1$. When $x \in\left[\frac{1}{2}, \frac{2}{3}\right)$, $[x]+[2 x]+[3 x]=2$. When $x \in\left[\frac{2}{3}, 1\right)$, $[x]+[2 x]+[3 x]=3$. Let $f(x)=[x]+[2 x]+[3 x]$. It is easy to see that $f(x+1)=f(x)+6$, so $[x]+[2 x]+[3 x]$ can take all integers congruent to $0,1,2,3$ modulo 6. It is easy to see that, in $\{1,2, \ldots, 100\}$, there are 67 such numbers.